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What’s the problem a different approach to problem solving.

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J. Todd Phillips , Founder & CEO, Parson Partners.

Surely you have experienced this scenario: An employee walks into a manager’s office and declares, “We have a problem.” The manager, not at all phased by this statement, replies calmly, “Well, I know you have the solution, right?” Everyone knows that they must bring a solution to every problem they identify.

For decades, managers have implored their team members to focus on solutions. Many argue that this empowers employees to think critically, solve problems independently, and communicate good news (a.k.a. “solutions”) not just bad news (a.k.a. “problems”). A quick Google search will produce hundreds of articles on this “solution-oriented” approach, touting it as one of the most effective management tools. These articles consistently repeat the chorus: “Focus on the solution, not the problem.”

However, as a lifelong problem-solver, I believe that taking a “problem-oriented” approach can be far more effective than many of these authors have been willing to admit. Business leaders, in particular, could benefit from being more problem-oriented, and much less solution-oriented.

Just what do I mean by a problem-oriented approach?

Let’s talk about it.

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The problem-oriented approach is a different way of thinking. It encourages leaders and teams to examine every possible aspect of any problem they may be facing before hammering out any possible approach to solving that problem. While it can easily be viewed as a time suck, or a costly delay when action is needed, I wager that it is much better to pause to examine a problem than risk failure with solutions adopted in haste.

Here are four steps that could get you to the right solution.

Step One: Get The Facts

This is an examination of what actually happened. Before jumping immediately to asking “what is the solution,” ask:

• Is it really a problem? How big is this problem?

• What actually happened? Who or what was impacted by the problem?

• What are we doing about it right now?

• What risks does the problem pose? What happens if we do nothing?

Once you’ve established the facts and have a legitimate problem, move on to the following steps.

Step Two: Examine Your Environment

Conventional wisdom advises us not to ask why something happened. In contrast, it’s really healthy to ask “why” repeatedly. This is a critical step that will help you get to the root causes of a problem. Go on a broad exploration to find out:

• Why did this happen?

• What conditions made it possible for this to occur?

• What conditions should have been in place?

• How could this have been avoided?

Step Three: Dig Into Your Processes

This step gets into the nitty gritty, the uncomfortable truth, of how you got to the point of having a problem in the first place. Take the time to work your way through:

• How exactly did this happen?

• What is not working?

• At what point did things go astray?

• What could we have done to avoid this?

Step Four: Consider The Human And Organizational Implications

This is perhaps the most critical step because it affects the welfare of your team. Try hard to avoid looking through the lens of assigning blame and ask:

• Who is responsible for the problem?

• Who is accountable for the problem?

• Who will be affected by the problem?

• Who should be informed about the problem?

• Who can assist with solving the problem?

Depending on the size of your organization and the nature of the problem, you might run through these questions with dispatch. Large, systemic problems may require a more significant investment of time. Whatever the circumstances, it is important to flip the paradigm and try the problem-oriented approach.

Once you have worked through these steps, either self-guided or with the help of a consultant, developing a solution—if indeed one is needed—becomes the easy part.

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

How to master the seven-step problem-solving process

In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.

Podcast transcript

Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.

Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].

Charles and Hugo, welcome to the podcast. Thank you for being here.

Hugo Sarrazin: Our pleasure.

Charles Conn: It’s terrific to be here.

Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?

Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”

You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”

I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.

I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.

Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.

Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.

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Simon London: So this is a concise problem statement.

Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.

Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.

How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.

Hugo Sarrazin: Yeah.

Charles Conn: And in the wrong direction.

Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?

Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.

What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.

Simon London: What’s a good example of a logic tree on a sort of ratable problem?

Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.

If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.

When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.

Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.

Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.

People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.

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Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?

Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.

Simon London: Not going to have a lot of depth to it.

Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.

Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.

Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.

Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.

Both: Yeah.

Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.

Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.

Simon London: Right. Right.

Hugo Sarrazin: So it’s the same thing in problem solving.

Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.

Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?

Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.

Simon London: Would you agree with that?

Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.

You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.

Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?

Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.

Simon London: Step six. You’ve done your analysis.

Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”

Simon London: But, again, these final steps are about motivating people to action, right?

Charles Conn: Yeah.

Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.

Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.

Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.

Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.

Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?

Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.

You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.

Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.

Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”

Hugo Sarrazin: Every step of the process.

Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?

Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.

Simon London: Problem definition, but out in the world.

Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.

Simon London: So, Charles, are these complements or are these alternatives?

Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.

Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?

Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.

The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.

Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.

Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.

Hugo Sarrazin: Absolutely.

Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.

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Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.

Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.

Charles Conn: It was a pleasure to be here, Simon.

Hugo Sarrazin: It was a pleasure. Thank you.

Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.

Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.

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A Crash Course in Critical Thinking

What you need to know—and read—about one of the essential skills needed today..

Posted April 8, 2024 | Reviewed by Michelle Quirk

• In research for "A More Beautiful Question," I did a deep dive into the current crisis in critical thinking.
• Many people may think of themselves as critical thinkers, but they actually are not.
• Here is a series of questions you can ask yourself to try to ensure that you are thinking critically.

Conspiracy theories. Inability to distinguish facts from falsehoods. Widespread confusion about who and what to believe.

These are some of the hallmarks of the current crisis in critical thinking—which just might be the issue of our times. Because if people aren’t willing or able to think critically as they choose potential leaders, they’re apt to choose bad ones. And if they can’t judge whether the information they’re receiving is sound, they may follow faulty advice while ignoring recommendations that are science-based and solid (and perhaps life-saving).

Moreover, as a society, if we can’t think critically about the many serious challenges we face, it becomes more difficult to agree on what those challenges are—much less solve them.

On a personal level, critical thinking can enable you to make better everyday decisions. It can help you make sense of an increasingly complex and confusing world.

In the new expanded edition of my book A More Beautiful Question ( AMBQ ), I took a deep dive into critical thinking. Here are a few key things I learned.

First off, before you can get better at critical thinking, you should understand what it is. It’s not just about being a skeptic. When thinking critically, we are thoughtfully reasoning, evaluating, and making decisions based on evidence and logic. And—perhaps most important—while doing this, a critical thinker always strives to be open-minded and fair-minded . That’s not easy: It demands that you constantly question your assumptions and biases and that you always remain open to considering opposing views.

In today’s polarized environment, many people think of themselves as critical thinkers simply because they ask skeptical questions—often directed at, say, certain government policies or ideas espoused by those on the “other side” of the political divide. The problem is, they may not be asking these questions with an open mind or a willingness to fairly consider opposing views.

When people do this, they’re engaging in “weak-sense critical thinking”—a term popularized by the late Richard Paul, a co-founder of The Foundation for Critical Thinking . “Weak-sense critical thinking” means applying the tools and practices of critical thinking—questioning, investigating, evaluating—but with the sole purpose of confirming one’s own bias or serving an agenda.

In AMBQ , I lay out a series of questions you can ask yourself to try to ensure that you’re thinking critically. Here are some of the questions to consider:

• Why do I believe what I believe?
• Are my views based on evidence?
• Have I fairly and thoughtfully considered differing viewpoints?
• Am I truly open to changing my mind?

Of course, becoming a better critical thinker is not as simple as just asking yourself a few questions. Critical thinking is a habit of mind that must be developed and strengthened over time. In effect, you must train yourself to think in a manner that is more effortful, aware, grounded, and balanced.

For those interested in giving themselves a crash course in critical thinking—something I did myself, as I was working on my book—I thought it might be helpful to share a list of some of the books that have shaped my own thinking on this subject. As a self-interested author, I naturally would suggest that you start with the new 10th-anniversary edition of A More Beautiful Question , but beyond that, here are the top eight critical-thinking books I’d recommend.

The Demon-Haunted World: Science as a Candle in the Dark , by Carl Sagan

This book simply must top the list, because the late scientist and author Carl Sagan continues to be such a bright shining light in the critical thinking universe. Chapter 12 includes the details on Sagan’s famous “baloney detection kit,” a collection of lessons and tips on how to deal with bogus arguments and logical fallacies.

Clear Thinking: Turning Ordinary Moments Into Extraordinary Results , by Shane Parrish

The creator of the Farnham Street website and host of the “Knowledge Project” podcast explains how to contend with biases and unconscious reactions so you can make better everyday decisions. It contains insights from many of the brilliant thinkers Shane has studied.

Good Thinking: Why Flawed Logic Puts Us All at Risk and How Critical Thinking Can Save the World , by David Robert Grimes

A brilliant, comprehensive 2021 book on critical thinking that, to my mind, hasn’t received nearly enough attention . The scientist Grimes dissects bad thinking, shows why it persists, and offers the tools to defeat it.

Think Again: The Power of Knowing What You Don't Know , by Adam Grant

Intellectual humility—being willing to admit that you might be wrong—is what this book is primarily about. But Adam, the renowned Wharton psychology professor and bestselling author, takes the reader on a mind-opening journey with colorful stories and characters.

Think Like a Detective: A Kid's Guide to Critical Thinking , by David Pakman

The popular YouTuber and podcast host Pakman—normally known for talking politics —has written a terrific primer on critical thinking for children. The illustrated book presents critical thinking as a “superpower” that enables kids to unlock mysteries and dig for truth. (I also recommend Pakman’s second kids’ book called Think Like a Scientist .)

Rationality: What It Is, Why It Seems Scarce, Why It Matters , by Steven Pinker

The Harvard psychology professor Pinker tackles conspiracy theories head-on but also explores concepts involving risk/reward, probability and randomness, and correlation/causation. And if that strikes you as daunting, be assured that Pinker makes it lively and accessible.

How Minds Change: The Surprising Science of Belief, Opinion and Persuasion , by David McRaney

David is a science writer who hosts the popular podcast “You Are Not So Smart” (and his ideas are featured in A More Beautiful Question ). His well-written book looks at ways you can actually get through to people who see the world very differently than you (hint: bludgeoning them with facts definitely won’t work).

A Healthy Democracy's Best Hope: Building the Critical Thinking Habit , by M Neil Browne and Chelsea Kulhanek

Neil Browne, author of the seminal Asking the Right Questions: A Guide to Critical Thinking, has been a pioneer in presenting critical thinking as a question-based approach to making sense of the world around us. His newest book, co-authored with Chelsea Kulhanek, breaks down critical thinking into “11 explosive questions”—including the “priors question” (which challenges us to question assumptions), the “evidence question” (focusing on how to evaluate and weigh evidence), and the “humility question” (which reminds us that a critical thinker must be humble enough to consider the possibility of being wrong).

Warren Berger is a longtime journalist and author of A More Beautiful Question .

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21 Problem Solving

Miriam Bassok, Department of Psychology, University of Washington, Seattle, WA

Laura R. Novick, Department of Psychology and Human Development, Vanderbilt University, Nashville, TN

• Published: 21 November 2012
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This chapter follows the historical development of research on problem solving. It begins with a description of two research traditions that addressed different aspects of the problem-solving process: ( 1 ) research on problem representation (the Gestalt legacy) that examined how people understand the problem at hand, and ( 2 ) research on search in a problem space (the legacy of Newell and Simon) that examined how people generate the problem's solution. It then describes some developments in the field that fueled the integration of these two lines of research: work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. Next, it presents examples of recent work on problem solving in science and mathematics that highlight the impact of visual perception and background knowledge on how people represent problems and search for problem solutions. The final section considers possible directions for future research.

People are confronted with problems on a daily basis, be it trying to extract a broken light bulb from a socket, finding a detour when the regular route is blocked, fixing dinner for unexpected guests, dealing with a medical emergency, or deciding what house to buy. Obviously, the problems people encounter differ in many ways, and their solutions require different types of knowledge and skills. Yet we have a sense that all the situations we classify as problems share a common core. Karl Duncker defined this core as follows: “A problem arises when a living creature has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action [i.e., by the performance of obvious operations], then there has to be recourse to thinking” (Duncker, 1945 , p. 1). Consider the broken light bulb. The obvious operation—holding the glass part of the bulb with one's fingers while unscrewing the base from the socket—is prevented by the fact that the glass is broken. Thus, there must be “recourse to thinking” about possible ways to solve the problem. For example, one might try mounting half a potato on the broken bulb (we do not know the source of this creative solution, which is described on many “how to” Web sites).

The above definition and examples make it clear that what constitutes a problem for one person may not be a problem for another person, or for that same person at another point in time. For example, the second time one has to remove a broken light bulb from a socket, the solution likely can be retrieved from memory; there is no problem. Similarly, tying shoes may be considered a problem for 5-year-olds but not for readers of this chapter. And, of course, people may change their goal and either no longer have a problem (e.g., take the guests to a restaurant instead of fixing dinner) or attempt to solve a different problem (e.g., decide what restaurant to go to). Given the highly subjective nature of what constitutes a problem, researchers who study problem solving have often presented people with novel problems that they should be capable of solving and attempted to find regularities in the resulting problem-solving behavior. Despite the variety of possible problem situations, researchers have identified important regularities in the thinking processes by which people (a) represent , or understand, problem situations and (b) search for possible ways to get to their goal.

A problem representation is a model constructed by the solver that summarizes his or her understanding of the problem components—the initial state (e.g., a broken light bulb in a socket), the goal state (the light bulb extracted), and the set of possible operators one may apply to get from the initial state to the goal state (e.g., use pliers). According to Reitman ( 1965 ), problem components differ in the extent to which they are well defined . Some components leave little room for interpretation (e.g., the initial state in the broken light bulb example is relatively well defined), whereas other components may be ill defined and have to be defined by the solver (e.g., the possible actions one may take to extract the broken bulb). The solver's representation of the problem guides the search for a possible solution (e.g., possible attempts at extracting the light bulb). This search may, in turn, change the representation of the problem (e.g., finding that the goal cannot be achieved using pliers) and lead to a new search. Such a recursive process of representation and search continues until the problem is solved or until the solver decides to abort the goal.

Duncker ( 1945 , pp. 28–37) documented the interplay between representation and search based on his careful analysis of one person's solution to the “Radiation Problem” (later to be used extensively in research analogy, see Holyoak, Chapter 13 ). This problem requires using some rays to destroy a patient's stomach tumor without harming the patient. At sufficiently high intensity, the rays will destroy the tumor. However, at that intensity, they will also destroy the healthy tissue surrounding the tumor. At lower intensity, the rays will not harm the healthy tissue, but they also will not destroy the tumor. Duncker's analysis revealed that the solver's solution attempts were guided by three distinct problem representations. He depicted these solution attempts as an inverted search tree in which the three main branches correspond to the three general problem representations (Duncker, 1945 , p. 32). We reproduce this diagram in Figure 21.1 . The desired solution appears on the rightmost branch of the tree, within the general problem representation in which the solver aims to “lower the intensity of the rays on their way through healthy tissue.” The actual solution is to project multiple low-intensity rays at the tumor from several points around the patient “by use of lens.” The low-intensity rays will converge on the tumor, where their individual intensities will sum to a level sufficient to destroy the tumor.

A search-tree representation of one subject's solution to the radiation problem, reproduced from Duncker ( 1945 , p. 32).

Although there are inherent interactions between representation and search, some researchers focus their efforts on understanding the factors that affect how solvers represent problems, whereas others look for regularities in how they search for a solution within a particular representation. Based on their main focus of interest, researchers devise or select problems with solutions that mainly require either constructing a particular representation or finding the appropriate sequence of steps leading from the initial state to the goal state. In most cases, researchers who are interested in problem representation select problems in which one or more of the components are ill defined, whereas those who are interested in search select problems in which the components are well defined. The following examples illustrate, respectively, these two problem types.

The Bird-and-Trains problem (Posner, 1973 , pp. 150–151) is a mathematical word problem that tends to elicit two distinct problem representations (see Fig. 21.2a and b ):

Two train stations are 50 miles apart. At 2 p.m. one Saturday afternoon two trains start toward each other, one from each station. Just as the trains pull out of the stations, a bird springs into the air in front of the first train and flies ahead to the front of the second train. When the bird reaches the second train, it turns back and flies toward the first train. The bird continues to do this until the trains meet. If both trains travel at the rate of 25 miles per hour and the bird flies at 100 miles per hour, how many miles will the bird have flown before the trains meet? Fig. 21.2 Open in new tab Download slide Alternative representations of Posner's ( 1973 ) trains-and-bird problem. Adapted from Novick and Hmelo ( 1994 ).

Some solvers focus on the back-and-forth path of the bird (Fig. 21.2a ). This representation yields a problem that would be difficult for most people to solve (e.g., a series of differential equations). Other solvers focus on the paths of the trains (Fig. 21.2b ), a representation that yields a relatively easy distance-rate-time problem.

The Tower of Hanoi problem falls on the other end of the representation-search continuum. It leaves little room for differences in problem representations, and the primary work is to discover a solution path (or the best solution path) from the initial state to the goal state .

There are three pegs mounted on a base. On the leftmost peg, there are three disks of differing sizes. The disks are arranged in order of size with the largest disk on the bottom and the smallest disk on the top. The disks may be moved one at a time, but only the top disk on a peg may be moved, and at no time may a larger disk be placed on a smaller disk. The goal is to move the three-disk tower from the leftmost peg to the rightmost peg.

Figure 21.3 shows all the possible legal arrangements of disks on pegs. The arrows indicate transitions between states that result from moving a single disk, with the thicker gray arrows indicating the shortest path that connects the initial state to the goal state.

The division of labor between research on representation versus search has distinct historical antecedents and research traditions. In the next two sections, we review the main findings from these two historical traditions. Then, we describe some developments in the field that fueled the integration of these lines of research—work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. In the fifth section, we present some examples of recent work on problem solving in science and mathematics. This work highlights the role of visual perception and background knowledge in the way people represent problems and search for problem solutions. In the final section, we consider possible directions for future research.

Our review is by no means an exhaustive one. It follows the historical development of the field and highlights findings that pertain to a wide variety of problems. Research pertaining to specific types of problems (e.g., medical problems), specific processes that are involved in problem solving (e.g., analogical inferences), and developmental changes in problem solving due to learning and maturation may be found elsewhere in this volume (e.g., Holyoak, Chapter 13 ; Smith & Ward, Chapter 23 ; van Steenburgh et al., Chapter 24 ; Simonton, Chapter 25 ; Opfer & Siegler, Chapter 30 ; Hegarty & Stull, Chapter 31 ; Dunbar & Klahr, Chapter 35 ; Patel et al., Chapter 37 ; Lowenstein, Chapter 38 ; Koedinger & Roll, Chapter 40 ).

All possible problem states for the three-disk Tower of Hanoi problem. The thicker gray arrows show the optimum solution path connecting the initial state (State #1) to the goal state (State #27).

Problem Representation: The Gestalt Legacy

Research on problem representation has its origins in Gestalt psychology, an influential approach in European psychology during the first half of the 20th century. (Behaviorism was the dominant perspective in American psychology at this time.) Karl Duncker published a book on the topic in his native German in 1935, which was translated into English and published 10 years later as the monograph On Problem-Solving (Duncker, 1945 ). Max Wertheimer also published a book on the topic in 1945, titled Productive Thinking . An enlarged edition published posthumously includes previously unpublished material (Wertheimer, 1959 ). Interestingly, 1945 seems to have been a watershed year for problem solving, as mathematician George Polya's book, How to Solve It , also appeared then (a second edition was published 12 years later; Polya, 1957 ).

The Gestalt psychologists extended the organizational principles of visual perception to the domain of problem solving. They showed that various visual aspects of the problem, as well the solver's prior knowledge, affect how people understand problems and, therefore, generate problem solutions. The principles of visual perception (e.g., proximity, closure, grouping, good continuation) are directly relevant to problem solving when the physical layout of the problem, or a diagram that accompanies the problem description, elicits inferences that solvers include in their problem representations. Such effects are nicely illustrated by Maier's ( 1930 ) nine-dot problem: Nine dots are arrayed in a 3x3 grid, and the task is to connect all the dots by drawing four straight lines without lifting one's pencil from the paper. People have difficulty solving this problem because their initial representations generally include a constraint, inferred from the configuration of the dots, that the lines should not go outside the boundary of the imaginary square formed by the outer dots. With this constraint, the problem cannot be solved (but see Adams, 1979 ). Without this constraint, the problem may be solved as shown in Figure 21.4 (though the problem is still difficult for many people; see Weisberg & Alba, 1981 ).

The nine-dot problem is a classic insight problem (see van Steenburgh et al., Chapter 24 ). According to the Gestalt view (e.g., Duncker, 1945 ; Kohler, 1925 ; Maier, 1931 ; see Ohlsson, 1984 , for a review), the solution to an insight problem appears suddenly, accompanied by an “aha!” sensation, immediately following the sudden “restructuring” of one's understanding of the problem (i.e., a change in the problem representation): “The decisive points in thought-processes, the moments of sudden comprehension, of the ‘Aha!,’ of the new, are always at the same time moments in which such a sudden restructuring of the thought-material takes place” (Duncker, 1945 , p. 29). For the nine-dot problem, one view of the required restructuring is that the solver relaxes the constraint implied by the perceptual form of the problem and realizes that the lines may, in fact, extend past the boundary of the imaginary square. Later in the chapter, we present more recent accounts of insight.

The entities that appear in a problem also tend to evoke various inferences that people incorporate into their problem representations. A classic demonstration of this is the phenomenon of functional fixedness , introduced by Duncker ( 1945 ): If an object is habitually used for a certain purpose (e.g., a box serves as a container), it is difficult to see

A solution to the nine-dot problem.

that object as having properties that would enable it to be used for a dissimilar purpose. Duncker's basic experimental paradigm involved two conditions that varied in terms of whether the object that was crucial for solution was initially used for a function other than that required for solution.

Consider the candles problem—the best known of the five “practical problems” Duncker ( 1945 ) investigated. Three candles are to be mounted at eye height on a door. On the table, for use in completing this task, are some tacks and three boxes. The solution is to tack the three boxes to the door to serve as platforms for the candles. In the control condition, the three boxes were presented to subjects empty. In the functional-fixedness condition, they were filled with candles, tacks, and matches. Thus, in the latter condition, the boxes initially served the function of container, whereas the solution requires that they serve the function of platform. The results showed that 100% of the subjects who received empty boxes solved the candles problem, compared with only 43% of subjects who received filled boxes. Every one of the five problems in this study showed a difference favoring the control condition over the functional-fixedness condition, with average solution rates across the five problems of 97% and 58%, respectively.

The function of the objects in a problem can be also “fixed” by their most recent use. For example, Birch and Rabinowitz ( 1951 ) had subjects perform two consecutive tasks. In the first task, people had to use either a switch or a relay to form an electric circuit. After completing this task, both groups of subjects were asked to solve Maier's ( 1931 ) two-ropes problem. The solution to this problem requires tying an object to one of the ropes and making the rope swing as a pendulum. Subjects could create the pendulum using either the object from the electric-circuit task or the other object. Birch and Rabinowitz found that subjects avoided using the same object for two unrelated functions. That is, those who used the switch in the first task made the pendulum using the relay, and vice versa. The explanations subjects subsequently gave for their object choices revealed that they were unaware of the functional-fixedness constraint they imposed on themselves.

In addition to investigating people's solutions to such practical problems as irradiating a tumor, mounting candles on the wall, or tying ropes, the Gestalt psychologists examined how people understand and solve mathematical problems that require domain-specific knowledge. For example, Wertheimer ( 1959 ) observed individual differences in students' learning and subsequent application of the formula for finding the area of a parallelogram (see Fig. 21.5a ). Some students understood the logic underlying the learned formula (i.e., the fact that a parallelogram can be transformed into a rectangle by cutting off a triangle from one side and pasting it onto the other side) and exhibited “productive thinking”—using the same logic to find the area of the quadrilateral in Figure 21.5b and the irregularly shaped geometric figure in Figure 21.5c . Other students memorized the formula and exhibited “reproductive thinking”—reproducing the learned solution only to novel parallelograms that were highly similar to the original one.

The psychological study of human problem solving faded into the background after the demise of the Gestalt tradition (during World War II), and problem solving was investigated only sporadically until Allen Newell and Herbert Simon's ( 1972 ) landmark book Human Problem Solving sparked a flurry of research on this topic. Newell and Simon adopted and refined Duncker's ( 1945 ) methodology of collecting and analyzing the think-aloud protocols that accompany problem solutions and extended Duncker's conceptualization of a problem solution as a search tree. However, their initial work did not aim to extend the Gestalt findings

Finding the area of ( a ) a parallelogram, ( b ) a quadrilateral, and ( c ) an irregularly shaped geometric figure. The solid lines indicate the geometric figures whose areas are desired. The dashed lines show how to convert the given figures into rectangles (i.e., they show solutions with understanding).

pertaining to problem representation. Instead, as we explain in the next section, their objective was to identify the general-purpose strategies people use in searching for a problem solution.

Search in a Problem Space: The Legacy of Newell and Simon

Newell and Simon ( 1972 ) wrote a magnum opus detailing their theory of problem solving and the supporting research they conducted with various collaborators. This theory was grounded in the information-processing approach to cognitive psychology and guided by an analogy between human and artificial intelligence (i.e., both people and computers being “Physical Symbol Systems,” Newell & Simon, 1976 ; see Doumas & Hummel, Chapter 5 ). They conceptualized problem solving as a process of search through a problem space for a path that connects the initial state to the goal state—a metaphor that alludes to the visual or spatial nature of problem solving (Simon, 1990 ). The term problem space refers to the solver's representation of the task as presented (Simon, 1978 ). It consists of ( 1 ) a set of knowledge states (the initial state, the goal state, and all possible intermediate states), ( 2 ) a set of operators that allow movement from one knowledge state to another, ( 3 ) a set of constraints, and ( 4 ) local information about the path one is taking through the space (e.g., the current knowledge state and how one got there).

We illustrate the components of a problem space for the three-disk Tower of Hanoi problem, as depicted in Figure 21.3 . The initial state appears at the top (State #1) and the goal state at the bottom right (State #27). The remaining knowledge states in the figure are possible intermediate states. The current knowledge state is the one at which the solver is located at any given point in the solution process. For example, the current state for a solver who has made three moves along the optimum solution path would be State #9. The solver presumably would know that he or she arrived at this state from State #5. This knowledge allows the solver to recognize a move that involves backtracking. The three operators in this problem are moving each of the three disks from one peg to another. These operators are subject to the constraint that a larger disk may not be placed on a smaller disk.

Newell and Simon ( 1972 ), as well as other contemporaneous researchers (e.g., Atwood & Polson, 1976 ; Greeno, 1974 ; Thomas, 1974 ), examined how people traverse the spaces of various well-defined problems (e.g., the Tower of Hanoi, Hobbits and Orcs). They discovered that solvers' search is guided by a number of shortcut strategies, or heuristics , which are likely to get the solver to the goal state without an extensive amount of search. Heuristics are often contrasted with algorithms —methods that are guaranteed to yield the correct solution. For example, one could try every possible move in the three-disk Tower of Hanoi problem and, eventually, find the correct solution. Although such an exhaustive search is a valid algorithm for this problem, for many problems its application is very time consuming and impractical (e.g., consider the game of chess).

In their attempts to identify people's search heuristics, Newell and Simon ( 1972 ) relied on two primary methodologies: think-aloud protocols and computer simulations. Their use of think-aloud protocols brought a high degree of scientific rigor to the methodology used by Duncker ( 1945 ; see Ericsson & Simon, 1980 ). Solvers were required to say out loud everything they were thinking as they solved the problem, that is, everything that went through their verbal working memory. Subjects' verbalizations—their think-aloud protocols—were tape-recorded and then transcribed verbatim for analysis. This method is extremely time consuming (e.g., a transcript of one person's solution to the cryptarithmetic problem DONALD + GERALD = ROBERT, with D = 5, generated a 17-page transcript), but it provides a detailed record of the solver's ongoing solution process.

An important caveat to keep in mind while interpreting a subject's verbalizations is that “a protocol is relatively reliable only for what it positively contains, but not for that which it omits” (Duncker, 1945 , p. 11). Ericsson and Simon ( 1980 ) provided an in-depth discussion of the conditions under which this method is valid (but see Russo, Johnson, & Stephens, 1989 , for an alternative perspective). To test their interpretation of a subject's problem solution, inferred from the subject's verbal protocol, Newell and Simon ( 1972 ) created a computer simulation program and examined whether it solved the problem the same way the subject did. To the extent that the computer simulation provided a close approximation of the solver's step-by-step solution process, it lent credence to the researcher's interpretation of the verbal protocol.

Newell and Simon's ( 1972 ) most famous simulation was the General Problem Solver or GPS (Ernst & Newell, 1969 ). GPS successfully modeled human solutions to problems as different as the Tower of Hanoi and the construction of logic proofs using a single general-purpose heuristic: means-ends analysis . This heuristic captures people's tendency to devise a solution plan by setting subgoals that could help them achieve their final goal. It consists of the following steps: ( 1 ) Identify a difference between the current state and the goal (or subgoal ) state; ( 2 ) Find an operator that will remove (or reduce) the difference; (3a) If the operator can be directly applied, do so, or (3b) If the operator cannot be directly applied, set a subgoal to remove the obstacle that is preventing execution of the desired operator; ( 4 ) Repeat steps 1–3 until the problem is solved. Next, we illustrate the implementation of this heuristic for the Tower of Hanoi problem, using the problem space in Figure 21.3 .

As can be seen in Figure 21.3 , a key difference between the initial state and the goal state is that the large disk is on the wrong peg (step 1). To remove this difference (step 2), one needs to apply the operator “move-large-disk.” However, this operator cannot be applied because of the presence of the medium and small disks on top of the large disk. Therefore, the solver may set a subgoal to move that two-disk tower to the middle peg (step 3b), leaving the rightmost peg free for the large disk. A key difference between the initial state and this new subgoal state is that the medium disk is on the wrong peg. Because application of the move-medium-disk operator is blocked, the solver sets another subgoal to move the small disk to the right peg. This subgoal can be satisfied immediately by applying the move-small-disk operator (step 3a), generating State #3. The solver then returns to the previous subgoal—moving the tower consisting of the small and medium disks to the middle peg. The differences between the current state (#3) and the subgoal state (#9) can be removed by first applying the move-medium-disk operator (yielding State #5) and then the move-small-disk operator (yielding State #9). Finally, the move-large-disk operator is no longer blocked. Hence, the solver moves the large disk to the right peg, yielding State #11.

Notice that the subgoals are stacked up in the order in which they are generated, so that they pop up in the order of last in first out. Given the first subgoal in our example, repeated application of the means-ends analysis heuristic will yield the shortest-path solution, indicated by the large gray arrows. In general, subgoals provide direction to the search and allow solvers to plan several moves ahead. By assessing progress toward a required subgoal rather than the final goal, solvers may be able to make moves that otherwise seem unwise. To take a concrete example, consider the transition from State #1 to State #3 in Figure 21.3 . Comparing the initial state to the goal state, this move seems unwise because it places the small disk on the bottom of the right peg, whereas it ultimately needs to be at the top of the tower on that peg. But comparing the initial state to the solver-generated subgoal state of having the medium disk on the middle peg, this is exactly where the small disk needs to go.

Means-ends analysis and various other heuristics (e.g., the hill-climbing heuristic that exploits the similarity, or distance, between the state generated by the next operator and the goal state; working backward from the goal state to the initial state) are flexible strategies that people often use to successfully solve a large variety of problems. However, the generality of these heuristics comes at a cost: They are relatively weak and fallible (e.g., in the means-ends solution to the problem of fixing a hole in a bucket, “Dear Liza” leads “Dear Henry” in a loop that ends back at the initial state; the lyrics of this famous song can be readily found on the Web). Hence, although people use general-purpose heuristics when they encounter novel problems, they replace them as soon as they acquire experience with and sufficient knowledge about the particular problem space (e.g., Anzai & Simon, 1979 ).

Despite the fruitfulness of this research agenda, it soon became evident that a fundamental weakness was that it minimized the importance of people's background knowledge. Of course, Newell and Simon ( 1972 ) were aware that problem solutions require relevant knowledge (e.g., the rules of logical proofs, or rules for stacking disks). Hence, in programming GPS, they supplemented every problem they modeled with the necessary background knowledge. This practice highlighted the generality and flexibility of means-ends analysis but failed to capture how people's background knowledge affects their solutions. As we discussed in the previous section, domain knowledge is likely to affect how people represent problems and, therefore, how they generate problem solutions. Moreover, as people gain experience solving problems in a particular knowledge domain (e.g., math, physics), they change their representations of these problems (e.g., Chi, Feltovich, & Glaser, 1981 ; Haverty, Koedinger, Klahr, & Alibali, 2000 ; Schoenfeld & Herrmann, 1982 ) and learn domain-specific heuristics (e.g., Polya, 1957 ; Schoenfeld, 1979 ) that trump the general-purpose strategies.

It is perhaps inevitable that the two traditions in problem-solving research—one emphasizing representation and the other emphasizing search strategies—would eventually come together. In the next section we review developments that led to this integration.

The Two Legacies Converge

Because Newell and Simon ( 1972 ) aimed to discover the strategies people use in searching for a solution, they investigated problems that minimized the impact of factors that tend to evoke differences in problem representations, of the sort documented by the Gestalt psychologists. In subsequent work, however, Simon and his collaborators showed that such factors are highly relevant to people's solutions of well-defined problems, and Simon ( 1986 ) incorporated these findings into the theoretical framework that views problem solving as search in a problem space.

In this section, we first describe illustrative examples of this work. We then describe research on insight solutions that incorporates ideas from the two legacies described in the previous sections.

Relevance of the Gestalt Ideas to the Solution of Search Problems

In this subsection we describe two lines of research by Simon and his colleagues, and by other researchers, that document the importance of perception and of background knowledge to the way people search for a problem solution. The first line of research used variants of relatively well-defined riddle problems that had the same structure (i.e., “problem isomorphs”) and, therefore, supposedly the same problem space. It documented that people's search depended on various perceptual and conceptual inferences they tended to draw from a specific instantiation of the problem's structure. The second line of research documented that people's search strategies crucially depend on their domain knowledge and on their prior experience with related problems.

Problem Isomorphs

Hayes and Simon ( 1977 ) used two variants of the Tower of Hanoi problem that, instead of disks and pegs, involved monsters and globes that differed in size (small, medium, and large). In both variants, the initial state had the small monster holding the large globe, the medium-sized monster holding the small globe, and the large monster holding the medium-sized globe. Moreover, in both variants the goal was for each monster to hold a globe proportionate to its own size. The only difference between the problems concerned the description of the operators. In one variant (“transfer”), subjects were told that the monsters could transfer the globes from one to another as long as they followed a set of rules, adapted from the rules in the original Tower of Hanoi problem (e.g., only one globe may be transferred at a time). In the other variant (“change”), subjects were told that the monsters could shrink and expand themselves according to a set of rules, which corresponded to the rules in the transfer version of the problem (e.g., only one monster may change its size at a time). Despite the isomorphism of the two variants, subjects conducted their search in two qualitatively different problem spaces, which led to solution times for the change variant being almost twice as long as those for the transfer variant. This difference arose because subjects could more readily envision and track an object that was changing its location with every move than one that was changing its size.

Recent work by Patsenko and Altmann ( 2010 ) found that, even in the standard Tower of Hanoi problem, people's solutions involve object-bound routines that depend on perception and selective attention. The subjects in their study solved various Tower of Hanoi problems on a computer. During the solution of a particular “critical” problem, the computer screen changed at various points without subjects' awareness (e.g., a disk was added, such that a subject who started with a five-disc tower ended with a six-disc tower). Patsenko and Altmann found that subjects' moves were guided by the configurations of the objects on the screen rather than by solution plans they had stored in memory (e.g., the next subgoal).

The Gestalt psychologists highlighted the role of perceptual factors in the formation of problem representations (e.g., Maier's, 1930 , nine-dot problem) but were generally silent about the corresponding implications for how the problem was solved (although they did note effects on solution accuracy). An important contribution of the work on people's solutions of the Tower of Hanoi problem and its variants was to show the relevance of perceptual factors to the application of various operators during search for a problem solution—that is, to the how of problem solving. In the next section, we describe recent work that documents the involvement of perceptual factors in how people understand and use equations and diagrams in the context of solving math and science problems.

Kotovsky, Hayes, and Simon ( 1985 ) further investigated factors that affect people's representation and search in isomorphs of the Tower of Hanoi problem. In one of their isomorphs, three disks were stacked on top of each other to form an inverted pyramid, with the smallest disc on the bottom and the largest on top. Subjects' solutions of the inverted pyramid version were similar to their solutions of the standard version that has the largest disc on the bottom and the smallest on top. However, the two versions were solved very differently when subjects were told that the discs represent acrobats. Subjects readily solved the version in which they had to place a small acrobat on the shoulders of a large one, but they refrained from letting a large acrobat stand on the shoulders of a small one. In other words, object-based inferences that draw on people's semantic knowledge affected the solution of search problems, much as they affect the solution of the ill-defined problems investigated by the Gestalt psychologists (e.g., Duncker's, 1945 , candles problem). In the next section, we describe more recent work that shows similar effects in people's solutions to mathematical word problems.

The work on differences in the representation and solution of problem isomorphs is highly relevant to research on analogical problem solving (or analogical transfer), which examines when and how people realize that two problems that differ in their cover stories have a similar structure (or a similar problem space) and, therefore, can be solved in a similar way. This research shows that minor differences between example problems, such as the use of X-rays versus ultrasound waves to fuse a broken filament of a light bulb, can elicit different problem representations that significantly affect the likelihood of subsequent transfer to novel problem analogs (Holyoak & Koh, 1987 ). Analogical transfer has played a central role in research on human problem solving, in part because it can shed light on people's understanding of a given problem and its solution and in part because it is believed to provide a window onto understanding and investigating creativity (see Smith & Ward, Chapter 23 ). We briefly mention some findings from the analogy literature in the next subsection on expertise, but we do not discuss analogical transfer in detail because this topic is covered elsewhere in this volume (Holyoak, Chapter 13 ).

Expertise and Its Development

In another line of research, Simon and his colleagues examined how people solve ecologically valid problems from various rule-governed and knowledge-rich domains. They found that people's level of expertise in such domains, be it in chess (Chase & Simon, 1973 ; Gobet & Simon, 1996 ), mathematics (Hinsley, Hayes, & Simon, 1977 ; Paige & Simon, 1966 ), or physics (Larkin, McDermott, Simon, & Simon, 1980 ; Simon & Simon, 1978 ), plays a crucial role in how they represent problems and search for solutions. This work, and the work of numerous other researchers, led to the discovery (and rediscovery, see Duncker, 1945 ) of important differences between experts and novices, and between “good” and “poor” students.

One difference between experts and novices pertains to pattern recognition. Experts' attention is quickly captured by familiar configurations within a problem situation (e.g., a familiar configuration of pieces in a chess game). In contrast, novices' attention is focused on isolated components of the problem (e.g., individual chess pieces). This difference, which has been found in numerous domains, indicates that experts have stored in memory many meaningful groups (chunks) of information: for example, chess (Chase & Simon, 1973 ), circuit diagrams (Egan & Schwartz, 1979 ), computer programs (McKeithen, Reitman, Rueter, & Hirtle, 1981 ), medicine (Coughlin & Patel, 1987 ; Myles-Worsley, Johnston, & Simons, 1988 ), basketball and field hockey (Allard & Starkes, 1991 ), and figure skating (Deakin & Allard, 1991 ).

The perceptual configurations that domain experts readily recognize are associated with stored solution plans and/or compiled procedures (Anderson, 1982 ). As a result, experts' solutions are much faster than, and often qualitatively different from, the piecemeal solutions that novice solvers tend to construct (e.g., Larkin et al., 1980 ). In effect, experts often see the solutions that novices have yet to compute (e.g., Chase & Simon, 1973 ; Novick & Sherman, 2003 , 2008 ). These findings have led to the design of various successful instructional interventions (e.g., Catrambone, 1998 ; Kellman et al., 2008 ). For example, Catrambone ( 1998 ) perceptually isolated the subgoals of a statistics problem. This perceptual chunking of meaningful components of the problem prompted novice students to self-explain the meaning of the chunks, leading to a conceptual understanding of the learned solution. In the next section, we describe some recent work that shows the beneficial effects of perceptual pattern recognition on the solution of familiar mathematics problems, as well as the potentially detrimental effects of familiar perceptual chunks to understanding and reasoning with diagrams depicting evolutionary relationships among taxa.

Another difference between experts and novices pertains to their understanding of the solution-relevant problem structure. Experts' knowledge is highly organized around domain principles, and their problem representations tend to reflect this principled understanding. In particular, they can extract the solution-relevant structure of the problems they encounter (e.g., meaningful causal relations among the objects in the problem; see Cheng & Buehner, Chapter 12 ). In contrast, novices' representations tend to be bound to surface features of the problems that may be irrelevant to solution (e.g., the particular objects in a problem). For example, Chi, Feltovich, and Glaser ( 1981 ) examined how students with different levels of physics expertise group mechanics word problems. They found that advanced graduate students grouped the problems based on the physics principles relevant to the problems' solutions (e.g., conservation of energy, Newton's second law). In contrast, undergraduates who had successfully completed an introductory course in mechanics grouped the problems based on the specific objects involved (e.g., pulley problems, inclined plane problems). Other researchers have found similar results in the domains of biology, chemistry, computer programming, and math (Adelson, 1981 ; Kindfield, 1993 / 1994 ; Kozma & Russell, 1997 ; McKeithen et al., 1981 ; Silver, 1979 , 1981 ; Weiser & Shertz, 1983 ).

The level of domain expertise and the corresponding representational differences are, of course, a matter of degree. With increasing expertise, there is a gradual change in people's focus of attention from aspects that are not relevant to solution to those that are (e.g., Deakin & Allard, 1991 ; Hardiman, Dufresne, & Mestre, 1989 ; McKeithen et al., 1981 ; Myles-Worsley et al., 1988 ; Schoenfeld & Herrmann, 1982 ; Silver, 1981 ). Interestingly, Chi, Bassok, Lewis, Reimann, and Glaser ( 1989 ) found similar differences in focus on structural versus surface features among a group of novices who studied worked-out examples of mechanics problems. These differences, which echo Wertheimer's ( 1959 ) observations of individual differences in students' learning about the area of parallelograms, suggest that individual differences in people's interests and natural abilities may affect whether, or how quickly, they acquire domain expertise.

An important benefit of experts' ability to focus their attention on solution-relevant aspects of problems is that they are more likely than novices to recognize analogous problems that involve different objects and cover stories (e.g., Chi et al., 1989 ; Novick, 1988 ; Novick & Holyoak, 1991 ; Wertheimer, 1959 ) or that come from other knowledge domains (e.g., Bassok & Holyoak, 1989 ; Dunbar, 2001 ; Goldstone & Sakamoto, 2003 ). For example, Bassok and Holyoak ( 1989 ) found that, after learning to solve arithmetic-progression problems in algebra, subjects spontaneously applied these algebraic solutions to analogous physics problems that dealt with constantly accelerated motion. Note, however, that experts and good students do not simply ignore the surface features of problems. Rather, as was the case in the problem isomorphs we described earlier (Kotovsky et al., 1985 ), they tend to use such features to infer what the problem's structure could be (e.g., Alibali, Bassok, Solomon, Syc, & Goldin-Meadow, 1999 ; Blessing & Ross, 1996 ). For example, Hinsley et al. ( 1977 ) found that, after reading no more than the first few words of an algebra word problem, expert solvers classified the problem into a likely problem category (e.g., a work problem, a distance problem) and could predict what questions they might be asked and the equations they likely would need to use.

Surface-based problem categorization has a heuristic value (Medin & Ross, 1989 ): It does not ensure a correct categorization (Blessing & Ross, 1996 ), but it does allow solvers to retrieve potentially appropriate solutions from memory and to use them, possibly with some adaptation, to solve a variety of novel problems. Indeed, although experts exploit surface-structure correlations to save cognitive effort, they have the capability to realize that a particular surface cue is misleading (Hegarty, Mayer, & Green, 1992 ; Lewis & Mayer, 1987 ; Martin & Bassok, 2005 ; Novick 1988 , 1995 ; Novick & Holyoak, 1991 ). It is not surprising, therefore, that experts may revert to novice-like heuristic methods when solving problems under pressure (e.g., Beilock, 2008 ) or in subdomains in which they have general but not specific expertise (e.g., Patel, Groen, & Arocha, 1990 ).

Relevance of Search to Insight Solutions

We introduced the notion of insight in our discussion of the nine-dot problem in the section on the Gestalt tradition. The Gestalt view (e.g., Duncker, 1945 ; Maier, 1931 ; see Ohlsson, 1984 , for a review) was that insight problem solving is characterized by an initial work period during which no progress toward solution is made (i.e., an impasse), a sudden restructuring of one's problem representation to a more suitable form, followed immediately by the sudden appearance of the solution. Thus, solving problems by insight was believed to be all about representation, with essentially no role for a step-by-step solution process (i.e., search). Subsequent and contemporary researchers have generally concurred with the Gestalt view that getting the right representation is crucial. However, research has shown that insight solutions do not necessarily arise suddenly or full blown after restructuring (e.g., Weisberg & Alba, 1981 ); and even when they do, the underlying solution process (in this case outside of awareness) may reflect incremental progress toward the goal (Bowden & Jung-Beeman, 2003 ; Durso, Rea, & Dayton, 1994 ; Novick & Sherman, 2003 ).

“Demystifying insight,” to borrow a phrase from Bowden, Jung-Beeman, Fleck, and Kounios ( 2005 ), requires explaining ( 1 ) why solvers initially reach an impasse in solving a problem for which they have the necessary knowledge to generate the solution, ( 2 ) how the restructuring occurred, and ( 3 ) how it led to the solution. A detailed discussion of these topics appears elsewhere in this volume (van Steenburgh et al., Chapter 24 ). Here, we describe briefly three recent theories that have attempted to account for various aspects of these phenomena: Knoblich, Ohlsson, Haider, and Rhenius's ( 1999 ) representational change theory, MacGregor, Ormerod, and Chronicle's ( 2001 ) progress monitoring theory, and Bowden et al.'s ( 2005 ) neurological model. We then propose the need for an integrated approach to demystifying insight that considers both representation and search.

According to Knoblich et al.'s ( 1999 ) representational change theory, problems that are solved with insight are highly likely to evoke initial representations in which solvers place inappropriate constraints on their solution attempts, leading to an impasse. An impasse can be resolved by revising one's representation of the problem. Knoblich and his colleagues tested this theory using Roman numeral matchstick arithmetic problems in which solvers must move one stick to a new location to change a false numerical statement (e.g., I = II + II ) into a statement that is true. According to representational change theory, re-representation may occur through either constraint relaxation or chunk decomposition. (The solution to the example problem is to change II + to III – , which requires both methods of re-representation, yielding I = III – II ). Good support for this theory has been found based on measures of solution rate, solution time, and eye fixation (Knoblich et al., 1999 ; Knoblich, Ohlsson, & Raney, 2001 ; Öllinger, Jones, & Knoblich, 2008 ).

Progress monitoring theory (MacGregor et al., 2001 ) was proposed to account for subjects' difficulty in solving the nine-dot problem, which has traditionally been classified as an insight problem. According to this theory, solvers use the hill-climbing search heuristic to solve this problem, just as they do for traditional search problems (e.g., Hobbits and Orcs). In particular, solvers are hypothesized to monitor their progress toward solution using a criterion generated from the problem's current state. If solvers reach criterion failure, they seek alternative solutions by trying to relax one or more problem constraints. MacGregor et al. found support for this theory using several variants of the nine-dot problem (also see Ormerod, MacGregor, & Chronicle, 2002 ). Jones ( 2003 ) suggested that progress monitoring theory provides an account of the solution process up to the point an impasse is reached and representational change is sought, at which point representational change theory picks up and explains how insight may be achieved. Hence, it appears that a complete account of insight may require an integration of concepts from the Gestalt (representation) and Newell and Simon's (search) legacies.

Bowden et al.'s ( 2005 ) neurological model emphasizes the overlap between problem solving and language comprehension, and it hinges on differential processing in the right and left hemispheres. They proposed that an impasse is reached because initial processing of the problem produces strong activation of information irrelevant to solution in the left hemisphere. At the same time, weak semantic activation of alternative semantic interpretations, critical for solution, occurs in the right hemisphere. Insight arises when the weakly activated concepts reinforce each other, eventually rising above the threshold required for conscious awareness. Several studies of problem solving using compound remote associates problems, involving both behavioral and neuroimaging data, have found support for this model (Bowden & Jung-Beeman, 1998 , 2003 ; Jung-Beeman & Bowden, 2000 ; Jung-Beeman et al., 2004 ; also see Moss, Kotovsky, & Cagan, 2011 ).

Note that these three views of insight have received support using three quite distinct types of problems (Roman numeral matchstick arithmetic problems, the nine-dot problem, and compound remote associates problems, respectively). It remains to be established, therefore, whether these accounts can be generalized across problems. Kershaw and Ohlsson ( 2004 ) argued that insight problems are difficult because the key behavior required for solution may be hindered by perceptual factors (the Gestalt view), background knowledge (so expertise may be important; e.g., see Novick & Sherman, 2003 , 2008 ), and/or process factors (e.g., those affecting search). From this perspective, solving visual problems (e.g., the nine-dot problem) with insight may call upon more general visual processes, whereas solving verbal problems (e.g., anagrams, compound remote associates) with insight may call upon general verbal/semantic processes.

The work we reviewed in this section shows the relevance of problem representation (the Gestalt legacy) to the way people search the problem space (the legacy of Newell and Simon), and the relevance of search to the solution of insight problems that require a representational change. In addition to this inevitable integration of the two legacies, the work we described here underscores the fact that problem solving crucially depends on perceptual factors and on the solvers' background knowledge. In the next section, we describe some recent work that shows the involvement of these factors in the solution of problems in math and science.

Effects of Perception and Knowledge in Problem Solving in Academic Disciplines

Although the use of puzzle problems continues in research on problem solving, especially in investigations of insight, many contemporary researchers tackle problem solving in knowledge-rich domains, often in academic disciplines (e.g., mathematics, biology, physics, chemistry, meteorology). In this section, we provide a sampling of this research that highlights the importance of visual perception and background knowledge for successful problem solving.

The Role of Visual Perception

We stated at the outset that a problem representation (e.g., the problem space) is a model of the problem constructed by solvers to summarize their understanding of the problem's essential nature. This informal definition refers to the internal representations people construct and hold in working memory. Of course, people may also construct various external representations (Markman, 1999 ) and even manipulate those representations to aid in solution (see Hegarty & Stull, Chapter 31 ). For example, solvers often use paper and pencil to write notes or draw diagrams, especially when solving problems from formal domains (e.g., Cox, 1999 ; Kindfield, 1993 / 1994 ; S. Schwartz, 1971 ). In problems that provide solvers with external representation, such as the Tower of Hanoi problem, people's planning and memory of the current state is guided by the actual configurations of disks on pegs (Garber & Goldin-Meadow, 2002 ) or by the displays they see on a computer screen (Chen & Holyoak, 2010 ; Patsenko & Altmann, 2010 ).

In STEM (science, technology, engineering, and mathematics) disciplines, it is common for problems to be accompanied by diagrams or other external representations (e.g., equations) to be used in determining the solution. Larkin and Simon ( 1987 ) examined whether isomorphic sentential and diagrammatic representations are interchangeable in terms of facilitating solution. They argued that although the two formats may be equivalent in the sense that all of the information in each format can be inferred from the other format (informational equivalence), the ease or speed of making inferences from the two formats might differ (lack of computational equivalence). Based on their analysis of several problems in physics and math, Larkin and Simon further argued for the general superiority of diagrammatic representations (but see Mayer & Gallini, 1990 , for constraints on this general conclusion).

Novick and Hurley ( 2001 , p. 221) succinctly summarized the reasons for the general superiority of diagrams (especially abstract or schematic diagrams) over verbal representations: They “(a) simplify complex situations by discarding unnecessary details (e.g., Lynch, 1990 ; Winn, 1989 ), (b) make abstract concepts more concrete by mapping them onto spatial layouts with familiar interpretational conventions (e.g., Winn, 1989 ), and (c) substitute easier perceptual inferences for more computationally intensive search processes and sentential deductive inferences (Barwise & Etchemendy, 1991 ; Larkin & Simon, 1987 ).” Despite these benefits of diagrammatic representations, there is an important caveat, noted by Larkin and Simon ( 1987 , p. 99) at the very end of their paper: “Although every diagram supports some easy perceptual inferences, nothing ensures that these inferences must be useful in the problem-solving process.” We will see evidence of this in several of the studies reviewed in this section.

Next we describe recent work on perceptual factors that are involved in people's use of two types of external representations that are provided as part of the problem in two STEM disciplines: equations in algebra and diagrams in evolutionary biology. Although we focus here on effects of perceptual factors per se, it is important to note that such factors only influence performance when subjects have background knowledge that supports differential interpretation of the alternative diagrammatic depictions presented (Hegarty, Canham, & Fabricant, 2010 ).

In the previous section, we described the work of Patsenko and Altmann ( 2010 ) that shows direct involvement of visual attention and perception in the sequential application of move operators during the solution of the Tower of Hanoi problem. A related body of work documents similar effects in tasks that require the interpretation and use of mathematical equations (Goldstone, Landy, & Son, 2010 ; Landy & Goldstone, 2007a , b). For example, Landy and Goldstone ( 2007b ) varied the spatial proximity of arguments to the addition (+) and multiplication (*) operators in algebraic equations, such that the spatial layout of the equation was either consistent or inconsistent with the order-of-operations rule that multiplication precedes addition. In consistent equations , the space was narrower around multiplication than around addition (e.g., g*m + r*w = m*g + w*r ), whereas in inconsistent equations this relative spacing was reversed (e.g., s * n+e * c = n * s+c * e ). Subjects' judgments of the validity of such equations (i.e., whether the expressions on the two sides of the equal sign are equivalent) were significantly faster and more accurate for consistent than inconsistent equations.

In discussing these findings and related work with other external representations, Goldstone et al. ( 2010 ) proposed that experience with solving domain-specific problems leads people to “rig up” their perceptual system such that it allows them to look at the problem in a way that is consistent with the correct rules. Similar logic guides the Perceptual Learning Modules developed by Kellman and his collaborators to help students interpret and use algebraic equations and graphs (Kellman et al., 2008 ; Kellman, Massey, & Son, 2009 ). These authors argued and showed that, consistent with the previously reviewed work on expertise, perceptual training with particular external representations supports the development of perceptual fluency. This fluency, in turn, supports students' subsequent use of these external representations for problem solving.

This research suggests that extensive experience with particular equations or graphs may lead to perceptual fluency that could replace the more mindful application of domain-specific rules. Fisher, Borchert, and Bassok ( 2011 ) reported results from algebraic-modeling tasks that are consistent with this hypothesis. For example, college students were asked to represent verbal statements with algebraic equations, a task that typically elicits systematic errors (e.g., Clement, Lochhead, & Monk, 1981 ). Fisher et al. found that such errors were very common when subjects were asked to construct “standard form” equations ( y = ax ), which support fluent left-to-right translation of words to equations, but were relatively rare when subjects were asked to construct nonstandard division-format equations (x = y/a) that do not afford such translation fluency.

In part because of the left-to-right order in which people process equations, which mirrors the linear order in which they process text, equations have traditionally been viewed as sentential representations. However, Landy and Goldstone ( 2007a ) have proposed that equations also share some properties with diagrammatic displays and that, in fact, in some ways they are processed like diagrams. That is, spatial information is used to represent and to support inferences about syntactic structure. This hypothesis received support from Landy and Goldstone's ( 2007b ) results, described earlier, in which subjects' judgments of the validity of equations were affected by the Gestalt principle of grouping: Subjects did better when the grouping was consistent rather than inconsistent with the underlying structure of the problem (order of operations). Moreover, Landy and Goldstone ( 2007a ) found that when subjects wrote their own equations they grouped numbers and operators (+, *, =) in a way that reflected the hierarchical structure imposed by the order-of-operations rule.

In a recent line of research, Novick and Catley ( 2007 ; Novick, Catley, & Funk, 2010 ; Novick, Shade, & Catley, 2011 ) have examined effects of the spatial layout of diagrams depicting the evolutionary history of a set of taxa on people's ability to reason about patterns of relationship among those taxa. We consider here their work that investigates the role of another Gestalt perceptual principle—good continuation—in guiding students' reasoning. According to this principle, a continuous line is perceived as a single entity (Kellman, 2000 ). Consider the diagrams shown in Figure 21.6 . Each is a cladogram, a diagram that depicts nested sets of taxa that are related in terms of levels of most recent common ancestry. For example, chimpanzees and starfish are more closely related to each other than either is to spiders. The supporting evidence for their close relationship is their most recent common ancestor, which evolved the novel character of having radial cleavage. Spiders do not share this ancestor and thus do not have this character.

Cladograms are typically drawn in two isomorphic formats, which Novick and Catley ( 2007 ) referred to as trees and ladders. Although these formats are informationally equivalent (Larkin & Simon, 1987 ), Novick and Catley's ( 2007 ) research shows that they are not computationally equivalent (Larkin & Simon, 1987 ). Imagine that you are given evolutionary relationships in the ladder format, such as in Figure 21.6a (but without the four characters—hydrostatic skeleton, bilateral symmetry, radial cleavage, and trocophore larvae—and associated short lines indicating their locations on the cladogram), and your task is to translate that diagram to the tree format. A correct translation is shown in Figure 21.6b . Novick and Catley ( 2007 ) found that college students were much more likely to get such problems correct when the presented cladogram was in the nested circles (e.g., Figure 21.6d ) rather than the ladder format. Because the Gestalt principle of good continuation makes the long slanted line at the base of the ladder appear to represent a single hierarchical level, a common translation error for the ladder to tree problems was to draw a diagram such as that shown in Figure 21.6c .

The difficulty that good continuation presents for interpreting relationships depicted in the ladder format extends to answering reasoning questions as well. Novick and Catley (unpublished data) asked comparable questions about relationships depicted in the ladder and tree formats. For example, using the cladograms depicted in Figures 21.6a and 21.6b , consider the following questions: (a) Which taxon—jellyfish or earthworm—is the closest evolutionary relation to starfish, and what evidence supports your answer? (b) Do the bracketed taxa comprise a clade (a set of taxa consisting of the most recent common ancestor and all of its descendants), and what evidence supports your answer? For both such questions, students had higher accuracy and evidence quality composite scores when the relationships were depicted in the tree than the ladder format.

Four cladograms depicting evolutionary relationships among six animal taxa. Cladogram ( a ) is in the ladder format, cladograms ( b ) and ( c ) are in the tree format, and cladogram ( d ) is in the nested circles format. Cladograms ( a ), ( b ), and ( d ) are isomorphic.

If the difficulty in extracting the hierarchical structure of the ladder format is due to good continuation (which leads problem solvers to interpret continuous lines that depict multiple hierarchical levels as depicting only a single level), then a manipulation that breaks good continuation at the points where a new hierarchical level occurs should improve understanding. Novick et al. ( 2010 ) tested this hypothesis using a translation task by manipulating whether characters that are the markers for the most recent common ancestor of each nested set of taxa were included on the ladders. Figure 21.6a shows a ladder with such characters. As predicted, translation accuracy increased dramatically simply by adding these characters to the ladders, despite the additional information subjects had to account for in their translations.

The Role of Background Knowledge

As we mentioned earlier, the specific entities in the problems people encounter evoke inferences that affect how people represent these problems (e.g., the candle problem; Duncker, 1945 ) and how they apply the operators in searching for the solution (e.g., the disks vs. acrobats versions of the Tower of Hanoi problem; Kotovsky et al., 1985 ). Such object-based inferences draw on people's knowledge about the properties of the objects (e.g., a box is a container, an acrobat is a person who can be hurt). Here, we describe the work of Bassok and her colleagues, who found that similar inferences affect how people select mathematical procedures to solve problems in various formal domains. This work shows that the objects in the texts of mathematical word problems affect how people represent the problem situation (i.e., the situation model they construct; Kintsch & Greeno, 1985 ) and, in turn, lead them to select mathematical models that have a corresponding structure. To illustrate, a word problem that describes constant change in the rate at which ice is melting off a glacier evokes a model of continuous change, whereas a word problem that describes constant change in the rate at which ice is delivered to a restaurant evokes a model of discrete change. These distinct situation models lead subjects to select corresponding visual representations (e.g., Bassok & Olseth, 1995 ) and solutions methods, such as calculating the average change over time versus adding the consecutive changes (e.g., Alibali et al., 1999 ).

In a similar manner, people draw on their general knowledge to infer how the objects in a given problem are related to each other and construct mathematical solutions that correspond to these inferred object relations. For example, a word problem that involves doctors from two hospitals elicits a situation model in which the two sets of doctors play symmetric roles (e.g., work with each other), whereas a mathematically isomorphic problem that involves mechanics and cars elicits a situation model in which the sets play asymmetric roles (e.g., mechanics fix cars). The mathematical solutions people construct to such problems reflect this difference in symmetry (Bassok, Wu, & Olseth, 1995 ). In general, people tend to add objects that belong to the same taxonomic category (e.g., doctors + doctors) but divide functionally related objects (e.g., cars ÷ mechanics). People establish this correspondence by a process of analogical alignment between semantic and arithmetic relations, which Bassok and her colleagues refer to as “semantic alignment” (Bassok, Chase, & Martin, 1998 ; Doumas, Bassok, Guthormsen, & Hummel, 2006 ; Fisher, Bassok, & Osterhout, 2010 ).

Semantic alignment occurs very early in the solution process and can prime arithmetic facts that are potentially relevant to the problem solution (Bassok, Pedigo, & Oskarsson, 2008 ). Although such alignments can lead to erroneous solutions, they have a high heuristic value because, in most textbook problems, object relations indeed correspond to analogous mathematical relations (Bassok et al., 1998 ). Interestingly, unlike in the case of reliance on specific surface-structure correlations (e.g., the keyword “more” typically appears in word problems that require addition; Lewis & Mayer, 1987 ), people are more likely to exploit semantic alignment when they have more, rather than less modeling experience. For example, Martin and Bassok ( 2005 ) found very strong semantic-alignment effects when subjects solved simple division word problems, but not when they constructed algebraic equations to represent the relational statements that appeared in the problems. Of course, these subjects had significantly more experience with solving numerical word problems than with constructing algebraic models of relational statements. In a subsequent study, Fisher and Bassok ( 2009 ) found semantic-alignment effects for subjects who constructed correct algebraic models, but not for those who committed modeling errors.

Conclusions and Future Directions

In this chapter, we examined two broad components of the problem-solving process: representation (the Gestalt legacy) and search (the legacy of Newell and Simon). Although many researchers choose to focus their investigation on one or the other of these components, both Duncker ( 1945 ) and Simon ( 1986 ) underscored the necessity to investigate their interaction, as the representation one constructs for a problem determines (or at least constrains) how one goes about trying to generate a solution, and searching the problem space may lead to a change in problem representation. Indeed, Duncker's ( 1945 ) initial account of one subject's solution to the radiation problem was followed up by extensive and experimentally sophisticated work by Simon and his colleagues and by other researchers, documenting the involvement of visual perception and background knowledge in how people represent problems and search for problem solutions.

The relevance of perception and background knowledge to problem solving illustrates the fact that, when people attempt to find or devise ways to reach their goals, they draw on a variety of cognitive resources and engage in a host of cognitive activities. According to Duncker ( 1945 ), such goal-directed activities may include (a) placing objects into categories and making inferences based on category membership, (b) making inductive inferences from multiple instances, (c) reasoning by analogy, (d) identifying the causes of events, (e) deducing logical implications of given information, (f) making legal judgments, and (g) diagnosing medical conditions from historical and laboratory data. As this list suggests, many of the chapters in the present volume describe research that is highly relevant to the understanding of problem-solving behavior. We believe that important advancements in problem-solving research would emerge by integrating it with research in other areas of thinking and reasoning, and that research in these other areas could be similarly advanced by incorporating the insights gained from research on what has more traditionally been identified as problem solving.

As we have described in this chapter, many of the important findings in the field have been established by a careful investigation of various riddle problems. Although there are good methodological reasons for using such problems, many researchers choose to investigate problem solving using ecologically valid educational materials. This choice, which is increasingly common in contemporary research, provides researchers with the opportunity to apply their basic understanding of problem solving to benefit the design of instruction and, at the same time, allows them to gain a better understanding of the processes by which domain knowledge and educational conventions affect the solution process. We believe that the trend of conducting educationally relevant research is likely to continue, and we expect a significant expansion of research on people's understanding and use of dynamic and technologically rich external representations (e.g., Kellman et al., 2008 ; Mayer, Griffith, Jurkowitz, & Rothman, 2008 ; Richland & McDonough, 2010 ; Son & Goldstone, 2009 ). Such investigations are likely to yield both practical and theoretical payoffs.

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Systematic review article, the critical thinking-oriented adaptations of problem-based learning models: a systematic review.

• Faculty of Social Sciences and Humanities, Universiti Teknologi Malaysia, Johor Bahru, Malaysia

Critical thinking is a significant twenty-first century skill that is prioritized by higher education. Problem-based learning is becoming widely accepted as an effective way to enhance critical thinking. However, as the results of studies that use PBL to develop CT have had mixed success, PBL models need to be modified to guarantee positive outcomes. This study is a systematic review that analyzed how studies have adapted Problem-Based Learning (PBL) to become more Critical Thinking (CT)-oriented, evaluated the effectiveness of these adaptations, and determined why certain adaptations were successful. The review was conducted in accordance with PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) by searching the scientific databases Scopus and Web of Science. Twenty journal articles were chosen based on their adherence to the inclusion criteria established by PICo (Population, Phenomenon of Interest, and Context). In these studies, PBL adaptations were categorized into five classifications, with activities centered on CT development being the most prevalent approach. Researchers utilized a variety of analytical methodologies to assess the effectiveness of these adaptations and derive significant insights and formulate valid conclusions. An analysis of all selected studies revealed positive outcomes, indicating that incorporating CT elements into PBL was effective in enhancing students' CT. These findings were categorized into nine factors that contribute to the successful adaptation of PBL to be CT-oriented.

1. Introduction

The twenty-first century is an era of innovation, requiring individuals to possess skills for academic excellence, success in the workplace, and the capability to cope with life. Examples of such transferable skills include communication, collaboration, creativity, problem-solving, and critical thinking (CT) ( Hidayati et al., 2022 ). Of these, CT is frequently cited as the most crucial ( National Association of Colleges Employers, 2016 ) for individuals to adapt to this quickly changing society ( Alper, 2010 ). Universities view the development of students' CT skills as one of their most significant educational objectives ( Facione, 2011 ; Erikson and Erikson, 2019 ) and must therefore continually refine their teaching techniques ( Bezanilla et al., 2019 ) and establish a learning environment that improves students' CT capabilities ( Evendi et al., 2022 ). In this way, universities can foster twenty-first-century talents with extraordinary academic performance and excellent professional skills ( Hidayati et al., 2022 ).

Problem-based learning is gaining popularity as a method for enhancing critical thinking. However, PBL models must be adapted to ensure beneficial outcomes, as the results of studies employing PBL to enhance CT have not always been positive. Thus, it is essential to determine which aspects contribute to the success of a PBL-adapted model for developing CT and explore the reason for the success. This paper offers a systematic review of how studies have altered PBL to become more focused on critical thinking, the evaluation of those modifications, and the factors that contribute to enhanced critical thinking.

1.1. Critical thinking

While the importance of CT has been widely acknowledged, scholars from different research fields have conceptualized and defined it differently. For instance, philosophy scholars view CT as the ability to challenge an assumption, evaluate the argument and relevant information, and draw correct conclusions ( Fisher, 2011 ); psychology scholars view CT as a broad range of thinking skills, including problem solving, decision making, and hypothesis testing ( Halpern, 2010 ). The literature generally conceptualizes CT as comprising two equally important elements—skills (CTSs) and dispositions (CTDs). Facione (1990) believes that critical thinkers are unsuccessful if they cannot apply their CT skills effectively.

For this paper, CT is understood as consisting of: (i) making judgments ( Chaffee, 1994 ; Snyder and Snyder, 2008 ; Papathanasiou et al., 2014 ; Ennis, 2018 ); (ii) evaluation ( Facione, 1990 ; Yanchar and Slife, 2004 ; Fisher, 2011 ; and (iii) reasoning ( Facione, 1990 ; Ennis, 2011 ; Elder and Paul, 2012 ). Characteristics commonly recognized as indispensable for CTD include: (1) open-mindedness ( Ennis, 1987 ; Facione, 1990 ); (2) fair-mindedness ( Facione, 1990 ; Elder and Paul, 2001 ); (3) inquisitiveness ( Facione, 1990 ; Elder and Paul, 2001 ); (4) respect for reason ( Ennis, 1987 ; Lipman, 1991 ); and (5) propensity to explore alternatives ( Elder and Paul, 2001 ).

CTSs and CTDs are not innate qualities but must be developed through learning and practice. However, conventional teaching approaches: (1) are not conducive to developing students' CT; (2) lack authenticity ( Sharma and Elbow, 2000 ); and (3) are inadequate for developing students' CTSs ( Drennan and Rohde, 2002 ). Education and teaching systems need to be designed to facilitate CT learning ( Dekker, 2020 ) by selecting the most recent effective instructional strategies ( Karakoc, 2016 ).

1.2. Problem-based learning

Problem-based learning (PBL) is a student-centered instructional method that enhances CT ( Facione et al., 2000 ; Choi et al., 2014 ; Carter et al., 2017 ), including CTSs ( Facione et al., 2000 ) and CTDs ( Dehkordi and Heydarnejad, 2008 ). PBL occurs among small groups of students who explore problems and find solutions collaboratively ( Yuan et al., 2008 ); it is a continual scientific learning process designed to accustom students to think critically ( Nurcahyo and Djono, 2018 ). PBL begins by challenging students to solve complicated, ill-structured problems ( Barrows, 1986 ) and provides opportunities inside and outside of the classroom to analyze information and consider different viewpoints ( Dwyer et al., 2015 ); students share their thoughts, listen to those of others, reflect on their own ideas, and ultimately obtain a suitable solution to a problem. The required self-directed learning, interpersonal communication, and reasoning foster CT ( Orique and McCarthy, 2015 ).

1.3. Problem-based learning and critical thinking

Liu and Pásztor (2022) meta-analysis of 50 relevant empirical studies with 5,210 participants and 58 effect sizes concluded that PBL was effective for fostering CT. However, Lee et al. (2016) meta-analysis of eight studies concluded that PBL was not effective for enhancing nursing students' CT. These contradictory conclusions suggest that teachers must adapt PBL according to the objectives to be attained ( Barrows, 1996 ). Researchers from different academic fields, such as Kamin et al. (2003) , Fujinuma and Wendling (2015) , and Evendi et al. (2022) have adapted PBL to improve students' CT.

This study thus sought to: (1) examine how studies have adapted PBL to be more focused on CT development; (2) examine the result of those studies; and (3) explore the reasons for successful modifications. It filled the gap left by the systematic reviews that are focused on the impacts of PBL model instead of adapted CT-oriented PBL models on CT development.

1.4. Research questions

The formulation of the research question for this study was based on the PICo framework, which has been developed specifically for qualitative reviews and identifies the key aspects of Population, Phenomenon of Interest, and Context ( JBI, 2011 ). Utilizing these concepts, the authors incorporated three primary aspects into the review: college students (Population), CT improvement (Phenomenon of Interest), and participation in CT-oriented PBL intervention (Context). The principal research question was thus: How can the PBL model be adapted to enhance students' critical thinking abilities? This broad question was further refined into several specific research questions:

(1) What adaptations can be made to PBL to enhance the CT of college students and what is the rationale for these adaptations?

(2) How are the results of CT-oriented PBL interventions evaluated?

(3) To what extent are these adapted PBL models successful and what factors contribute to their success?

2. Methodology

A protocol encompassing search terms, databases, screening criteria, and analytical methods was established to guide the literature search and generate the initial data set ( Yang et al., 2017 ). The Preferred Reporting Items for Systematic Review and Meta-Analyses (PRISMA) ( Page et al., 2021 ) were employed to identify pertinent papers concerning PBL adaptations for teaching CTSs and CTDs at the undergraduate level in higher education. Two databases were utilized: Scopus and Web of Science (WOS).

2.1. Search strategy

The key search terms were derived from several sources: previous studies; an online thesaurus; keywords suggested by WOS and Scopus; and the research questions.

Two independent researchers identified research articles published in Scopus or WOS between January 2001 and mid-August 2022 by using a combination of the key search terms with a Boolean operator, phrase searching, and truncation to produce the search string. For WOS, the search string was TS = (PBL or “problem based learning” or “problem-based learning”) AND (“critical thinking” or “think critically”) AND (university or college or undergraduate or “higher education” or “tertiary education”). For Scopus, the search string was TITLE-ABS-KEY (PBL or “problem based learning” or “problem-based learning”) AND (“critical thinking” or “think critically”) AND (university or college or undergraduate or “higher education” or “tertiary education”).

2.2. Inclusion and exclusion criteria

The inclusion and exclusion criteria were based on PICo ( JBI, 2011 ). Articles were included if they: (1) undertook empirical research; (2) involved undergraduate students; (3) used PBL-adapted models as the main instructional intervention; (4) included research tools to collect CTS and CTD data; (5) explored students' learning experiences; (6) evaluated CTS and/or CTD as the main research outcome; and (7) published in an English peer-reviewed scientific journal.

Studies were excluded if they: (1)were review papers or not empirical papers; (2) did not adapt PBL models for their own research purposes; (3) involved non-undergraduate college students; (4) did not collect CTS and CTD data; (5) did not evaluate CTS and/or CTD as the main research outcome; (6) did not report CTS and/or CTD outcomes; (7) published in languages other than English; and (8) were not published in peer-reviewed journals, e.g., conference proceedings or book chapters.

2.3. Selection of articles

Articles were screened and selected according to PRISMA. Duplicate records and non-research or non-English articles were removed. Two independent reviewers then screened as many articles as possible to not miss any potentially eligible article. Records with a title and/or abstract that suggested the work involved PBL and CT were retained even though they did not fully meet the inclusion criteria for the title and/or abstract. The reviewers then rigorously applied the inclusion and exclusion criteria as they examined the full text of the retained articles. This meant that all eligible articles involved a modified PBL as the pedagogical intervention and evaluated CTS or CTD as the main research outcome. Finally, a database of selected articles was created for data extraction and analysis.

Figure 1 shows the number of records included at the identification, screening, selection and inclusion stages of the review process. The initial database searches uncovered 719 publications. After 70 duplicate records were eliminated, the literature was screened for journal or review articles that were written in English. This reduced the number of records to 499. After evaluating the abstracts of these articles, 292 records were deleted. The entire text of the remaining 207 papers were reviewed; 187 articles that failed to meet the inclusion criteria were excluded, leaving 20 journal articles to be included in this systematic review.

Figure 1 . The flow diagram of the literature search using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA).

2.4. Data extraction

To extract pertinent information from the 20 studies, Harris et al. (2014) guidelines were employed. These guidelines facilitated the extraction of information such as the author(s), year of publication, types of intervention implemented, types of data collection methods, types of data analysis methods, main findings of the study, and the effectiveness of the interventions in achieving their intended outcomes.

3. Results and discussion

The findings of the study are presented in three distinct sub-sections, each corresponding to a specific research question. The first sub-section details the types of PBL adaptations that were made to improve CT. The second sub-section presents the details of data collection and analysis implemented by each study. The last sub-section discusses the reasons for the observed improvements in student's CT as a result of these interventions.

3.1. The CT-oriented adaptations made to PBL models

An analysis revealed five distinct approaches to adapting Problem-Based Learning (PBL) to enhance Critical Thinking (CT) skills: (1) the implementation of CT-specific tools; (2) the incorporation of CT-focused activities; (3) the utilization of digital technologies; (4) the integration with other pedagogical methods; and (5) the integration with discipline-specific knowledge. As depicted in Table 1 , CT-oriented activities ( n = 6) emerged as the most prevalent strategy for augmenting CT, followed by the utilization of instructional technologies ( n = 5) and the assimilation of other instructional modes ( n = 4). Conversely, CT-oriented instruments ( n = 3) and the combination of PBL with subject-specific knowledge ( n = 2) were identified as the least frequently employed tactics for adapting PBL to foster CT development.

Table 1 . The author(s), publication date, and intervention used in studies by approach to PBL adaptation.

3.1.1. CT-oriented tools

As is depicted in Table 1 , the aforementioned studies employed various adaptations of Problem-Based Learning (PBL) with the objective of enhancing critical thinking (CT). These adaptations encompassed the utilization of CT-oriented guiding questions ( Carbogim et al., 2017 ), concept mapping ( Orique and McCarthy, 2015 ), and a CT assessment rubric ( Suryanti and Nurhuda, 2021 ). In their studies, guiding questions were implemented to stimulate and direct cognitive processes, concept maps served as a visual instrument for representing concerned issues and facilitating the development of solving plans, and the CT assessment rubric was employed to furnish lucid guidelines and expectations that facilitated self-assessment and engendered a more profound engagement with the subject matter. These aforementioned instruments possess the capacity to facilitate the development of students' critical thinking aptitudes by providing a framework for the organization and analysis of information.

3.1.2. CT-oriented activities

The studies examined in this text employed various critical thinking-oriented activities within a problem-based learning (PBL) framework to enhance the development of critical thinking skills. These activities were collaborative in nature, a characteristic inherent to PBL ( Yuan et al., 2008 ), and allowed learners to practice cognitive and/or meta-cognitive skills. With regard to the incorporation of cognitive skills, Hsu (2021) , for example, advocates for the integration of collaborative learning with PBL as it requires learners to cooperatively analyze, synthesize, and evaluate ideas to solve complex problems. Additionally, Mumtaz and Latif (2017) and Latif et al. (2018) incorporated debate among learners as it provides an opportunity for deeper analysis and appraisal of issues. The others recognized the significant correlation between meta-cognitive skills and CT improvement. For example, Fujinuma and Wendling (2015) integrated team-based active learning into their PBL model focused on meta-cognitive development to improve critical thinking. Rivas et al. (2022) emphasized individual and interactive meta-cognitive development through reflective activities because effective use of critical thinking skills requires a certain degree of consciousness and regulation of them. Rodríguez et al. (2022) used peer assessment within a PBL framework to develop a four-stage metacognitive approach due to the positive correlation between metacognition and active learning ( Biasutti and Frate, 2018 ), which can help foster higher order thinking skills ( Kim et al., 2020 ). These CT-oriented adaptations suggest that future studies could consider creating active learning environments through collaborative activities to foster cognitive and meta-cognitive skills to enhance critical thinking.

3.1.3. Digital strategies

Included research examined the incorporation of digital technologies into PBL to enhance CT. Sendag and Odabasi (2009) and Evendi et al. (2022) adapted traditional face-to-face PBL to an electronic format known as e-PBL in response to the increasing prevalence of online learning and the demonstrated efficacy of e-PBL in enhancing learning outcomes. Other studies investigated the use of videos in problem-based learning because they can present ill-structured problems in a more vivid manner ( Kamin et al., 2003 ; Roy and McMahon, 2012 ). Digital mind maps were used in conjunction with PBL by Hidayati et al. (2022) because they can create an engaging learning environment and facilitate deeper learning regardless of the learning styles of the learners.

3.1.4. PBL integrated with other pedagogical models

Researchers attempted to combine other pedagogical mode with PBL to enhance CT development. Lim (2020) integrated problem-based learning (PBL) with simulation-based learning to enable students to tackle problems that mirror real-life scenarios, thereby enhancing their professional skills and critical thinking abilities. Similarly, Xing et al. (2021) employed a clinical case-based PBL approach in conjunction with the “Status-Background-Assessment-Recommendation” (SBAR) teaching model to facilitate communication ( Abdellatif et al., 2007 ). Carbogim et al. (2018) combined PBL with the Active Learning Model for Critical Thinking (ALMCT), which comprises a series of questions designed to promote deeper understanding and exploration of meanings, relationships, and outcomes through inquiry within a clinical context or case. Aein (2018) modified PBL by incorporating inter-professional learning (IPL) to foster teamwork, enhance communication, and overcome inter-professional barriers. These studies share a common focus on the medical field and aim to improve students' professional competencies and critical thinking skills by presenting simulated real-world cases and promoting communication and collaboration among students.

3.1.5. PBL integrated with subject knowledge

Silviarza et al. (2020) and Silviariza and Handoyo (2021) are the sole authors among the studies reviewed to have undertaken research on the integration of problem-based learning (PBL) with the instruction of subject knowledge. They contend that the ability to critically solve problems is of paramount importance in the study of geography ( Nagel, 2008 ). Academics may contemplate the incorporation of problem-based learning (PBL) methodologies within fields of study that necessitate the utilization of critical thinking competencies for problem resolution and knowledge acquisition. Such an approach has the potential to augment not only students' comprehension of the subject matter but also their capacity for critical thinking.

3.2. The evaluation of CT-oriented PBL interventions

The efficacy of Problem-Based Learning (PBL) adaptations in enhancing Critical Thinking (CT) was investigated by examining the results of individual studies. To determine the overall effectiveness of modified PBL models on the development of CT skills or dispositions (CTS or CTD), it is necessary to scrutinize the instruments employed for data collection and the analytical methods utilized. Table 2 provides an overview of the article title, publication year, data collection instrument, and data analysis approach utilized in the study.

Table 2 . Evaluation of included educational intervention.

3.2.1. Data collection

The instruments employed by the studies included in this analysis can be classified according to their use in collecting either quantitative or qualitative data, as delineated in Table 2 . Quantitative instruments comprise questionnaires (e.g., Mumtaz and Latif, 2017 ; Carbogim et al., 2018 ; Latif et al., 2018 ; Lim, 2020 ; Silviarza et al., 2020 ; Hsu, 2021 ; Xing et al., 2021 ), tests (e.g., Sendag and Odabasi, 2009 ; Silviariza and Handoyo, 2021 ; Hidayati et al., 2022 ; Rivas et al., 2022 ; Evendi et al., 2022 ), and assessment rubrics (e.g., Orique and McCarthy, 2015 ; Suryanti and Nurhuda, 2021 ; Rodríguez et al., 2022 ), with questionnaires being the most commonly utilized instrument. On the other hand, several studies have employed qualitative instruments to collect CT-related data, which are less varied than their quantitative counterparts. Qualitative instruments primarily encompass recorded learning activities (e.g., Kamin et al., 2003 ; Roy and McMahon, 2012 ; Evendi et al., 2022 ), interviews (e.g., Carbogim et al., 2017 ; Aein, 2018 ; Xing et al., 2021 ), and open-ended questions (e.g., Fujinuma and Wendling, 2015 ; Mumtaz and Latif, 2017 ). Based on an analysis of the tools utilized by the studies involved in this investigation, future research exploring the adaptations of PBL for CT can employ quantitative (e.g., Silviarza et al., 2020 ), qualitative (e.g., Aein, 2018 ), or mixed methods (e.g., Carbogim et al., 2017 ).

As indicated in Table 2 , researchers employ one of two approaches in constructing data collection instruments for quantitative data: either directly utilizing tools developed by others or developing their own research instruments. For instance, widely used and well-developed instruments include the Chinese adaptation of the California Critical Thinking Disposition Inventory (CCTDI) and the California Critical Thinking Skills Test (CCTST). Xing et al. (2021) employed the Chinese version of the CCTDI to investigate the impact of modified PBL on learners' CT disposition, while Carbogim et al. (2018) utilized the CCTST to assess students' CT skills. These extensively used tools have been demonstrated to be valid and reliable for data collection and analysis. Alternatively, researchers have endeavored to design their own instruments tailored to their specific study requirements. For example, Silviarza et al. (2020) and Hidayati et al. (2022) developed an essay test and a CTS test, respectively, based on the CT indicators proposed by Ennis (2011) . These self-made instruments were subjected to validity and reliability checks prior to being employed for data collection (e.g., Hidayati et al., 2022 ). Both of the above-discussed approaches, when implemented with established credibility and validity, are effective in collecting the desired data. On the other hand, most studies employing qualitative tools do not test validity and reliability in the same manner as quantitative studies (e.g., Kamin et al., 2003 ; Roy and McMahon, 2012 ), but instead utilize triangulation to enhance validity and reliability (e.g., Rodríguez et al., 2022 ).

3.2.2. Data analysis

As delineated in Table 2 , the studies included in this analysis employed distinct analytical methodologies based on their data collection methods. It is only through the application of analytical techniques that are appropriately tailored to the data and research objectives that researchers can derive meaningful insights and draw valid conclusions from their data.

For quantitative data, researchers utilized descriptive analysis to determine the means and proportions of CT-related data. Several studies employed this method, including Mumtaz and Latif (2017) , Carbogim et al. (2018) , Latif et al. (2018) , Suryanti and Nurhuda (2021) , and Rivas et al. (2022) . In addition to descriptive analysis, other statistical techniques were also frequently employed. Analysis of variance (ANOVA) was used by Sendag and Odabasi (2009) and Fujinuma and Wendling (2015) to compare the means of multiple groups and determine whether there were any statistically significant differences between them. The t -test technique to compare the means of experimental and control group was also commonly used, as seen in studies by Carbogim et al. (2018) , Latif et al. (2018) , Silviarza et al. (2020) , and Xing et al. (2021) .

In contrast to the quantitative methods described above, content analysis was typically applied to qualitative data. Studies that employed this method include Kamin et al. (2003) . In addition to content analysis, narrative summary was also used to present and interpret qualitative data (e.g., Mumtaz and Latif, 2017 ).

3.3. Examination of the findings from PBL-adapted interventions

3.3.1. interventional outcomes.

The results of individual studies were examined to explore the success of PBL adaptations for improving CT. Table 3 summarizes the CT development outcomes of each intervention. All the studies had positive outcomes with students showing increased CT. This indicates that the planful integration of CT elements into PBL was effective and necessary for enhancing students' CT which cannot be assured with PBL that do not have CT-oriented adaptations ( Lee et al., 2016 ).

Table 3 . The main findings of each study.

3.3.2. Positive findings

Although all of their studies reported positive outcomes in the development of critical thinking (CT), the depth of their research varied. Some studies documented general improvements in CT as a result of instructional interventions, while others reported enhancements in specific CT sub-skills. For instance, Silviarza et al. (2020) discovered that engaging students in debates and encouraging them to confirm information through research promoted critical thinking. Similarly, Aein (2018) found that challenging students to respond to difficulties posed by their peers with concealed features of disorders prompted them to think critically about current and potential health concerns. On the other hand, several researchers confirmed that problem-based learning (PBL) oriented toward CT improved CT sub-skills. Latif et al. (2018) , for example, reported that exposing students to challenging real-life situations encouraged them to conduct research based on their arguments, fostering the CT processes of analysis and interpretation. Carbogim et al. (2017) argued that pairing PBL with guided questions enhanced students' abilities to analyze, reason, and generate solutions for safe care action, demonstrating intellectual stimulation for CT.

Although critical thinking (CT) encompasses both critical thinking skills (CTSs) and critical thinking dispositions (CTDs), only three studies have specifically investigated the development of students' CTDs. Carbogim et al. (2018) employed the Portuguese version of the California Critical Thinking Disposition Inventory (CCTDI) to evaluate CTDs and discovered that integrating problem-based learning (PBL) with the Active Learning Model for Critical Thinking (ALMCT) influenced the acquisition of an analytical disposition. Hsu (2021) utilized Yeh and study of substitute teachers' professional knowledge (1999 ) Inventory of Critical-Thinking Disposition (ICTD) to determine that support for social contacts enhanced students' CT cognitive development. Lim (2020) applied Yoon (2004) self-report questionnaire to assess CTDs and found a correlation between CTDs and problem-solving abilities. These findings indicate that current research primarily concentrates on the development of CTS, suggesting that future studies should not overlook the development of CTD.

3.3.3. Success factors

An analysis of the key CT-related findings from each study, as presented in Table 3 , was conducted to explore the reasons for successful adaptation of problem-based learning (PBL). These findings were categorized into nine factors that contribute to the successful adaptation of PBL to be CT-oriented, as delineated in Table 4 . These factors comprise self-directed learning, CT-related activities, interaction, problem-solving skills, metacognitive activities, authentic learning, positive atmosphere, self-efficacy, and role of teacher. These factors can serve as the principles upon which CT-oriented PBL models should be based.

Table 4 . Classification of the main findings from the studies by theme.

As is shown in Table 4 , the nine principles are identified. The principle of self-directed learning refers to students accepting responsibility for their own learning and actively participating in the learning process ( Kamin et al., 2003 ). CT-related activities refer to the activities of students applying their learning to enhance CT, such as debating (e.g., Latif et al., 2018 ). Interaction refers to students: (1) being assigned to small groups and sharing their learning within the group and across groups ( Kamin et al., 2003 ; Fujinuma and Wendling, 2015 ; Silviarza et al., 2020 ); (2) sharing their knowledge with other students ( Orique and McCarthy, 2015 ); (3) peer discussions on how to solve problems ( Lim, 2020 ; Hidayati et al., 2022 ); (4) challenging each others' views ( Aein, 2018 ); and (5) debating with each other ( Rivas et al., 2022 ). CT propensity in PBL has also been found to be associated with problem-solving abilities and metacognitive skills ( Rodríguez et al., 2022 ). Authentic learning in PBL is key to developing students' CT skills which involve authentic real-world problem that contain diverse, difficult, and ill-structured answers ( Hidayati et al., 2022 ) and utilizing relevant real-world experiences to solve it ( Latif et al., 2018 ). The problems are authentic ( Hidayati et al., 2022 ), relevant to learners' real-world experiences ( Latif et al., 2018 ), and contain diverse, difficult, and ill-structured answers. There was scant scholarly attention given to the learning environment and self-efficacy even though a positive learning environment can assist students to enhance their CT ( Evendi et al., 2022 ). Likewise, self-efficacy has received scant scholarly attention. After simulated PBL, students' learning self-efficacy was positively linked to CT propensity and problem-solving ability ( Lim, 2020 ). Teachers had a significant impact on PBL students, particularly when they assumed the role of facilitator rather than merely transmitting information ( Hsu, 2021 ), were less the center of attention in the classroom ( Sendag and Odabasi, 2009 ), and provided examples that were appropriate for the students' level of learning.

The principles for PBL adaptations for CT development align with those of original PBL models but are optimized to maximize CT development. For instance, Carter et al. (2017) assert that students should be at the center of learning, Barrows (1986) posits that PBL problems should be ill-structured, and Yuan et al. (2008) contend that students should collaborate to solve problems. These principles are intrinsic to PBL. Consequently, the design of new PBL models to enhance CT should adhere to the fundamental principles or characteristics of PBL.

4. Conclusions

In this study, a systematic review was undertaken of published articles associated with PBL adaptations as educational interventions to improve students' CT skills and dispositions. Using the 20 articles that met the inclusion criteria and the PICo approach, this paper explored the methods used to adapt the PBL model to optimize CT development, examined the effectiveness of those models and explored the reasons why these adaptations were successful with the intent to fulfill the gap of the limited number of systematic reviews on adapting the original PBL model to be a more CT oriented model.

Five distinct categories of the strategies employed to adapt PBL were found: activities centered on CT development, incorporation of digital technologies, integration of alternative pedagogical approaches, utilization of CT-specific instruments, and combination of PBL with discipline-specific knowledge. These adaptations were found to be effective in augmenting students' CT skills and dispositions, although the methodologies employed for data collection and analysis varied across studies. Future research is warranted to investigate the potential of these adaptations in diverse educational contexts.

Nine factors that contribute to the successful adaptation of PBL to be more CT-oriented were identified. They are: self-directed learning, CT-related activities, interaction with peers and teachers, problem-solving skills, metacognitive activities, authentic learning, positive atmosphere, high self-efficacy, and supportive teachers. These principles are congruent with those of traditional PBL models but have been specifically designed to optimize CT development. Future research could explore the relative significance of each of these factors in fostering CT development and examine their interplay. Additionally, researchers could investigate the effective integration of these factors into PBL models across diverse educational contexts and disciplines.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Keywords: higher education, problem-based learning, critical thinking, educational intervention, systematic review, pedagogical adaption

Citation: Yu L and Zin ZM (2023) The critical thinking-oriented adaptations of problem-based learning models: a systematic review. Front. Educ. 8:1139987. doi: 10.3389/feduc.2023.1139987

Received: 08 January 2023; Accepted: 02 May 2023; Published: 24 May 2023.

Reviewed by:

Copyright © 2023 Yu and Zin. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Zuhana Mohamed Zin, zuhana.kl@utm.my

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Ways of thinking in STEM-based problem solving

Lyn d. english.

Queensland University of Technology, Brisbane, Australia

Associated Data

The data sets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

This article proposes an interconnected framework, Ways of thinking in STEM-based Problem Solving , which addresses cognitive processes that facilitate learning, problem solving, and interdisciplinary concept development. The framework comprises critical thinking, incorporating critical mathematical modelling and philosophical inquiry, systems thinking, and design-based thinking, which collectively contribute to adaptive and innovative thinking. It is argued that the pinnacle of this framework is learning innovation, involving the generation of powerful disciplinary knowledge and thinking processes that can be applied to subsequent problem challenges. Consideration is first given to STEM-based problem solving with a focus on mathematics. Mathematical and STEM-based problems are viewed here as goal-directed, multifaceted experiences that (1) demand core, facilitative ways of thinking, (2) require the development of productive and adaptive ways to navigate complexity, (3) enable multiple approaches and practices, (4) recruit interdisciplinary solution processes, and (5) facilitate the growth of learning innovation. The nature, role, and contributions of each way of thinking in STEM-based problem solving and learning are then explored, with their interactions highlighted. Examples from classroom-based research are presented, together with teaching implications.

Introduction

With the prevailing emphasis on integrated STEM education, the power of mathematical problem solving has been downplayed. Over two decades we have witnessed a decline in research on mathematical problem solving and thinking, with more questions than answers emerging (English & Gainsburg, 2016 ; Lester & Cai, 2016 ). This is of major concern, especially since work and non-work life increasingly call for resources beyond “textbook” problem solving (Chin et al., 2019 ; Krause et al., 2021 ). Such changing demands could not have been more starkly exposed than in the recent COVID 19 crisis, where mathematics played a crucial role in public and personal discourse, in describing and modelling current and potential scenarios, and in explaining and justifying societal regulations and restrictions. As Krause et al. ( 2021 ) highlighted, “No mathematical task we can create could be a richer application of mathematics than this real situation” (p. 88).

Modelling and statistical analyses that led the search for strategies to “flatten the curve” with minimal social or economic detriment were prominent in the media (Rhodes & Lancaster, 2020 ; Rhodes et al., 2020 ). As nations strive to rebuild their economies including grappling with crippling energy costs, advanced modelling again plays a key role (Aviso et al., 2022 ; Oxford Economics, 2022 ; Teng et al., 2022 ). Unfortunately, the gap between the mathematical modelling applied during the pandemic and how the public interpreted the models has been “palpable and evident” (Aguilar & Castaneda, 2021 ). Sadly, as Di Martino (Krause et al., 2021 ) pointed out regarding his nation:

People’s reactions in this pandemic underlined the spread of a widely negative attitude toward mathematics among the adult population in Italy. We have witnessed the proliferation of strange, unscientific, and dangerous theories but also the risk of refusing to approach facts that involve math and the resulting dependence to fully rely on others when mathematics is used to justify decisions. Also, on this occasion many people showed their own fear of math and their rejection of mathematical arguments as relevant factors in justification (p. 93).

This heightened visibility of mathematics in society coupled with a general lack of mathematical literacy sparked major questions about the repercussions for education and research (Bakker & Wagner, 2020 ; Kollosche & Meyerhöfer, 2021 ). One such repercussion is the need to reconsider perspectives on STEM-based problem solving and how different ways of thinking can enhance or hinder solutions. With reference to engineering education, Dalal et al. ( 2021 ) indicated how numerous calls for a focus on ways of thinking have largely been taken for granted or at least treated at a superficial level. As these authors pointed out, while perceived as a theoretical concept, ways of thinking “can and should be used in practice as a structure for solution-oriented outlooks and innovation” (p. 109).

Given the above points, I propose an interconnected framework, Ways of thinking in STEM-based Problem Solving (Fig.  1 ), which addresses cognitive processes that facilitate learning, problem solving, decision-making, and interdisciplinary concept development (cf. Slavit et al., 2021 ). The framework comprises critical thinking (including critical mathematical modelling and philosophical inquiry), systems thinking, and design-based thinking. Collectively, these thinking skills contribute to adaptive and innovative thinking (McKenna, 2014 ) and ultimately lead to the development of learning innovation (Sect.  3.4 ; English, 2018 ).

These thinking skills have been chosen because of their potential to enhance STEM-based problem solving and interdisciplinary concept development (English et al., 2020 ; Park et al., 2018 ; Slavit et al., 2021 ). Highlighting these ways of thinking, however, is not denying the importance of other thinking skills such as creativity, which is incorporated within the adaptive and innovative thinking component of the proposed framework (Fig.  1 ), and is considered multidimensional in nature (OECD, 2022 ). Other key skills such as communication and collaboration (Stehle & Peters-Burton, 2019 ) are acknowledged but not explored here.

In line with Dalal et al. ( 2021 ), I consider the proposed ways of thinking as providing an organisational structure both individually and interactively when enacted in practice—notwithstanding the contextual and instructional influences that can have an impact here (Slavit et al., 2022 ). Prior to exploring these ideas, I consider STEM-based problem solving with a focus on mathematics.

STEM-based problem solving: a focus on mathematics

Within our STEM-intensive society, we face significant challenges in promoting STEM education from the earliest grades while also maintaining the integrity of the individual disciplines (Tytler, 2016 ). With the increasing need for STEM skills across multiple workforce domains, contrasted with difficulties in STEM implementation in many schools (e.g., Dong et al., 2020 ), the urgency to advance STEM education has never been greater. With the massive disruption caused by COVID-19, coupled with problematic international relations, our school students’ futures have become even more uncertain—we cannot ignore the rapid changes that will continue to impact their lives. Unlike business and industry, where disruption creates a “force-to-innovate” approach (Crittenden, 2017 , p. 14), much of school education seems oblivious to preparing students for these disruptive forces or at least are restricted in doing so by set curricula.

Preparing our students for an increasingly uncertain and complex future requires rethinking the nature of their learning experiences, in particular, the need for more relevant and innovative problems that are challenging but manageable, and importantly, facilitate adaptive learning and problem solving (McKenna, 2014 ). A failure to provide such opportunities may have detrimental effects on young students’ learning and their future achievements (Engel et al., 2016 ). Despite mathematics being cited as the core of STEM education and foundational to the other disciplines (e.g., Larson, 2017 ; Roberts et al., 2022 ; Shaughnessy, 2013 ), it is frequently ignored in integrated STEM activities (English, 2016 ; Maass et al., 2019 ; Mayes, 2019 ; Shaughnessy, 2013 ). For example, quantitative reasoning, which is critical to integrated STEM problem solving, is frequently “misrepresented, underdeveloped, and ignored in STEM classrooms” (Mayes, 2019, p. 113). Likewise, Tytler ( 2016 ) warned that there needs to be an explicit focus on the mathematical concepts and thinking processes that arise in STEM activities. Without this focus, STEM programs run the risk of reducing the valuable contributions of mathematical thinking. If children fail to see meaningful links between their learning in mathematics and the other STEM domains, they can lose interest not only in mathematics but also in the other disciplines (Kelley & Knowles, 2016 ).

Traditional notions of mathematical problem solving (e.g., Charles, 1985 ) are now quite inadequate when applied to our current world. At a time of increasing creative disruption, it is essential for mathematical problem solvers to be adaptive in dealing with unforeseen local, national, and international problems. Increasingly, STEM-based problems in the real world encompass more than just disciplinary content and practices. While not denying the essential nature of these components, issues pertaining to cultural, social, political, and ethical dimensions (Kollosche & Meyerhöfer, 2021 ; Pheasants, 2020) can also impact the solution process, necessitating the application of appropriate thinking skills. As Pheasants stressed, “If STEM education is to prepare students to grapple with complex problems in the real world, then more attention ought to be given to approaches that are inclusive of the non-STEM dimensions that exist in those problems.”

In light of the above arguments, I view mathematical and STEM-based problems as goal-directed experiences that (1) demand STEM-relevant ways of thinking, (2) require the development of productive and adaptive ways to navigate complexity, (3) enable multiple approaches and practices (Roberts et al., 2022 ), (4) recruit interdisciplinary solution processes, and (5) facilitate growth of learning innovation for all students regardless of their background (English, 2018 ). In contrast to traditional expectations, such problems need to embody affordances that facilitate learning innovation, where all students can move beyond their existing competence in standard problem solving and be challenged to generate new knowledge in solving unanticipated problems. Even students who achieve average results on standardised tests display conceptual understanding and advanced mathematical thinking not normally seen in the classroom—especially when current common practices emphasise number skills at the expense of problem solving and reasoning with numbers (Kazemi, 2020 ).

Limited attention, however, has been paid to how problem experiences can be developed that press beyond basic content knowledge (Anderson, 2014; Li, Schoenfeld et al., 2019), encompass the STEM disciplines, and develop important ways of thinking. In their recent article, Slavit et al. ( 2021 ) argued that STEM education should be “grounded in our knowledge of how students think in STEM-focused learning environments” (p. 1), and that fostering twenty-first-century skills is essential. Yet, as these authors highlighted, there is not much research on STEM ways of thinking, with even fewer theoretical perspectives and frameworks on which to draw. In the next section, I consider these ways of thinking, defined in Table ​ Table1, 1 , and provide examples of their applications to STEM-based problem solving.

Critical thinking

Although long recognised as a significant process in a range of fields, research on critical thinking in education, especially in primary education, has been limited (Aktoprak & Hursen, 2022 ). Critical thinking has long been associated with mathematical reasoning and problem solving, but their association remains under-theorized (Jablonka, 2020 ). Likewise, connections between critical thinking and design thinking have had limited attention largely due to their shared conceptual structures not being articulated (Ericson, 2022 ). As a twenty-first century skill, critical thinking is increasingly recognised as essential in STEM and mathematics education (Kollosche & Meyerhöfer, 2021 ) but is sadly lacking in many school curricula (Braund, 2021 ). As applied to STEM-based problem solving, critical thinking builds on inquiry skills (Nichols et al., 2019 ) and entails evaluating and judging problem situations including statements, claims, and propositions made, analysing arguments, inferring, and reflecting on solution approaches and conclusions drawn. Although critical thinking can contribute significantly to each of the other ways of thinking, its application is often neglected. For example, critical thinking is increasingly needed in design and design thinking, which play a key role in product development, environmental projects, and even in forms of social interaction (as discussed in Sect.  3.3 ; Ericson, 2022 ).

Critical mathematical modelling

One rich source of problem experiences that foster critical thinking is that of modelling. The diverse field of mathematical modelling has long been prominent in the secondary years (e.g., Ärlebäck & Doerr, 2018 ) but remains under-researched in the primary years, especially in relation to its everyday applications. Effective engagement with social, political, and environmental issues through modelling and statistics demands critical thinking, yet such aspects are not often considered in school curricula (Jablonka, 2020 ). This is of particular concern, given the pressing need to tackle such issues in today’s world.

As noted in several publications, the interdisciplinary nature of mathematical modelling makes it ideal for STEM-based problem solving (English, 2016 ; Maass et al., 2019 ; Zawojewski et al., 2008 ). Numerous definitions of models and modelling exist in the literature (e.g., Blum & Leiss, 2007 ; Brady et al., 2015 ). For this article, modelling involves developing conceptual innovations in response to real-world needs; effective modelling requires moving beyond the conventional ways of thinking applied in typical school problems (Lesh et al., 2013 ) to include contextual and critical analysis.

Much has been written about the role of modelling during COVID-19. Mathematical models played a major role in grappling with COVID 19, but their projections were a source of controversy (Rhodes & Lancaster, 2020 ). There seems little appreciation of the critical nature of mathematical models in society (Barbosa, 2006 ) and how assumptions in the modelling process can sway decisions. STEM-based problem solving needs to incorporate not just modelling itself, but also critical mathematical modelling. Critiquing what a model yields, and what is learned, is of increasing social importance (Aguilar & Castaneda, 2021 ; Barbosa, 2006 ). Indeed, as Braund ( 2021 ) illustrated, the Covid-19 pandemic has revealed the urgent need for “critical STEM literacy” (p. 339)—an awareness of the complex and problematic interactions of STEM and politics, and a knowledge and understanding of the underlying STEM concepts and representations is essential:

There are two imperatives that emerge: first, that there is sufficient STEM literacy to negotiate the complex COVID-19 information landscape to enable personal decision taking and second, that this is accompanied by a degree of criticality so that politicians and experts are called to account (Braund, 2021 , p. 339).

Kollosche ( 2021 ) shed further light on the lack of critical thinking in the media’s reporting on COVID, with his argument that “most newspaper reports were effective in creating the problems” because of their focus on ideal forms of mathematical concepts and modelling, without discussing the assumptions and methods behind the reported data. Of concern is that “mass media still fail to present scientific models and results in a way that allows for mathematical reflection and a critical evaluation of such information by citizens.”

Modelling experiences that draw on students’ cultural and community contexts (Anhalt et al., 2018 ; English, 2021a , 2021b ; Turner et al., 2009 ) provide rich opportunities for critical thinking from a citizen’s perspective. Such opportunities can also assist students in appreciating that mathematics is not merely a means of calculating answers but is also a vehicle for social justice, where critical thinking plays a key role (Cirillo et al., 2016 ; Greer et al., 2007 ). In their studies of critical thinking in cultural and community contexts, Turner and her colleagues (Turner et al., 2009 , 2021 , 2022 ) explored culturally responsive, community-based approaches to mathematical modelling with elementary teachers and students. Using a range of authentic modelling contexts, Turner and her colleagues illustrated how students’ modelling processes generated a number of issues that required them to think critically about their lives and their lives within their community. In one activity, students were applying design thinking and processes as they redesigned their local park. They generated, for example, mathematical models to estimate how long children would have to wait to use the swings—this informed their decision that the park did not meet the needs of the community. This community-based modelling highlighted “ongoing negotiation between students’ experiences and intentions related to the community park, the constraints of the actual context, and the mathematical issues that arose” (Turner et al., 2009 , p. 148).

Another example of modelling involving critical thinking in cultural and community contexts was implemented in a sixth-grade Cyprus classroom. Students were required to develop a model for their country to purchase water supplies from a choice of nearby nations (English & Mousoulides, 2011 ). Students were to consider travel distances, water price, available supply per week, oil tanker capacity, costs of water and oil, and quality of the port facilities in the neighbouring countries. The targeted model had to select the best option not only for the present but also for the future. Students’ models ranged from a basic form, where port facilities and water supply were ignored, to more sophisticated models, where all factors were integrated, with carbon emissions also considered. One of the student groups who took into account environmental factors commented, “It would be better for the country to spend a little more money and reduce oil consumption. And there are other environmental issues, like pollution of the Mediterranean Sea.” The more sophisticated models reflected systems thinking (Sect.  3.2 ), where the impact of partial factors such as oil consumption on the whole domain (ocean ecosystems and community) was also considered.

Philosophical Inquiry

One underrepresented means of fostering critical thinking in mathematical and STEM-based problem solving is through philosophical inquiry (Calvert et al., 2017 ; English, 2013 , 2022 ; Kennedy, 2012 ; Mukhopadhyay & Greer, 2007 ). Such inquiry encourages a range of thinking skills in identifying hidden assumptions, determining alternative courses of action, and reflecting on conclusions drawn and claims made. Several studies have shown how engaging children in communities of philosophical inquiry nurtures critical thinking dispositions, which become both a goal and a method (Bezençon, 2020 ; Daniel et al., 2017 ; Lipman, 2003 , 2008 ). At the same time, philosophical inquiry can lead to “conceptual deepening” (Bezençon, 2017), where analysis of mathematical and related STEM concepts as they apply beyond the classroom can be fostered. Given the increased societal awareness of mathematics and STEM in recent years, philosophical inquiry can be a powerful tool in enhancing students’ understanding and appreciation of how these disciplines shape societies. At the same time, philosophical inquiry can stimulate consideration of ethical issues in the applications of these disciplines (Bezençon, 2020 ). For example, Mukhopadhyay and Greer ( 2007 ) indicated how mathematics education should “convey the complexity of mathematical modeling social phenomena and a sense of what demarcates questions that can be answered by empirical evidence from those that depend on value systems and world-views” (p. 186).

A comprehensive review by O’Reilly et al. ( 2022 ) identified pedagogical approaches to scaffolding early critical thinking skills including inquiry-based teaching using classroom dialogue or questioning techniques. Such techniques include philosophical inquiry and encouraging children to construct, share, and justify their ideas regarding a task or investigation. Other opportunities for philosophical inquiry include group problem solving, peer sharing of created models, and facilitating critical and constructive peer feedback. For example, Gallagher and Jones ( 2021 ) reported on integrating mathematical modelling and economics, where beginning teachers were presented with a task involving a problematic community issue following a school shooting. In such cases, numerous courses of action are typically proposed for addressing the problem. Not surprisingly, various community opinions exist on such proposals, giving rise to valuable contexts for philosophical inquiry and critical modelling, where data and their sources are carefully analysed. With the escalation of statistical data from the mass media, it is imperative to commence the foundations of critical and philosophical thinking early. Students’ skills in asking critical questions as they work with data in constructing and improving a model, reflect on what their models convey, consider consequences of their models, and justify and communicate their conclusions require nurturing throughout school (Gibbs & Young Park, 2022 ).

Systems thinking

Systems thinking cuts across the STEM disciplines as well as many other fields outside education. It is considered a key component of “critical thinking and problem solving” in 21st Century Learning (P21, 2015 ) and is often cited as a “habit of mind” in engineering education (e.g., Lippard et al., 2018 ; Lucas et al., 2014 ). Numerous definitions exist for systems thinking (e.g., Bielik et al., 2022 ; Damelin et al., 2017 ; Jacobson & Wilenski, 2022 ), with Bielik et al. ( 2022 ) identifying such thinking as the ability to “consider the system boundaries, the components of the system, the interactions between system components and between different subsystems, and emergent properties and behaviour of the system” (p. 219). In more basic terms, Shin et al. ( 2022 ) refer to systems thinking as “the ability to understand a problem or phenomenon as a system of interacting elements that produces emergent behavior” (p. 936).

Systems thinking interacts with the other thinking forms including those displayed in Fig.  1 , as well as computational thinking (Shin et al., 2022), critical thinking (Curwin et al., 2018 ) and mathematical thinking more broadly (Baioa & Carreira, 2022 ). Systems thinking is considered especially important in conceptualizing a problematic situation within a larger context and in perceiving problems in new and different ways (Stroh, 2018 ). Of special relevance to today’s world is the realisation that perfect solutions do not exist and the choices one makes in applying systems thinking will impact on other parts of the system (Meadows, 2008 ). What is often not considered in today’s complex societies—at least not to the extent required—is that we live in a world of intrinsically linked systems, where disruption in one part will reverberate in others. We see so many instances where particular courses of action are advocated or mandated in societal systems, while the impact on sub-components is perilously ignored. Examples are evident in many nations’ responses to COVID-19, where escalating lockdowns impacted economies and communities, whose demands had to be balanced against purely epidemiological factors. The reverberations of such actions stretch far and wide over long periods. Likewise, the various impacts of current climate actions are frequently ignored, such as how the construction of vast areas of renewable resources (e.g., wind turbines) can have deleterious effects on the surrounding environments including wildlife.

Despite its centrality across the STEM domains, systems thinking is almost absent from mathematics education (Curwin et al., 2018 ). This is despite claims by many researchers that modelling, systems thinking, and associated thinking processes should be significant components of students’ education (Bielik et al., 2022 ; Jacobson & Wilenski, 2022 ). Indeed, systems thinking is featured prominently in the US A Framework for K-12 Science Education (NRC, 2012 ) and the Next Generation Science Standards (NGSS Lead States, 2013 ), and has received considerable attention in science education (e.g., Borge, 2016 ; Hmelo-Silver et al., 2017 ; York et al., 2019 ) and engineering education (e.g., Lippard & Riley, 2018 ; Litzinger, 2016 ).

Given the complexity of systems thinking in today’s world, and the diverse ways in which it is applied, students require opportunities to experience how systems thinking can interact with other forms such as design thinking and critical thinking (Curwin et al., 2018 ; Shin et al., 2022). Such interactions occur in many popular STEM investigations including one in which fifth-grade students designed, constructed, and experimented with a loaded paper plane (paper clips added) in determining how load impacts on the distance travelled (English, 2021b ). Students observed that changing one design feature (e.g., wingspan or load position) unsettles some other features (e.g., fuselage depth decreases wingspan). The investigation yielded an appreciation of the intricacy of interactions among a system’s components, and their scarcely predictable mutual effects.

Other studies have revealed how very young children can engage in basic systems thinking within STEM contexts. For example, Feriver et al. ( 2019 ) administered a story reading session to individual 4- to 6-year-old children in preschools in Turkey and Germany, and then followed this with individual semi-structured interviews about the story. The reading session was based on the story book, “The Water Hole” (Base, 2001 ), which draws on basic concepts of systems within an ecosystem context. Their study found the young children to have some complex understanding of systems thinking in terms of detecting obvious gradual changes and two-step domino and/or multiple one-way causalities, as well as describing the behaviour of a balancing loop (corrective actions that try to reduce the gap between a desired level or goal and the actual lever, such as temperature and plant growth). However, the children understandably experienced difficulties in several areas, in which even adults have problems. For example, detecting a reinforcing loop, identifying unintended consequences, detecting hidden components and processes, adopting a multi-dimensional perspective, and predicting how a system would behave in the future were problematic for them. In another study, Gillmeister ( 2017 ) showed how preschool children have a more complex understanding of systems thinking than previously claimed. Their ability to utilize simple systems thinking tools, such as stock-flow maps, feedback loops and behaviour over time graphs, was evident.

Although the research has not been extensive, current findings indicate how we might capitalise on the seeds of early systems thinking across the STEM fields. With the pervasive nature of systems thinking, it is argued that its connections to other forms of thinking across STEM should be nurtured (cf., Svensson, 2022 ). This includes links to design-based thinking where designed products, for example, operate “within broader systems and systems of systems” (Buchanan, 2019 ).

Design-based thinking and STEM-based problem solving

Design-based thinking plays a major role in complex problem solving, yet its contribution to mathematics learning has been largely ignored, especially at the primary levels. Design is central in technology and engineering practice (English et al., 2020 ; Guzey et al., 2019 ), from bridge construction through to the development of medical tools. Design contributes to all phases of problem solving and drives students toward innovative rather than predetermined outcomes (Goldman & Zielezinski, 2016 ). As applied to STEM education, design thinking is generally viewed as a set of iterative processes of understanding a problem and developing an appropriate solution. It includes problem scoping, idea generation, systems thinking, designing and creating, testing and reflecting, redesigning and recreating, and communicating. Both learning about design and learning through design can help students develop more informed analytical approaches to mathematical and STEM-based problem solving (English et al., 2020 ; Strimel et al., 2018 ).

Learning about design in solving complex problems emphasises design thinking processes per se, that is, students learn about design itself. Design thinking as a means for learning about design is not as prevalent in integrated STEM education. Although learning through and about design should not be divorced during problem solving (van Breukelen et al., 2017 ), one learning goal can take precedence over the other. Both require greater attention, especially in today’s design-focused world (Tornroth & Wikberg Nilsson, 2022 ).

A plurality of solutions of varying levels of sophistication is possible in applying design thinking processes, so students from different achievement levels can devise solutions (Goldman & Kabayadondo, 2017 )—and research suggests that lower-achieving students benefit most (Chin et al., 2019 ). The question of how best to develop design learning across grades K-12, however, has not received adequate attention. This is perhaps not surprising given that comparatively few studies have investigated the design thinking of grades 6–12 and even fewer across the elementary years (Kelley & Sung, 2017 ; Strimel et al., 2018 ).

Also overlooked is how design-based thinking can foster concept development, that is, how it can foster “learning while designing”, or generative learning (English et al., 2020 ). Design-based thinking provides natural opportunities to develop understanding of the required STEM concepts (Hjalmarson et al., 2020 ). As these authors pointed out, when students create designs, they represent models of their thinking. When students have to express their conceptual understanding in the form of design, such as an engineering designed product, their knowledge (e.g., of different material properties) is tested. Studies have revealed such learning occurs when elementary and middle school students design and construct various physical artifacts. For example, in a fifth-grade study involving designing and building an optical instrument that enabled one to see around corners, King and English ( 2017 ) observed how students applied and enriched their understanding of scientific concepts of light and how it travels through a system, together with their mathematical knowledge of geometric properties, angles and measurement.

In a study in the secondary grades (Langman et al. ( 2019 ), student groups completed modules that included a model-eliciting activity (Lesh & Zawojewski, 2007 ) involving iterative design thinking processes. Students were to interpret, assess, and compare images of blood vessel networks grown in scaffolds, develop a procedure or tool for measuring (or scoring) this vessel growth, and demonstrate how to apply their procedure to the images, as well as to any image of a blood vessel network. The results showed how students designed a range of mathematical models of varying levels of sophistication to evaluate the quality of blood vessel networks and developed a knowledge of angiogenesis in doing so.

In another study implemented in a 6th-grade classroom, students were involved in both learning about and learning through design in creating a new sustainable town with the goal of at least 50% renewable energy sources. The students were also engaged in systems thinking, as well as critical thinking, as they planned, developed, and critically analysed the layout and interactions of different components of their town system (e.g., where to place renewable energy sources to minimise impact on the residences and recreational areas; where to situate essential services to reach different town components). Students also had to consider the budgetary constraints in their town designs. Their learning about design was apparent in their iterative processes of problem scoping, idea generation and modification, balancing of benefits and trade-offs (dealing with system subcomponents), critical reflections on their designs, and improvements of the overall town design. Learning though design was evident as students displayed content knowledge pertaining to renewable energy and community needs, applied spatial reasoning in positioning town features, and considered budgetary constraints in reaching their “best” design.

Engineering design processes form a significant component of design thinking and learning, with foundational links across the STEM disciplines including mathematical modelling. Engineering design-based problems help students appreciate how they can apply different ideas and approaches from the STEM disciplines, with more than one outcome possible (Guzey et al., 2019 ). Such design thinking engages students in interpreting problems, developing initial design ideas, selecting and testing a promising design, analysing results from their prototype solution, and revising to improve outcomes.

It is of concern that limited attention has been devoted to engineering design-based thinking in mathematics and the other STEM disciplines in the primary grades. This is despite research indicating how very young children can engage in design-based thinking when provided with appropriate opportunities (e.g., Cunningham, 2018 ; Elkin et al., 2018 ). Elkin et al., for example, used robotics in early childhood classrooms to introduce foundational engineering design thinking processes. Their study illustrated how these young learners used engineering design journals and engaged in design thinking as they engineered creative solutions to challenging problems presented to them. It seems somewhat paradoxical that foundational engineering design thinking is a natural part of young children’s inquiry about their world, yet this important component has been largely ignored in these informative years.

In sum, design-based thinking is a powerful and integrative tool for mathematical and STEM-based problem solving and requires greater focus in school curricula. Both learning about and through design have the potential to improve learning and problem solving well beyond the school years (Chin et al., 2019 ). At the same time, design-based thinking, together with the other ways of thinking, can contribute significantly to learning innovation (English, 2018 ).

Adaptive and innovative thinking for learning innovation

Disruption is rapidly becoming the norm in almost all spheres of life. The recent national and international upheavals have further stimulated disruptive thinking (or disruptive innovation), where perspectives on commonly accepted (and often inefficient) solutions to problems are rejected for more innovative approaches and products. Given the pressing need for problem solvers capable of developing new and adaptable knowledge, rather than applying limited simplistic procedures or strategies, we need to foster what I term, learning innovation (English, 2018 ; Fig.  2 ). Such learning builds on core content to generate more powerful disciplinary knowledge and thinking processes that can, in turn, be adapted and applied to solving subsequent challenging problems.

Learning innovation

Figure  2 (adapted from McKenna, 2014 ) illustrates how learning innovation can be fostered through the growth of mathematical and STEM knowledge, together with STEM ways of thinking. The optimal adaptability corridor represents the growth of mathematical and STEM-based problem solving from novice to adaptable solver . Adaptable problem solvers (Hatano & Oura, 2003 ) have developed the flexibility, curiosity, and creativity to tackle novel problems—skills that are needed in jobs of the future (Denning & Noray, 2020 ; OECD, 2019 ). Without the disciplinary knowledge, ways of thinking, and engagement in challenging but approachable problems, a student risks remaining merely a routine problem solver—one who is skilled solely in applying previously taught procedures to solve sets of familiar well-worn problems, as typically encountered at school. Learning innovation remains a challenging and unresolved issue across curriculum domains and is proposed as central to dealing effectively with disruption.

Particularly rich experiences for developing learning innovation involve interdisciplinary modelling, incorporating critical mathematical modelling (e.g., Hallström and Schönborn, 2019 ; Lesh et al., 2013 ). As noted, a key feature of model-eliciting experiences is the affordances they provide all students to exhibit “extraordinary abilities to remember and transfer their tools to new situations” (Lesh et al., 2013 , p. 54). Modelling enables students to apply more sophisticated STEM concepts and generate solutions that extend beyond their usual classroom problems. Such experiences require different ways of thinking in problem solving as they deal with, for example, conflicting constraints and trade-offs, alternative paths to follow, and various tools and representations to utilise. In essence, interdisciplinary modelling may be regarded as a way of creating STEM concepts, with modeling and concept development being highly interdependent and mutually supportive (cf., Lesh & Caylor, 2007 ).

Concluding points

The ill-defined problems of today, coupled with unexpected disruptions across all walks of life, demand advanced problem-solving by all citizens. The need to update outmoded forms of problem solving, which fail to take into account increasing global challenges, has never been greater (Cowin, 2021 ). The ways-of-thinking framework has been proposed as a powerful means of enhancing problem-solving skills for dealing with today’s unprecedented game-changers. Specifically, critical thinking (including critical mathematical modelling and philosophical inquiry), systems thinking, and design-based thinking are advanced as collectively contributing to the adaptive and innovative skills required for problem success. It is argued that the pinnacle of this framework is learning innovation, which can be within reach of all students. Fostering students’ agency for developing learning innovation is paramount if they are to take some control of their own problem solving and learning (English, 2018 ; Gadanidis et al., 2016 ; Roberts et al., 2022 ).

Establishing a culture of empowerment and equity, with an asset-based approach, where the strengths of all students are recognised, can empower students as learners and achievers in an increasingly uncertain world (Celedón-Pattichis et al., 2018 ). Teacher actions that encourage students to express their ideas, together with a program of future-oriented mathematical and STEM-based problems, can nurture students’ problem-solving confidence and dispositions (Goldman & Zielezinski, 2016 ; Roberts et al., 2022 ). In particular, mathematical and STEM-based modelling has been advocated as a rich means of developing multiple ways of thinking that foster adaptive and innovative learners—learners with a propensity for developing new knowledge and skills, together with a willingness to tackle ill-defined problems of today and the future. Such propensity for dealing effectively with STEM-based problem solving is imperative, beginning in the earliest grades. The skills gained can thus be readily transferred across disciplines, and subsequently across career opportunities.

Acknowledgements

Sentiments expressed in this article have arisen from recent Australian Research Council grants # DP 220100303 and DP 150100120. Views expressed in this article are those of the author and not the Council.

Open Access funding enabled and organized by CAUL and its Member Institutions.

Data availability

Declarations.

There are no financial or non-financial interests that are directly or indirectly related to this submission.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Solutions Oriented: How To Cultivate A Results-Driven Mindset

• September 18, 2023
• HR Management

Table of Contents

Ah, the thrill of facing a problem head-on and emerging victorious! Every problem-solver, from a novice to a seasoned expert, knows this feeling. And if you’ve ever found yourself drowning in an issue, wondering why others seem to navigate it effortlessly, you might have noticed a common trait among them – they’re solutions oriented.

What does it mean to be “solutions or solution oriented person”? Is it just a modern-day jargon, or is there more to it? Picture this: Two people are stuck in a dense forest. The first one panics, thinking of all the wild animals, the cold night, and the uncertainty of getting out. The second one, while acknowledging these threats, starts thinking, “How can I climb a tree to see a way out?” or “Can I use the sun’s position to determine the direction?” The second person is a solutions oriented leader or solution oriented leader.

This mindset isn’t about denying problems or being unrealistically optimistic. It’s about focusing energy on: finding solutions, the right answers, learning, and adapting. It’s the difference between seeing a dead-end versus a detour. Being solutions oriented means constantly looking for avenues, even in seemingly impossible situations. It’s about resilience, innovation, and tenacity.

Solutions oriented means focusing on results, finding answers, no risks and relentlessly pursuing the best possible outcomes. Dive in to learn how to cultivate this mindset and succeed in any challenge.

In this guide, we’ll embark on an enlightening journey into the solution oriented mindset and other solution oriented approaches. We’ll delve deep into what it means to be solutions oriented, how you can cultivate this mindset, and the multifaceted benefits it brings to your personal and professional life. Whether you’re a young professional grappling with the challenges of the corporate world or a stay-at-home parent figuring out daily household conundrums, the solutions oriented mindset is your ally.

The world doesn’t stop throwing curveballs. What matters is how we catch them, or better yet, how we hit them back. So, tighten your belts, fellow traveler. By the end of this exploration, you’ll be armed with the tools, insights, and mindset to tackle any challenge that comes your way. Onward and upward!

Understanding A Solutions Oriented Approach

The term “solutions oriented organization” often pops up in corporate jargon, self-help books, and even casual conversations with business leader. But what does it truly encompass? Let’s dive deep into its essence and understand the fundamentals of this approach.

Defining “Solutions Oriented”:

Being solutions or solution oriented team goes beyond the simple act of solving problems. It’s an ingrained mindset, a holistic approach to challenges. Imagine life’s hurdles as a labyrinth. A solutions or solution oriented person doesn’t merely wander aimlessly, hoping for an exit. Instead, they meticulously study the maze, anticipate dead ends, and strategize their route.

Shift From Problem Focus To Solution Focus:

It’s easy for leaders to get trapped in a whirlwind of problems. They’re daunting, often overwhelming, and can cloud our judgment. However, the essence of a problem focused, solutions oriented approach is a steadfast, focused focus on the ‘how’ rather than the ‘why’. While understanding the root of the organization or problem is crucial, dwelling on it without forward momentum serves no purpose. The energy spent lamenting on a problem is better used crafting solutions.

Embrace The Learning Curve:

Every challenge you face is cloaked in lessons. When adopting a solutions oriented mindset, one understands that no challenge is void of value. It’s not about how many times you fall but how you rise after every fall, absorbing the lessons and ensuring the stumbles refine, not define you.

The Proactive vs. Reactive Dichotomy:

A reactive mindset waits for problems to arise and then scrambles to address them. It’s often associated with panic, hasty decisions, and short-term fixes. On the other hand, a proactive, solutions oriented mindset anticipates challenges and prepares for them. It doesn’t merely put out fires; it prevents them.

Continuous Evolution:

The world is in perpetual motion. What worked yesterday may be obsolete today. Being a solutions oriented leader means constantly updating your leadership toolkit, learning, unlearning, and relearning. It’s a commitment to evolution, ensuring you’re always equipped with the best strategies to tackle contemporary leadership challenges.

Key Points:

“Solutions Oriented” is a holistic, proactive approach to challenges.

Focus energy on crafting solutions rather than dwelling on problems.

Every challenge presents opportunities to learn and grow.

Anticipate and prepare for challenges instead of merely reacting to them.

Commit to continuous evolution to remain adept at handling new challenges.

Cultivating A Solutions Oriented Mindset

It’s crucial to recognize that a solutions oriented mindset isn’t a switch you can simply flip on. It’s a garden you cultivate, nurturing it with the right habits, perspectives, and environment. As you grow this solution oriented mindset, not only do you become adept at addressing challenges, but you also evolve as an individual. Let’s uncover the steps and practices to cultivate this empowering mindset.

Stay Curious – The Power of ‘Why’ and ‘How’:

Remember as a child, when every discovery was accompanied by a barrage of ‘whys’ and ‘hows’? This innate curiosity is the foundation of a solutions oriented approach. Instead of accepting things at face value, delve deeper. Whether you’re facing a problem or learning something new, always question the status quo. The quest for understanding drives innovation.

Accept Failures Graciously – Lessons in Disguise:

We’ve been conditioned to view failures as setbacks. In truth, they are invaluable lessons. Every misstep brings with it insights that textbooks and tutorials often can’t offer. By embracing failures, analyzing what went wrong, and iterating based on those insights, you fine-tune your approach and inch closer to effective business solutions .

Surround Yourself With Like-Minded People – Environment Matters:

Your environment, both physical and social, plays a pivotal role in shaping your mindset. Surrounding yourself with solutions oriented individuals ensures that you’re continually inspired, challenged, and supported. Their constructive feedback, diverse perspectives, and shared drive for solutions can act as catalysts for your growth.

Setting Clear Goals – The North Star:

A solutions oriented mindset thrives on clarity. When you have clear goals, it becomes easier to chart a path to achieve them and find solutions aligned with those objectives. These goals act as your North Star, guiding you through challenges and helping you maintain focus on what truly matters.

Develop Resilience – The Art of Bouncing Back:

Resilience is the bedrock of a solutions oriented mindset. It’s not about avoiding failures, but about how quickly and effectively you can bounce back from them. Cultivating resilience involves embracing discomfort, practicing patience, and understanding that the path to solutions will often be riddled with obstacles. Instead of being disheartened, view them as parts of the journey, honing your skills and resolve.

Continuous Learning – Keeping the Toolbox Updated:

In a rapidly changing world, resting on one’s laurels is a recipe for obsolescence. Adopt a learner’s mindset. Attend workshops, read books, participate in discussions, and always seek to expand your horizons. The more tools (knowledge and skills) you have in your toolbox, the better equipped you are to devise innovative solutions.

Nurture innate curiosity; question and understand the ‘why’ and ‘how’.

Embrace failures as rich learning experiences.

Your environment, including the people around you, can either foster or hinder a solutions oriented approach.

Set clear , actionable goals to guide your problem-solving journey.

Build resilience; it’s the backbone of facing and overcoming challenges.

Dedicate yourself to continuous learning to stay adaptive and innovative.

Software Tools To Boost Your Solutions Oriented Approach

In today’s digital age, it’s not just about having the right mindset but also about harnessing the right tools. While a solutions oriented approach is about your mental and emotional faculties, certain software tools can amplify your capacity to solve problems and create impactful solutions. These tools can help streamline processes, organize thoughts, and drive collaboration. Let’s take a closer look at some of these indispensable tools.

Trello – Visualize and Organize Your Ideas:

Trello provides a visual way to organize tasks, ideas, and projects. It’s based on the Kanban methodology and allows users to create boards, lists, and cards to prioritize and categorize tasks. For someone aiming to adopt a solutions oriented mindset, it’s vital to have clarity, and Trello offers just that. By visually mapping out tasks, one can identify bottlenecks, streamline processes, and foster collaboration.

MindMeister – Mapping Your Thoughts:

MindMeister is a collaborative mind-mapping tool. It’s fantastic for brainstorming sessions, organizing thoughts, and visualizing complex concepts. Whether you’re tackling a personal project or a business challenge, this tool helps lay out all facets of a problem, enabling a comprehensive solutions oriented approach.

Evernote – Centralized Note-Taking:

With Evernote , you can keep all your ideas, research, and notes in one centralized place. Its robust search capabilities ensure that you never lose track of crucial information. Being solutions and solution oriented leader often means collating information from varied sources, and Evernote helps you manage this seamlessly.

Slack – Enhancing Collaboration:

Slack is more than just a messaging app; it’s a hub for teamwork. For solutions to truly shine, collaboration is key. Slack provides channels for different projects, ensuring that conversations are organized and accessible. Integrated file sharing, third-party app integrations, and the ability to quickly search across conversations make it a powerhouse for collaborative problem solving.

Coursera – Continuous Learning and Skill Development:

Knowledge is power, especially in a solutions oriented approach. Coursera offers a plethora of courses from universities and institutions around the world, covering diverse topics. From critical thinking to technical skills, continuous learning becomes effortless with such a platform.

Asana – Task and Project Management:

For larger projects, especially in team settings, Asana shines bright. With a clean interface and robust features, it’s perfect for tracking team progress, delegating tasks, and ensuring that every team member is aligned towards a solution.

Trello aids in visualizing tasks, thereby bringing clarity to the problem-solving process.

MindMeister is invaluable for brainstorming and dissecting complex challenges.

Evernote ensures all your notes and research are organized and easily accessible.

Slack fosters effective communication, making collaborative problem-solving a breeze.

Coursera empowers individuals with knowledge, a cornerstone of the solutions oriented approach.

Asana is perfect for managing larger projects, ensuring everyone is in sync and geared towards a solution.

The Perks Of Being Solutions Oriented

Opting for a solutions oriented approach isn’t just a productive move; it’s transformative. While it’s evident that this approach offers an effective way to navigate challenges, the perks of a solution oriented leader and team extend beyond just problem-solving. They permeate various aspects of personal and professional life, creating ripples of positive change. Let’s delve into the multifaceted benefits of being a solutions oriented leader.

Boosted Confidence & Self-Efficacy:

When you consistently focus on finding creative solutions and witness your strategies turning into successful business outcomes, it naturally boosts your confidence. You start believing in your abilities, cultivating a sense of self-efficacy. This isn’t just about feeling good; it’s about knowing that you possess the skills and mindset to tackle challenges head-on.

Enhanced Resilience & Adaptability:

Challenges are inevitable. However, a solutions oriented approach equips you with resilience. When faced with setbacks, instead of succumbing to frustration, you see them as temporary roadblocks. This mindset fosters adaptability, allowing you to pivot and modify your strategies based on evolving circumstances.

Strengthened Collaborative Skills:

A solutions oriented lead individual understands the value of collaboration. By seeking diverse perspectives, brainstorming, and pooling together collective expertise, a team and solutions become more robust and holistic. This collaborative approach to leadership not only resolves challenges but also fosters a culture of teamwork and mutual respect.

Increased Value in Professional Settings:

In the corporate world, problem solvers are invaluable. By consistently showcasing a solutions oriented approach, you position yourself as an asset. Leaders and peers recognize and appreciate individuals who can transform challenges into opportunities, leading to career advancements and growth opportunities.

Promotion of Continuous Learning:

Being solutions oriented often means you’re on the lookout for knowledge, resources and skills that can aid in crafting solutions. This inherent curiosity and drive promote a culture of continuous learning, ensuring you remain updated, relevant, and ever-evolving, both personally and professionally.

Reduction of Stress & Anxiety:

Dwelling on problems can be mentally taxing, leading to increased stress and anxiety. However, when you shift your focus to developing solutions yourself, it brings clarity and a sense of purpose. Knowing that you’re taking proactive steps to address challenges can significantly reduce feelings of overwhelm and helplessness.

Inspiration to Others:

Your approach to challenges doesn’t just benefit you; it serves as an inspiration to others. By modeling a solutions oriented mindset, you motivate those around you to adopt similar strategies, creating a ripple effect of positive problem-solving.

A solutions oriented approach cultivates confidence and a belief in one’s abilities.

It fosters resilience and the ability to adapt to changing scenarios.

Enhances teamwork and collaboration, making problem-solving a collective effort.

Positions you as a valuable asset in professional environments, paving the way for growth.

Champions continuous learning , ensuring personal and professional evolution.

Acts as a buffer against stress, promoting mental well-being.

Serves as an inspiration, motivating others to become solution seekers.

FAQ – Unraveling the Solutions Oriented Approach

Navigating the world with a solutions oriented mindset can be a rewarding journey, but like any paradigm shift, it comes with its own set of queries. Here are some frequently asked questions to provide deeper insights and clarity.

Isn’t focusing solely on solutions too simplistic?

No, it’s not about oversimplifying problems. A solutions oriented approach encourages diving deep into challenges to understand their intricacies. It’s about shifting focus from merely highlighting issues to actively brainstorm solutions more problems and seeking ways to resolve and solve whatever problem arises from them, ensuring a balanced perspective that acknowledges complexity while seeking resolution.

How can I differentiate between being solutions oriented and just being optimistic?

While both traits can overlap, they are distinct. Being optimistic means maintaining a positive outlook regardless of circumstances. A solutions oriented individual, on the other hand, couples this positive outlook with actionable strategies. They don’t just hope for the best; they actively work towards the best outcome.

Are there situations where this approach might not be ideal?

Every approach has its context. While a solutions oriented mindset is beneficial in many workplace scenarios, there are moments, especially in personal or emotional situations with clients, where simply listening and empathizing is more appropriate than immediately jumping to solutions.

How do I deal with individuals who are resistant to solutions?

Resistance can stem from fear, skepticism, or past experiences. It’s essential to communicate effectively with leaders, empathize with their concerns, provide feedback, and sometimes even showcase small wins or proofs of concept to build trust and demonstrate the viability of proposed solutions.

Can this approach be taught or is it innate?

While some individuals might naturally gravitate towards problem-solving, a solutions oriented approach can definitely be cultivated. Through practices like continuous learning, seeking feedback, and fostering resilience, anyone can develop and hone this mindset.

How does one avoid getting overwhelmed when seeking solutions?

It’s crucial to break challenges down into smaller, manageable parts. Tackling each aspect step by step not only makes the process less daunting but also allows for clearer, more targeted solutions.

Is it possible to be too solutions oriented?

Balance is key. While being proactive is commendable, hastily jumping to solutions without fully understanding a problem can be counterproductive. It’s essential to strike a balance between analysis and action.

How can I measure the effectiveness of my solutions oriented approach?

Feedback is invaluable. Regularly seek feedback from peers, superiors, or those affected by your solutions. Additionally, self-reflection and tracking the tangible outcomes of your strategies can provide insights into areas of improvement.

Can this mindset be applied to personal challenges as well?

Absolutely! From personal development goals to interpersonal relationships, a solutions oriented approach can offer clarity, direction, and constructive strategies to navigate challenges.

Are there any risks associated with this approach?

Like any approach, there’s no one-size-fits-all solution faster this. There might be instances where a proposed solution doesn’t pan out as expected. It’s essential to be adaptable, learn from such experiences, and iterate your solution accordingly.

The solutions oriented approach is not about oversimplification but rather a shift in focus towards actionable strategies.

It differs from mere optimism by coupling a positive outlook with actionable steps.

This mindset is flexible and can be applied in a variety of situations, both personal and professional.

It can be cultivated, and continuous feedback and reflection are vital to its effectiveness.

Balance is key; understanding problems thoroughly before proposing solutions is crucial.

As we’ve journeyed forward through the facets of a solutions oriented mindset, it’s evident that this is not merely a methodology but a transformative way of living. Embracing such an approach reshapes the way we perceive challenges, turning them into opportunities waiting to be unlocked.

Historically, humankind’s greatest advancements have stemmed from an innate desire to explore and find solutions. From the wheel to the World Wide Web, our legacy is paved with examples of transcending barriers through innovative solutions. And while the scale of these solutions varies, the underlying principle remains constant: a focused drive to better our circumstances.

But why does this solution oriented approach resonate so deeply? For one, it provides a sense of purpose. In a world inundated with challenges, both big and small, it’s easy to feel overwhelmed. However, a solutions oriented mindset reframes these challenges, giving us a mission and a sense of direction. Instead of being bogged down by problems, we become architects of change, actively crafting strategies to improve our world.

Moreover, this mindset fosters personal growth. Every time we face a challenge with a solutions oriented approach, we grow — in skills, knowledge, and character. We learn the art of resilience, the power of collaboration, and the value of continuous learning. It’s a journey of self-improvement, where every challenge faced is a lesson learned.

Additionally, this approach transcends the personal sphere. By being solutions oriented, we inspire those around us. It’s contagious. Teams work more cohesively, communities come together, and positive change becomes a collaborative whole team effort.

In essence, adopting a solutions and solution oriented leadership mindset is akin to lighting a beacon in the face of adversity. It illuminates paths that might otherwise remain obscured. It offers hope, not just through hollow optimism, for example, but through actionable strategies that promise to lead to tangible change.

As you move forward, armed with this newfound understanding, remember: challenges are but puzzles waiting to be solved. And with a solutions oriented approach, you hold the pieces that can craft the future into a brighter, more promising picture for future you.

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Do You Understand the Problem You’re Trying to Solve?

To solve tough problems at work, first ask these questions.

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Problem solving skills are invaluable in any job. But all too often, we jump to find solutions to a problem without taking time to really understand the dilemma we face, according to Thomas Wedell-Wedellsborg , an expert in innovation and the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

In this episode, you’ll learn how to reframe tough problems by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for just one root cause can be misleading.

Key episode topics include: leadership, decision making and problem solving, power and influence, business management.

HBR On Leadership curates the best case studies and conversations with the world’s top business and management experts, to help you unlock the best in those around you. New episodes every week.

• Listen to the original HBR IdeaCast episode: The Secret to Better Problem Solving (2016)
• Find more episodes of HBR IdeaCast
• Discover 100 years of Harvard Business Review articles, case studies, podcasts, and more at HBR.org .

HANNAH BATES: Welcome to HBR on Leadership , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock the best in those around you.

Problem solving skills are invaluable in any job. But even the most experienced among us can fall into the trap of solving the wrong problem.

Thomas Wedell-Wedellsborg says that all too often, we jump to find solutions to a problem – without taking time to really understand what we’re facing.

He’s an expert in innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

  In this episode, you’ll learn how to reframe tough problems, by asking questions that reveal all the factors and assumptions that contribute to the situation. You’ll also learn why searching for one root cause can be misleading. And you’ll learn how to use experimentation and rapid prototyping as problem-solving tools.

This episode originally aired on HBR IdeaCast in December 2016. Here it is.

SARAH GREEN CARMICHAEL: Welcome to the HBR IdeaCast from Harvard Business Review. I’m Sarah Green Carmichael.

Problem solving is popular. People put it on their resumes. Managers believe they excel at it. Companies count it as a key proficiency. We solve customers’ problems.

The problem is we often solve the wrong problems. Albert Einstein and Peter Drucker alike have discussed the difficulty of effective diagnosis. There are great frameworks for getting teams to attack true problems, but they’re often hard to do daily and on the fly. That’s where our guest comes in.

Thomas Wedell-Wedellsborg is a consultant who helps companies and managers reframe their problems so they can come up with an effective solution faster. He asks the question “Are You Solving The Right Problems?” in the January-February 2017 issue of Harvard Business Review. Thomas, thank you so much for coming on the HBR IdeaCast .

THOMAS WEDELL-WEDELLSBORG: Thanks for inviting me.

SARAH GREEN CARMICHAEL: So, I thought maybe we could start by talking about the problem of talking about problem reframing. What is that exactly?

THOMAS WEDELL-WEDELLSBORG: Basically, when people face a problem, they tend to jump into solution mode to rapidly, and very often that means that they don’t really understand, necessarily, the problem they’re trying to solve. And so, reframing is really a– at heart, it’s a method that helps you avoid that by taking a second to go in and ask two questions, basically saying, first of all, wait. What is the problem we’re trying to solve? And then crucially asking, is there a different way to think about what the problem actually is?

SARAH GREEN CARMICHAEL: So, I feel like so often when this comes up in meetings, you know, someone says that, and maybe they throw out the Einstein quote about you spend an hour of problem solving, you spend 55 minutes to find the problem. And then everyone else in the room kind of gets irritated. So, maybe just give us an example of maybe how this would work in practice in a way that would not, sort of, set people’s teeth on edge, like oh, here Sarah goes again, reframing the whole problem instead of just solving it.

THOMAS WEDELL-WEDELLSBORG: I mean, you’re bringing up something that’s, I think is crucial, which is to create legitimacy for the method. So, one of the reasons why I put out the article is to give people a tool to say actually, this thing is still important, and we need to do it. But I think the really critical thing in order to make this work in a meeting is actually to learn how to do it fast, because if you have the idea that you need to spend 30 minutes in a meeting delving deeply into the problem, I mean, that’s going to be uphill for most problems. So, the critical thing here is really to try to make it a practice you can implement very, very rapidly.

There’s an example that I would suggest memorizing. This is the example that I use to explain very rapidly what it is. And it’s basically, I call it the slow elevator problem. You imagine that you are the owner of an office building, and that your tenants are complaining that the elevator’s slow.

Now, if you take that problem framing for granted, you’re going to start thinking creatively around how do we make the elevator faster. Do we install a new motor? Do we have to buy a new lift somewhere?

The thing is, though, if you ask people who actually work with facilities management, well, they’re going to have a different solution for you, which is put up a mirror next to the elevator. That’s what happens is, of course, that people go oh, I’m busy. I’m busy. I’m– oh, a mirror. Oh, that’s beautiful.

And then they forget time. What’s interesting about that example is that the idea with a mirror is actually a solution to a different problem than the one you first proposed. And so, the whole idea here is once you get good at using reframing, you can quickly identify other aspects of the problem that might be much better to try to solve than the original one you found. It’s not necessarily that the first one is wrong. It’s just that there might be better problems out there to attack that we can, means we can do things much faster, cheaper, or better.

SARAH GREEN CARMICHAEL: So, in that example, I can understand how A, it’s probably expensive to make the elevator faster, so it’s much cheaper just to put up a mirror. And B, maybe the real problem people are actually feeling, even though they’re not articulating it right, is like, I hate waiting for the elevator. But if you let them sort of fix their hair or check their teeth, they’re suddenly distracted and don’t notice.

But if you have, this is sort of a pedestrian example, but say you have a roommate or a spouse who doesn’t clean up the kitchen. Facing that problem and not having your elegant solution already there to highlight the contrast between the perceived problem and the real problem, how would you take a problem like that and attack it using this method so that you can see what some of the other options might be?

THOMAS WEDELL-WEDELLSBORG: Right. So, I mean, let’s say it’s you who have that problem. I would go in and say, first of all, what would you say the problem is? Like, if you were to describe your view of the problem, what would that be?

SARAH GREEN CARMICHAEL: I hate cleaning the kitchen, and I want someone else to clean it up.

THOMAS WEDELL-WEDELLSBORG: OK. So, my first observation, you know, that somebody else might not necessarily be your spouse. So, already there, there’s an inbuilt assumption in your question around oh, it has to be my husband who does the cleaning. So, it might actually be worth, already there to say, is that really the only problem you have? That you hate cleaning the kitchen, and you want to avoid it? Or might there be something around, as well, getting a better relationship in terms of how you solve problems in general or establishing a better way to handle small problems when dealing with your spouse?

SARAH GREEN CARMICHAEL: Or maybe, now that I’m thinking that, maybe the problem is that you just can’t find the stuff in the kitchen when you need to find it.

THOMAS WEDELL-WEDELLSBORG: Right, and so that’s an example of a reframing, that actually why is it a problem that the kitchen is not clean? Is it only because you hate the act of cleaning, or does it actually mean that it just takes you a lot longer and gets a lot messier to actually use the kitchen, which is a different problem. The way you describe this problem now, is there anything that’s missing from that description?

SARAH GREEN CARMICHAEL: That is a really good question.

THOMAS WEDELL-WEDELLSBORG: Other, basically asking other factors that we are not talking about right now, and I say those because people tend to, when given a problem, they tend to delve deeper into the detail. What often is missing is actually an element outside of the initial description of the problem that might be really relevant to what’s going on. Like, why does the kitchen get messy in the first place? Is it something about the way you use it or your cooking habits? Is it because the neighbor’s kids, kind of, use it all the time?

There might, very often, there might be issues that you’re not really thinking about when you first describe the problem that actually has a big effect on it.

SARAH GREEN CARMICHAEL: I think at this point it would be helpful to maybe get another business example, and I’m wondering if you could tell us the story of the dog adoption problem.

THOMAS WEDELL-WEDELLSBORG: Yeah. This is a big problem in the US. If you work in the shelter industry, basically because dogs are so popular, more than 3 million dogs every year enter a shelter, and currently only about half of those actually find a new home and get adopted. And so, this is a problem that has persisted. It’s been, like, a structural problem for decades in this space. In the last three years, where people found new ways to address it.

So a woman called Lori Weise who runs a rescue organization in South LA, and she actually went in and challenged the very idea of what we were trying to do. She said, no, no. The problem we’re trying to solve is not about how to get more people to adopt dogs. It is about keeping the dogs with their first family so they never enter the shelter system in the first place.

In 2013, she started what’s called a Shelter Intervention Program that basically works like this. If a family comes and wants to hand over their dog, these are called owner surrenders. It’s about 30% of all dogs that come into a shelter. All they would do is go up and ask, if you could, would you like to keep your animal? And if they said yes, they would try to fix whatever helped them fix the problem, but that made them turn over this.

And sometimes that might be that they moved into a new building. The landlord required a deposit, and they simply didn’t have the money to put down a deposit. Or the dog might need a $10 rabies shot, but they didn’t know how to get access to a vet.

And so, by instigating that program, just in the first year, she took her, basically the amount of dollars they spent per animal they helped went from something like $85 down to around $60. Just an immediate impact, and her program now is being rolled out, is being supported by the ASPCA, which is one of the big animal welfare stations, and it’s being rolled out to various other places.

And I think what really struck me with that example was this was not dependent on having the internet. This was not, oh, we needed to have everybody mobile before we could come up with this. This, conceivably, we could have done 20 years ago. Only, it only happened when somebody, like in this case Lori, went in and actually rethought what the problem they were trying to solve was in the first place.

SARAH GREEN CARMICHAEL: So, what I also think is so interesting about that example is that when you talk about it, it doesn’t sound like the kind of thing that would have been thought of through other kinds of problem solving methods. There wasn’t necessarily an After Action Review or a 5 Whys exercise or a Six Sigma type intervention. I don’t want to throw those other methods under the bus, but how can you get such powerful results with such a very simple way of thinking about something?

THOMAS WEDELL-WEDELLSBORG: That was something that struck me as well. This, in a way, reframing and the idea of the problem diagnosis is important is something we’ve known for a long, long time. And we’ve actually have built some tools to help out. If you worked with us professionally, you are familiar with, like, Six Sigma, TRIZ, and so on. You mentioned 5 Whys. A root cause analysis is another one that a lot of people are familiar with.

Those are our good tools, and they’re definitely better than nothing. But what I notice when I work with the companies applying those was those tools tend to make you dig deeper into the first understanding of the problem we have. If it’s the elevator example, people start asking, well, is that the cable strength, or is the capacity of the elevator? That they kind of get caught by the details.

That, in a way, is a bad way to work on problems because it really assumes that there’s like a, you can almost hear it, a root cause. That you have to dig down and find the one true problem, and everything else was just symptoms. That’s a bad way to think about problems because problems tend to be multicausal.

There tend to be lots of causes or levers you can potentially press to address a problem. And if you think there’s only one, if that’s the right problem, that’s actually a dangerous way. And so I think that’s why, that this is a method I’ve worked with over the last five years, trying to basically refine how to make people better at this, and the key tends to be this thing about shifting out and saying, is there a totally different way of thinking about the problem versus getting too caught up in the mechanistic details of what happens.

SARAH GREEN CARMICHAEL: What about experimentation? Because that’s another method that’s become really popular with the rise of Lean Startup and lots of other innovation methodologies. Why wouldn’t it have worked to, say, experiment with many different types of fixing the dog adoption problem, and then just pick the one that works the best?

THOMAS WEDELL-WEDELLSBORG: You could say in the dog space, that’s what’s been going on. I mean, there is, in this industry and a lot of, it’s largely volunteer driven. People have experimented, and they found different ways of trying to cope. And that has definitely made the problem better. So, I wouldn’t say that experimentation is bad, quite the contrary. Rapid prototyping, quickly putting something out into the world and learning from it, that’s a fantastic way to learn more and to move forward.

My point is, though, that I feel we’ve come to rely too much on that. There’s like, if you look at the start up space, the wisdom is now just to put something quickly into the market, and then if it doesn’t work, pivot and just do more stuff. What reframing really is, I think of it as the cognitive counterpoint to prototyping. So, this is really a way of seeing very quickly, like not just working on the solution, but also working on our understanding of the problem and trying to see is there a different way to think about that.

If you only stick with experimentation, again, you tend to sometimes stay too much in the same space trying minute variations of something instead of taking a step back and saying, wait a minute. What is this telling us about what the real issue is?

SARAH GREEN CARMICHAEL: So, to go back to something that we touched on earlier, when we were talking about the completely hypothetical example of a spouse who does not clean the kitchen–

THOMAS WEDELL-WEDELLSBORG: Completely, completely hypothetical.

SARAH GREEN CARMICHAEL: Yes. For the record, my husband is a great kitchen cleaner.

You started asking me some questions that I could see immediately were helping me rethink that problem. Is that kind of the key, just having a checklist of questions to ask yourself? How do you really start to put this into practice?

THOMAS WEDELL-WEDELLSBORG: I think there are two steps in that. The first one is just to make yourself better at the method. Yes, you should kind of work with a checklist. In the article, I kind of outlined seven practices that you can use to do this.

But importantly, I would say you have to consider that as, basically, a set of training wheels. I think there’s a big, big danger in getting caught in a checklist. This is something I work with.

My co-author Paddy Miller, it’s one of his insights. That if you start giving people a checklist for things like this, they start following it. And that’s actually a problem, because what you really want them to do is start challenging their thinking.

So the way to handle this is to get some practice using it. Do use the checklist initially, but then try to step away from it and try to see if you can organically make– it’s almost a habit of mind. When you run into a colleague in the hallway and she has a problem and you have five minutes, like, delving in and just starting asking some of those questions and using your intuition to say, wait, how is she talking about this problem? And is there a question or two I can ask her about the problem that can help her rethink it?

SARAH GREEN CARMICHAEL: Well, that is also just a very different approach, because I think in that situation, most of us can’t go 30 seconds without jumping in and offering solutions.

THOMAS WEDELL-WEDELLSBORG: Very true. The drive toward solutions is very strong. And to be clear, I mean, there’s nothing wrong with that if the solutions work. So, many problems are just solved by oh, you know, oh, here’s the way to do that. Great.

But this is really a powerful method for those problems where either it’s something we’ve been banging our heads against tons of times without making progress, or when you need to come up with a really creative solution. When you’re facing a competitor with a much bigger budget, and you know, if you solve the same problem later, you’re not going to win. So, that basic idea of taking that approach to problems can often help you move forward in a different way than just like, oh, I have a solution.

I would say there’s also, there’s some interesting psychological stuff going on, right? Where you may have tried this, but if somebody tries to serve up a solution to a problem I have, I’m often resistant towards them. Kind if like, no, no, no, no, no, no. That solution is not going to work in my world. Whereas if you get them to discuss and analyze what the problem really is, you might actually dig something up.

Let’s go back to the kitchen example. One powerful question is just to say, what’s your own part in creating this problem? It’s very often, like, people, they describe problems as if it’s something that’s inflicted upon them from the external world, and they are innocent bystanders in that.

SARAH GREEN CARMICHAEL: Right, or crazy customers with unreasonable demands.

THOMAS WEDELL-WEDELLSBORG: Exactly, right. I don’t think I’ve ever met an agency or consultancy that didn’t, like, gossip about their customers. Oh, my god, they’re horrible. That, you know, classic thing, why don’t they want to take more risk? Well, risk is bad.

It’s their business that’s on the line, not the consultancy’s, right? So, absolutely, that’s one of the things when you step into a different mindset and kind of, wait. Oh yeah, maybe I actually am part of creating this problem in a sense, as well. That tends to open some new doors for you to move forward, in a way, with stuff that you may have been struggling with for years.

SARAH GREEN CARMICHAEL: So, we’ve surfaced a couple of questions that are useful. I’m curious to know, what are some of the other questions that you find yourself asking in these situations, given that you have made this sort of mental habit that you do? What are the questions that people seem to find really useful?

THOMAS WEDELL-WEDELLSBORG: One easy one is just to ask if there are any positive exceptions to the problem. So, was there day where your kitchen was actually spotlessly clean? And then asking, what was different about that day? Like, what happened there that didn’t happen the other days? That can very often point people towards a factor that they hadn’t considered previously.

SARAH GREEN CARMICHAEL: We got take-out.

THOMAS WEDELL-WEDELLSBORG: S,o that is your solution. Take-out from [INAUDIBLE]. That might have other problems.

Another good question, and this is a little bit more high level. It’s actually more making an observation about labeling how that person thinks about the problem. And what I mean with that is, we have problem categories in our head. So, if I say, let’s say that you describe a problem to me and say, well, we have a really great product and are, it’s much better than our previous product, but people aren’t buying it. I think we need to put more marketing dollars into this.

Now you can go in and say, that’s interesting. This sounds like you’re thinking of this as a communications problem. Is there a different way of thinking about that? Because you can almost tell how, when the second you say communications, there are some ideas about how do you solve a communications problem. Typically with more communication.

And what you might do is go in and suggest, well, have you considered that it might be, say, an incentive problem? Are there incentives on behalf of the purchasing manager at your clients that are obstructing you? Might there be incentive issues with your own sales force that makes them want to sell the old product instead of the new one?

So literally, just identifying what type of problem does this person think about, and is there different potential way of thinking about it? Might it be an emotional problem, a timing problem, an expectations management problem? Thinking about what label of what type of problem that person is kind of thinking as it of.

SARAH GREEN CARMICHAEL: That’s really interesting, too, because I think so many of us get requests for advice that we’re really not qualified to give. So, maybe the next time that happens, instead of muddying my way through, I will just ask some of those questions that we talked about instead.

THOMAS WEDELL-WEDELLSBORG: That sounds like a good idea.

SARAH GREEN CARMICHAEL: So, Thomas, this has really helped me reframe the way I think about a couple of problems in my own life, and I’m just wondering. I know you do this professionally, but is there a problem in your life that thinking this way has helped you solve?

THOMAS WEDELL-WEDELLSBORG: I’ve, of course, I’ve been swallowing my own medicine on this, too, and I think I have, well, maybe two different examples, and in one case somebody else did the reframing for me. But in one case, when I was younger, I often kind of struggled a little bit. I mean, this is my teenage years, kind of hanging out with my parents. I thought they were pretty annoying people. That’s not really fair, because they’re quite wonderful, but that’s what life is when you’re a teenager.

And one of the things that struck me, suddenly, and this was kind of the positive exception was, there was actually an evening where we really had a good time, and there wasn’t a conflict. And the core thing was, I wasn’t just seeing them in their old house where I grew up. It was, actually, we were at a restaurant. And it suddenly struck me that so much of the sometimes, kind of, a little bit, you love them but they’re annoying kind of dynamic, is tied to the place, is tied to the setting you are in.

And of course, if– you know, I live abroad now, if I visit my parents and I stay in my old bedroom, you know, my mother comes in and wants to wake me up in the morning. Stuff like that, right? And it just struck me so, so clearly that it’s– when I change this setting, if I go out and have dinner with them at a different place, that the dynamic, just that dynamic disappears.

SARAH GREEN CARMICHAEL: Well, Thomas, this has been really, really helpful. Thank you for talking with me today.

THOMAS WEDELL-WEDELLSBORG: Thank you, Sarah.  

HANNAH BATES: That was Thomas Wedell-Wedellsborg in conversation with Sarah Green Carmichael on the HBR IdeaCast. He’s an expert in problem solving and innovation, and he’s the author of the book, What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve .

We’ll be back next Wednesday with another hand-picked conversation about leadership from the Harvard Business Review. If you found this episode helpful, share it with your friends and colleagues, and follow our show on Apple Podcasts, Spotify, or wherever you get your podcasts. While you’re there, be sure to leave us a review.

We’re a production of Harvard Business Review. If you want more podcasts, articles, case studies, books, and videos like this, find it all at HBR dot org.

This episode was produced by Anne Saini, and me, Hannah Bates. Ian Fox is our editor. Music by Coma Media. Special thanks to Maureen Hoch, Adi Ignatius, Karen Player, Ramsey Khabbaz, Nicole Smith, Anne Bartholomew, and you – our listener.

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Future-Oriented Thinking and Activity in Mathematical Problem Solving

• First Online: 13 February 2019

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Part of the book series: ICME-13 Monographs ((ICME13Mo))

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The purpose of this chapter is to highlight the importance of “thinking ahead” in mathematical problem solving. This process, though seemingly central to the work of mathematicians, seems to be largely overlooked in the mathematics education literature. This chapter presents my recent attempts to characterize future-oriented processes in mathematical work and summarizes evidence of mathematicians engaging in such processes. The main new results presented here concern students’ future thinking in mathematical situations. Student participants’ work in problem situations was analysed through the lens of mathematical foresight . This analysis serves to deepen the mathematical foresight model and opens up a number of directions for future research.

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Maciejewski, W. (2019). Future-Oriented Thinking and Activity in Mathematical Problem Solving. In: Liljedahl, P., Santos-Trigo, M. (eds) Mathematical Problem Solving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-10472-6_2

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What are the 5 thinking styles? Understanding different types of thinkers

• There are five different types of thinkers with their own thinking styles: synthesists, idealists, pragmatists, analysts, and realists.
• Synthesists stand out with their creativity and curiosity; they like to consider different ideas, views, and possibilities.
• Idealists are always setting and working toward big goals—they set the bar high and expect others to do the same.
• Pragmatists take a logical approach to problem-solving; they focus on immediate results, as opposed to long-term effects.
• Analysts are interested in the facts and data points—they have a clear procedure for doing all things.
• Realists are the perfect problem-solvers; tackle problems head-on and don’t feel challenged by your everyday conundrum.

We employ different ways of thinking. Some of us take a creative approach, while others are more analytic; some are focused on the short-term, while others think about the long-term. While we all have unique minds, our tendencies have been summed up into five recognized thinking styles: synthesists, or the creative thinkers; idealists, or the goal-setters; pragmatists, or the logical thinkers; analysts, or the rational intellectuals; and finally, realists, or the perfect problem-solvers. Which type of thinker are you?

Synthesists: The Creative Type of Thinker

Synthesists are largely defined by their creative and curious nature. Instead of leading with logic, they love to explore more abstract ideas. They ask, “What if?” and consider a range of views and possibilities. Some perceive synthesists as being argumentative, as they’re quick to bring attention to opposing views—but these creative thinkers can prevent this perception by first acknowledging others’ ideas before presenting alternatives.

Idealists: The Goal-setting Type of Thinker

Idealists set high standards and are always working toward larger-than-life goals . While others might perceive them as perfectionists, in their minds, they’re simply putting their best foot forward. These individuals are future-oriented, they value teamwork, and they expect everyone to work hard. However, it’s important for idealists to realize that others have their own standards and expectations—which might not match up with the idealist’s standards and expectations.

Pragmatists: The Logical Type of Thinker

Pragmatists don’t waste any time—they take action. They tackle problems logically, step-by step. They’re focused on getting things done, but they aren’t interested in understanding the big picture like idealists are. Rather than considering what’s best in the long-term, they think short-term. While pragmatists get things done, they can benefit from taking a step back and reflecting on big ideas.

Analysts: The Rational/Intellectual Type of Thinker

Analysts work methodically. They gather all of the facts and data, measuring and categorizing along the way. Their personality is rooted in being thorough, accurate, and rational; analysts are always looking for a formula or outlined procedure for solving problems. These individuals tend to discount other ideas, but should open their minds, as other ideas offer unique value.

Realists: The Perfect Problem-solving Type of Thinker

Realists are quick on their feet, and they do whatever it takes to solve the problem at hand. That said, realists bore easily—they don’t feel challenged by everyday problems or stressors as most do. Yet, they want to be challenged. Realists can benefit, like pragmatists, from taking a step back and looking at a problem from different angles. They should take a little more time to gather all of the information that is available to them and find the best solution (which isn’t always the first solution) before acting.

Published Mar 8, 2019

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How to adopt a solution-oriented mindset.

"When presented with a problem, you start at the solution and reverse-engineer your way back. You figure out how to get to the solution by any legitimate means necessary ." ~ Christopher Penn

Every business has problems. How do you deal with them? Focusing on the solution seems logical, but in practice, it rarely happens. That's not surprising since a solution-oriented approach means changing our way of thinking. You approach problems differently from conventional methods by starting and acting with the desired goal. In focusing on the way the unfair situation might be, complaining about the disruption, or expressing your dissatisfaction, you worsen it, leading to more problems.

It is crucial to have a problem-solving mindset for any business, especially if you are an HR manager or CEO of a small or medium business. A growth mindset allows the business to stay on track to explore new opportunities. Read on to learn the best ways to develop a solution-oriented mindset.

Understanding the Problem

Any business will encounter problems and make mistakes; how you handle them makes the difference. First, you will look at the existing solution and identify the next closest option.It's crucial not to shy away from challenges.

Understanding the problem and learning to work within it is the only way to thrive in business. Classifying the problem is the first step to problem-solving in business. You set yourself up for success in this challenging environment, which will allow you to identify opportunities. A solution-oriented team works together, finds creative ways to solve the problem, and resolves it quickly. The group addresses challenges rather than avoiding them.

How to Develop a Growth Mindset

Developing a solution-oriented team requires commitment, discipline, and time, while the first step is to allow the team to evolve and motivate them to work together for a solution.

1. Change Your Attitude

Problem-solving mindsets recognize problems as growth opportunities and focus on achieving success by finding solutions. Challenges are unique, and you can influence the situation by looking at it from a new perspective and taking a step back. You can also gain a fresh perspective by brainstorming with others on things you might have missed otherwise. Having a fresh mindset on a problem will allow you to develop a new approach and find a solution.

 Once a problem arises, you need to stay optimistic to find solutions. You must discipline yourself to be hungry for answers. Motivating yourself to overcome the obstacle in front of you requires a paradigm shift. The decision is either to let the problem consume you or to face it head-on and take control with the attitude of a champion.

Take action and monitor your progress after identifying the problem and making a list of all possible solutions. A positive outcome is more likely with more information. Go through all the options, select the best one for the situation, and set measurable objectives.

2. Impactful Leadership

By strengthening employees' decision-making skills and encouraging them to focus on what works and what doesn't, solution-driven leaders improve their ability to resolve inconsistencies. It's your responsibility as a leader to create an environment where your team members solve problems rather than avoid them.

You speak far louder through your actions than through your words. Make sure your team knows you will support each other and work together to find solutions to challenges. A solution-driven organization attracts and retains talent. A mindset that attracts clients, including the best talent, requires a culture that cultivates this mindset throughout the organization.

There are many different leadership styles, but all influential leaders share some common characteristics. These include:

• They have a clear vision and can communicate it effectively. Lead by example. You need to be able to walk the talk and meet high standards yourself.
• They set high standards for others and expect them to meet them. Accountability is key.
• They take responsibility for their own actions and decisions. You need to be accountable for your own actions if you want others to be accountable.
• They're not afraid to take risks. You need to be willing to take risks in order to achieve your goals.
• They're always learning and growing. You need to be constantly learning and growing in order to stay ahead of the curve.

3. Encourage Critical Thinking

Using critical thinking skills to solve problems, you have to analyze the root cause and critically look at them. Without getting overwhelmed by analyzing the root causes and less critical aspects, you can tackle a problem.

You must think beyond your self-imposed limits to achieve innovative solutions that exceed the average ideas' shortlist and challenge yourself to think outside the box. An integrated approach enables you to effectively combine knowledge and experience from different fields. Your solutions make a significant difference using this approach.

A problem analysis sets you up for future success by focusing on long-term solutions. Keep your leadership role in mind. As a team, you should encourage critical thinking, letting them take the lead and provide feedback if necessary.

4. Coach On-the-Go

It will be challenging to create a solution-driven mindset as you build a team and mentor a diverse group of individuals. You are responsible for helping your team understand the problem and develop solutions to overcome it. By providing real-time coaching, your team will be able to address any challenges the organization faces and take a proactive approach to their professional performance.

5. Communicate Openly

You need to create a safe environment for your team members to communicate honestly and transparently if you want them to think critically. Consider everyone's thoughts and suggestions and show you value them by genuinely listening to what they have to say. Give your team the chance to develop a viable solution and test it.

Leading With a Purpose

A solution-driven approach creates a mindset that encourages leaders to develop a team that identifies solutions because they can think critically, communicate openly, and understand how this approach supports the business. Developing a solution-oriented mindset requires discipline, practice, and time. To thrive in your business, You must take a proactive approach and focus your resources on solving problems rather than creating new ones.

DevelopING Solutions

Now that you've transformed your thinking from problem-focused to a growth mindset, you'll need a process for developing solutions. Only by creating a solution-centered plan of action will you be able to achieve your goals. With your mindset upgraded and the problem at hand defined, here are a few steps to get you started:

1. Gather information . Once you've identified the problem, it's time to start gathering information. This can include research, interviews, surveys, and data analysis. Remember that information is cheap. There's a lot of it. And, if you don't have the right information, you're likely to make bad decisions.

3. Brainstorm solutions. Once you have a good understanding of the problem and more information, it's time to start brainstorming possible solutions. Be creative and think outside the box. Begin by asking yourself: What do I want to achieve? What are my goals? Keep in mind that your goals should be specific, measurable, achievable, relevant, and time-bound (SMART).

4. Evaluate solutions. After you've generated a list of options, it's time to evaluate them. Consider factors such as feasibility, cost, and expected outcomes. Do the possible solutions address the root cause of the problem? Which solution is most likely to succeed?

5. Implement a solution. Once you've selected the best solution, it's time to put it into action. Develop a plan and make sure you have the resources you need to succeed. To determine the resources needed, ask yourself: What do I need to make this happen? Who can help me?

6. Monitor and adjust. Even after you've implemented a solution, it's important to monitor the results and make adjustments as needed. Questions to ask at this stage include: Is the solution working? What could be improved? Are there any unforeseen consequences?

A solution-centric mindset is a powerful tool for problem-solving in business. Quite simply, it is a key leadership skill. If you want to be an impactful leader, it's essential to develop this way of thinking.

With a solution-oriented mindset, you'll see problems as opportunities to find creative solutions that make things better. And, by choosing to see problems in a more positive light, you'll be able to communicate a growth mindset to the rest of the organization. So, if you're ready to start on this journey, visit platinum-grp.com to see how an all-in-one HCM solution can provide a compliant, efficient system to maximize the growth of your business and the capacity of your team.

About Platinum Group

Platinum Group is a human capital management resource with solutions to help you streamline operations so you’ll have time to manage your business. For more information about Platinum Group, or to  schedule a demo  of iSolved, please  visit our website.

Tags: HR Growth Mindset effective teams compassionate leadership

Michael Murphy

Michael is the founder of Platinum Group. His passion is in helping businesses to simplify their employee management and accounting processes.

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How to take a solution-oriented approach to resolving problems

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Employees expect leaders to solve problems both big and small. But a leader’s attention will be focused on issues of significance (financial crises, unexpected mergers, and acquisitions), which means medium-sized problems are often put aside, to return later with a vengeance! As Noble Peace Prize winner and former US Secretary of State Henry Kissinger said, “All too frequently a problem evaded is a crisis invited”.

Great leaders don’t play the blame game. Instead they use a “solution-oriented” approach to resolve problems.

They use the why lens. Highly respected leaders only solve problems within their control. Ones connected to their biggest why. They consider problems from a fundamental point of view.

· Is this our problem?

· Why should we solve this problem?

· What happens if we don’t?

· How would the solution contribute to accomplishing our most important goals?

Once they have answers, they explore solutions. Around 2013, Royal Philips in Amsterdam noticed the lighting market was stagnating. CEO Frans van Houten asked those types of questions. Armed with the answers, he concluded it would not make sense for Philips to continue with lighting. Philips now focuses on healthcare technology. By approaching problems through the why lens, van Houten was able to change the direction of the company and keep it operable. A clear benefit of applying solution-oriented problem solving.

They are inspired by problems. Without problems, a business will lose its fire, passion, and dynamism. While many leaders perceive problems as distracters, first-class leaders embrace problems as opportunities to make breakthroughs. Leaders know that if they are unable to solve the problem their competitors will, pushing them out of the market.

Problems fuel great leaders, providing opportunities to learn and grow to the next level. Great leaders don’t say, “Why me?” or “Why now?”. They say, “Try me” or “Let’s make the most of it.”. The greater the problem, the hungrier they are for a solution. Leaders like Richard Branson, Elon Musk, and Bill Gates view problems as golden opportunities to disrupt the market and revolutionize the customer experience.

They openly admit there is a problem. Great leaders acknowledge there is a problem and demonstrate the severity of the problem and the benefit of the solution to stakeholders, partners, and shareholders. By establishing an open environment, great leaders avoid creating silos. This way, the leader not only takes responsibility for making the problem transparent, they explore different dimensions of the problem, consequently benefiting from others’ ideas.

They separate problems from people. Great leaders separate problems from people. They ask questions until they understand the issue. A clear understanding of a problem delivers two-thirds of the solution. When people attribute blame, highly qualified leaders focus on the problem at hand, keeping emotions controlled. By doing so, they can approach the situation fairly and find a suitable solution.

They have a plan. Great leaders do not guess. They identify the core of the problem, forecast scenarios, and produce backup plans before formulating and sharing with stakeholders. This creates the trust and commitment necessary for implementation. They assess actions and adjust whenever necessary. By analyzing, they focus on the easiest implementation route and work around any blocks standing in the way.

Top leaders make sure their organization stands steady when in crisis. They create a thorough problem-solving process. Great leaders avoid panic at all costs. They remain cool and retain a sense of humor. They know if they panic, their team members will lose hope and motivation.

They engage those affected by the problem. Those who have a stake in the problem and the relevant solution often know the most. Solution-oriented leaders listen to the needs and concerns of all involved parties. When respected by the majority, leaders have buy-in and are able to focus on solutions. This caring attitude helps them build great relationships. When the relationship is good, people are prepared to walk that extra mile for their leaders.

Great leaders create an environment where team members can freely share their views without feeling insecure about their position. It is the leader’s responsibility to guarantee freedom to speak up without fear of negative consequences.

They don’t point fingers. Great leaders know that finger pointing does not solve problems. It only adds new ones. It makes employees singled out feel broken, guilty, and belittled. Instead of blaming anyone, the leader starts problem solving by narrowing down the issue. When the problem has been addressed, and potentially solved, they ask their team members what they learned from the experience and how they can improve vulnerable areas.

Now examine how you approach problems. What are the first things you do when you encounter a severe problem? What can you take away from the above to ensure your future approach to problem solving is more solution-oriented?

Problem vs. Solution Focused Thinking

Every person approaches a problem in a different way. Some focus on the problem or the reason why a problem emerged (problem focused thinking). Others prefer to think about possible solutions that help them to solve a problem (solution focused thinking).  Problem Oriented Thinking:  Approaching a difficult situation problem-oriented might be helpful if we attempt to avoid similar problems or mistakes in the future, but when it comes to solving the problem we simply waste large amounts of our precious time! Problem-focused thinking does not help us at all to solve difficult situations, which is especially necessary in times where one must find quick solutions to an upcoming problem. Furthermore, the problem focused approach can have negative effects on one’s motivation, but more on this later.

The whole “problem vs. solution oriented thinking” – approach does not only apply when a person faces a problem or a difficult situation (as previously mentioned), but is also being applied in one’s everyday life, when we have to face a challenging task or when having to perform several duties. In fact: if we really focus our attention on this topic we can discover that the majority of our decisions and our attitudes towards tasks, problems and upcoming situations will either be problem or solution oriented. In order to demonstrate you the problem and solution focused approach I have chosen to give you the example of a college student:

Let’s say there is a college student that really does not like math at all (it doesn’t matter what subject he does not like, but I do not like math as well) . Just like every other college student, he will have to do some homework for math and if he wants to pass the exams he will have to study a lot, whether he likes math or not. The student would be approaching the subject math problem-oriented if he would continuously imagine all the negative aspects of math that he does not like and might ask himself the question, “Why do I have to study for math? For what kind of reason?” . The college student would be talking with his fellow students about the pointlessness of math, which will only strengthen his negative opinion about math. Rather than focusing his energy on studying for math he will get uptight and spends large amounts of his time in an ineffective way, that won’t help him to pass the exams.

When I was in school I heard similar questions whole the time, especially when it came to subjects that the majority of my classmates did not like. To be honest, when I was younger I was asking myself these questions as well, especially in subjects that I knew were pointless for the profession I wanted to become. When I grew older I started to scrutinize this behavior and noticed how senseless it was to focus all my attention on problem focused thinking, especially as this only decreased my motivation and strengthened my resentment towards these subjects.

Discovering that one is majorly approaching tasks and challenges problem focused can be really difficult, but once we are aware of this we can start to change our focus from the problem towards the solution and make use of the solution-focused thinking.

Let us come back to the example of the college student that was thinking problem oriented. In order to think solution oriented, he would need to completely accept the fact that math is a part of his schedule and will, therefore, be tested in his exams, whether he likes math or not. By accepting this fact he will easily destroy the root cause for questions that focus on the reason for something (“Why?”) and that only waste his time.

We start to think solution oriented once we are aware that we cannot change certain facts/problems and will only spend our time in an inefficient way when we seek for the possible reasons for these situations. By clarifying the reasons why the task we have to face (e.g. math) might be important, for example, to get accepted to a good university or to increase our GPA, we can bring the solution focused thinking to a further level.

It is really astounding to see how many people are thinking problem oriented, especially as this behavior starts in school and can be found in the professional world as well, for example when an employee has to face a new task that he is not familiar with, or has little to no knowledge about. Those that think problem-oriented would be imagining all the negative consequences they might have to face or all the mistakes they might commit when trying to solve the task. The employee will talk about his difficult situation with different colleagues, his partner or friends, which will only increase his fear of the upcoming task.

When you focus only on the problem, you might miss a new path.

The employee that quite in the contrary knows of the benefits of solution focused thinking does not struggle with the new task for a second, as he is too busy to take necessary preparations to solve it. He will completely accept the new task as a challenge, or even consider the task as a chance to prove his boss that he is capable of solving even the more advanced tasks.

How to avoid problem focused thinking?

#1 self-knowledge:.

In order to avoid problem focused thinking and to replace it with solution-oriented thinking we firstly need to discover that we approach different tasks, problems, challenges, etc. in a problem-oriented way. This is the utmost important step to do. You can identify whether you approach tasks problem-oriented by paying attention towards the questions that arise when you have to face a task that you do not like, which might be indicators for problem focused thinking:

• Why do I have to perform this task?
• What is the reason that I have to study this subject?
• Why do I even spend time with this?

#2 Fight problem-oriented questions:

The very first step to approach problems with solution focused thinking is to avoid questions that mainly focus on the reason or the problem in general. You need to clarify yourself that the question for the “WHY” will only waste important time that you could have invested to solve a given problem.

#3 Clarity:

When you come to the conclusion that a task needs to be done you will see the pointlessness of further evaluating the usefulness or non-usefulness of a task. So when you have to face a task that you dislike you could ask yourself the question, “Has this task to be fulfilled?” and when you conclude that the answer is “Yes”, then you know that every further attempt to evaluate the reasons and the “Why’s” is a waste of time.

#4 Why is it important to solve this task?

Questioning and clarifying the importance of a task will finally erase the root cause of every problem-oriented question. By clarifying the reasons why a task needs to be performed we can effectively change our focus from the problem to possible solutions.

#5 Think about the solution:

The final step to profit from solution focused thinking the most is to ask yourself different questions on how you can solve a given task or problem:

• How can I solve this task?
• How can I address this problem?
• What would be the first step to solving this problem?
• What kind of preparations will be necessary for this task?

Why does problem focused thinking decrease motivation?

Just imagine yourself having to study for an upcoming test (whether it is for school or a professional development is unimportant). While you are sitting in front of your table you start thinking about the exam and how much you dislike the whole subject. Questions that address the reason why you have to study for this subject start to arise and will ensure that you lose even the slightest interest in your task. Without being interested and a dozen of different questions that start to arise we finally lack the motivation to study for the exam !

Problem vs. Solution oriented thinking was presented by our Personality Growth Website. What is your preferred way of thinking? We’re excited to hear about your experiences in the comments section below.

About Author

Steve is the founder of Planet of Success , the #1 choice when it comes to motivation, self-growth and empowerment. This world does not need followers. What it needs is people who stand in their own sovereignty. Join us in the quest to live life to the fullest!

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Just saying Problem focused approach wastes time is ridiculous. It depends on what situation you’re in. If you’re preparing for an exam like olympiads, Problem focused approach is Best whereas while in actual exam, a solution focused approach might be better. You’re not going to learn and understand anything unless you ask yourself the questions like Why, What and How. But I can’t expect the same fro someone who has disliked Maths.

Did you read the first part of this? They specifically mentioned that starting with a problem oriented perspective is fine, but to eventually “fight it” by answering those questions so that you can get to a solution oriented perspective. Essentially, the big picture here is to not get stuck in problem orientation — it’s quite simple.

The issue of stress is ignored here. Tolerance for ambiguity is reduced by stress. When stressed, any additional requirement is a “problem.” This starts a downward spiral. A willingness to reduce our personal stress (with good diet, aerobic exercise, adequate sleep, etc.) can allow us to acknowledge our willingness (and culpability) in accepting new challenges, which can then take us away from an “Everything is a problem” attitudes.

Hello Jane, this is an incredibly important remark you make here. Thank you for sharing it. I hadn’t considered it from this perspective, but you are absolutely right.

I hate to be offensive, but I also don’t like to say, “No offense”, so I will tell you something that will probably offend you, Steve. But if you hadn’t considered it from that perspective, then you probably aren’t fully qualified to be writing articles like this. You obviously haven’t studied the full depths and ramifications of the issue.

Furthermore, you are telling people to ignore emotions which are a signal to them that something is wrong. Certainly, people can become TOO overtaken by those emotions, but just ignoring those emotions pushes them aside and suppresses them. Ultimately, it is those reactions and emotions that are the barometer of everything that we do. I’m not saying that there isn’t merit to what you are saying, but putting it in such black and white terms ignores so many factors that people deal with.

Finally, there is a strong value to considering problems, and even dwelling on them. It is a natural psychological process. The “why” is often crucial. It also leads to critical thinking and evaluating. Maybe there is a better process that could be undertaken to do the set of tasks much more efficiently, which leads to innovating thinking. It allows for questioning of morality, efficiency, ramifications and consequences. Even visceral reactions to problems can be an indicator of a deeper problem that needs to be addressed. Shutting any these down can cause numerous problems down the road.

I’m not saying that the article doesn’t provide merit, but the fact that you haven’t brought up many of the innumerable other factors to be considered really makes me think that you shouldn’t be writing articles like this, because you simply have only cursory knowledge of the psychology involved.

I’m sorry if that stings, but I think you may be doing more harm than good by saying these things.

Thanks for sharing your opinion. No offense taken.

Wonderful Steve. I so agree that a person’s success depends on their ability to be solution oriented. I am a follower of Dr. Wayne Dyer, and your philosophy sounds fully compatible.

Thanks Sherwin. I am glad someone agrees.

The only reason one (stakeholder) would recognize a situation and label it as a problem is when it demands a solution. Thus problem and solution co-exist – the latter waiting to be discovered. Difficult for me to understand what a problem oriented approach would be.

“Why should I do this task?” simply means that one is not a stakeholder. If so, the problem simply does not exist!

My intention behind writing this article was to point out that some people only focus on the problem, whereas other people take notice of the problem but more eager to find a solution. The first approach involves complaining, but does not lead anywhere. The second approach is not so prone to complaining, but actively seeks for solutions to the problem.

The key term here is orientation not exclusivity. I consider myself to be a solution-oriented person and also know that it is essential that I define what a problem actually entails before I set about trying to resolve it. Sometimes this process is met with a significant amount of resistance due to the emotional discomfort that can arise during my search to define something. Logic dictates that it is seldom a black and white scenario. Acceptance of a problem can be a bigger challenge than we initially realise. Also over-simplifying issues around problem-solving will not do justice to the sometimes complex nature of any problem and/or solution. I do believe the concept of being solution-oriented is a health directed approach and leaves less room for unhealthy manipulation. That is where I see the value in this kind of orientation. Mental and physical health always come into any equation (yes, I said that) involving problems and solutions that need attention to improve health and well being. Thanks for your thoughts and intentions Steve. I believe you are on the right track.

Thank you Louise for sharing your brilliantly articulated thoughts on this subject. I absolutely agree with you.

I’d like to add a comment as an observer of my own behavior. I notice that I complain more when I’m more physically and mentally fatigued which drains me even more. And like an earlier commenter mentioned stress plays a factor in how we choose to spend our time and what we focus on in our thoughts. All the feel good endorphins and the dopamine, serotonin and oxytocin produced in our brains has a huge effect on how we think. I agree that diet and exercise plays a huge part in how we view the world and the obstacles that are placed in front of us everyday.The more of those chemicals produced the more positive thoughts and the less fatigued you feel. I love this article BTW.

What a clearly written and extremely helpful/useful article! I thank you for it.

You’re welcome. Thanks for your feedback.

The mentality in this article is common in business management etc, but unfortunately, it is not so simple as it would have you believe. The described solution-driven thinking implies falling in line with the current power structure and establishment, and naturally is promoted wide and far.

I consider problem-oriented thinking closely linked with critical thinking, and that we have too little of today. If you don’t ask questions like “what?” and “why?”, and instead simply accept the circumstances you’re in, then you also strip away important aspects of participating in society. Circumstances can and do change, and just accepting them means someone else will change it in your stead.

Sure, sometimes you need to stay focused on solving the task at hand. Knowing the difference I’d argue is part of what critical thinking is about, which the world is in dire need of.

Excellent argumentation. Thanks for your contribution.

problems were not here without any solution. There should always be one answer for it, no matter how big or small the problem is. always think on the positive side and you’ll see the solution is just always in front of you or just within your grasp.

Nice words for to understand about the problems. How to be aware in problems. Thank you

While trying to focus on solutions to a couple of problems currently plaguing my empire, I have no choice but to consider the problems, and considering the problems makes me more and more angry and totally distracts me from finding the solution :-/

Lovely topic I was recently faced with a challenge of getting my little daughter back on track after she suddenly took a 360 degree turn in personality and this was the exact debate the edu psych at school and I were having . Do I molicottle the situation and just over compliment her to improve self esteem or do i use the problem solution way of thinking which I agre with and he disagrees with ,wow tough one but I feel equip a young impressionable mind with so many negative influences in her way ,the best approach as a mom in help in my child succeed in her future is the solution based technique and in order for us to find solutions we need to identify the problem else the word solution lol would never have been invented as an antonym ….hahhah

Very good article. When you linger too long on problem, it makes you stressful whereas solution focused approach brings up your dormant resources. Although the situation is same the way your brain chemistry works is very different with these two different approach.

When presented with a problem my instinct is to find a way to fix it, I’m led to believe this is more a male trait than a female trait.

Males are tunnel vision, females periphery vision.

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Students to brainstorm recycling improvement ideas as part of UF IGNITE program

A student-led organization at the University of Florida's Engineering Innovation Institute will host an event Saturday to address issues and improvements with the recycling of glass and plastic in Gainesville.

UF IGNITE (Innovation Gator Network for Inspiring Technological Entrepreneurship), started in September 2023, is an innovation leadership group inspired and led by students. Based out of the Engineering Innovation Institute (EII), the group aims to provide a culture of innovation, networking and entrepreneurship within the Herbert Wertheim College of Engineering  and across the university itself.

Over the weekend, IGNITE's Creativity for Engineers Program will host its first Design Thinking Social Project which will allow UF students — through the power of design thinking — to improve the recycling of waste in the community.

The event aims to address issues with waste disposal — specifically plastic and glass — at the Leveda Brown Environmental Park and Transfer Station and explore creative solutions through design thinking methodologies. With the help of local artists and innovators, students will use creative and artistic principles to solve the problem of excess glass and plastic waste within the community.

Representatives from the transfer station will explain problems to students and why it's so difficult to dispose of the glass and plastic waste. From there, innovative community members will guide students through an ideation phase where they come up with innovative solutions to the problems presented.

"When it comes to the recycling center, it's mixed glass, and there's a lot of plastic that also gets mixed into it, and they really don't have a good way of filtering it without using an incredible amount of resources," said Dow Walker, IGNITE Creativity in Engineering coordinator and UF student. "It's just not economically feasible for the transfer station to manually sort this. So, what's been happening is they're collecting it because they... don't have anything to do with it, they don't have anybody to sell it to or anywhere to put it... that's just an issue that they're dealing with right now, is just they don't know what they could possibly do with it."

Members of the Gainesville's innovation community, such as former startGNV executive board member and current EII professor Melissa White, will guide students on "a journey to reimagine recycling practices and tackle ongoing challenges at the park," a news release said.

Additionally, local artist Jen Garrett will help students explore creative ways to turn waste into meaningful art. A news release said she will help students "explore creative ways to repurpose waste materials into meaningful works of art, enriching our community in the process." Garett is known for her sculptures internationally and around Gainesville, such as the “Bounce” sculpture for the new Alachua County Sports Complex in Celebration Pointe.

"One of the big reasons that glass and plastic waste is dirty when it comes to the transfer center is because people aren't super educated on how exactly they should be disposing of glass and plastic waste," Walker said. "So what ends up happening is, you know, it gets dirty and it gets mixed... We wanted to create an artistic solution to this... We will have a few engineering focus groups that'll work on the exact process that the plant will go through to get rid of this waste once it gets there, but in terms of artwork and how we're going to approach this artistically, I imagine that one of the solutions will be raising awareness to the community about how they should be getting rid of this waste."

Solutions will be pitched to park representatives at the end of the workshop, and their feedback will be considered, in hopes of the transfer station eventually implementing the ideas.

The design thinking event will take place from 9 a.m. to 3 p.m. at UF's Herbert Wertheim Laboratory for Engineering Excellence .

IGNITE Programs

The IGNITE Creativity for Engineers Program aims to inspire innovative solutions to challenges in engineering through collaboration among students from various fields such as business, engineering and art. It promotes teamwork, collaboration and innovation across academic programs in an effort to inspire "creative collision" on campus, a news release said. While other IGNITE programs are geared towards engineering students, the creativity program welcomes students of all majors with a focus on art and business students.

Since the start of 2024, IGNITE has hosted a monthly series, including five creativity workshops to promote artistic thinking within the College of Engineering. A news release said these workshops feature different types of artists in theatre, painting, comics, dance and music "in hopes of cultivating a new generation of well-rounded and creative students."

Students can also take part in opportunities outside of the classroom through other IGNITE programs — a total of eight — such as a weekly seminar series, a student-led startup incubator and a student and industry engagement program, among others. Similar to the Creativity Program, a news release said these additional programs put emphasis on "inspiring a new generation of innovative and entrepreneurial minded engineers, empowering them to explore their ideas and make meaningful contributions to the academic and professional communities."

As of now, 15 students are registered for the Design Thinking Social Project on Saturday, but Walker said he expects around 30 to attend.