novel problem solving examples

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Knowledge Representations: Individual Differences in Novel Problem Solving

Associated data.

Data can be accessed by contacting the authors of the study.

The present study investigates how the quality of knowledge representations contributes to rule transfer in a problem-solving context and how working memory capacity (WMC) might contribute to the subsequent failure or success in transferring the relevant information. Participants were trained on individual figural analogy rules and then asked to rate the subjective similarity of the rules to determine how abstract their rule representations were. This rule representation score, along with other measures (WMC and fluid intelligence measures), was used to predict accuracy on a set of novel figural analogy test items, of which half included only the trained rules, and half were comprised of entirely new rules. The results indicated that the training improved performance on the test items and that WMC largely explained the ability to transfer rules. Although the rule representation scores did not predict accuracy on the trained items, rule representation scores did uniquely explain performance on the figural analogies task, even after accounting for WMC and fluid intelligence. These results indicate that WMC plays a large role in knowledge transfer, even when transferring to a more complex problem-solving context, and that rule representations may be important for novel problem solving.

1. Knowledge Representations: Individual Differences in Novel Problem Solving

Research on novel problem solving (i.e., problems with which the solver is not already familiar) is incredibly diverse, with problem solving being studied in the context of intelligence and reasoning (e.g., Bethell-Fox et al. 1984 ; Carpenter et al. 1990 ; Snow 1980 ), analogical transfer (e.g., Cushen and Wiley 2018 ; Gick and Holyoak 1980 ), expertise (e.g., Chi et al. 1981 ; Novick 1988 ; Wiley 1998 ), and even skill acquisition (e.g., Anderson 1987 ; Patsenko and Altmann 2010 ). Separately, these domains have addressed different aspects of problem solving (e.g., learning, transfer, knowledge, individual differences, strategy use, etc.) but the lack of communication across those areas has left a large hole in our understanding of how all of these complex processes interact with each other. In particular, studies involving reasoning tasks primarily focus on the role of stable individual differences, such as working memory capacity (WMC; Ackerman et al. 2005 ; Jarosz and Wiley 2012 ; Unsworth et al. 2014 ). In contrast, studies using classic problem-solving tasks or domain-specific tasks (e.g., physics problems) have focused more on strategies and knowledge ( Chi et al. 1981 ; Holyoak and Koh 1987 ; Novick 1988 ). Although individual differences in reasoning and problem solving ( Kubricht et al. 2017 ; Ricks et al. 2007 ; Sohn and Doane 2003 , 2004 ) have been studied from both a working memory and a knowledge perspective, there remain questions about how the two interact.

2. Working Memory Capacity and Problem Solving

Much of the early work that investigated individual differences in problem solving used tasks designed to measure fluid intelligence (Gf) because they have a great degree of variability and are intended to be novel, and thus they should not be driven by individual differences in knowledge ( Carroll 1993 ). These tasks were helpful in trying to isolate the non-knowledge-based cognitive processes that contributed to reasoning and problem solving. Early work in this area used tasks such as geometric analogies ( Bethell-Fox et al. 1984 ) or Raven’s Advanced Progressive Matrices (RAPM; Raven et al. 1962 ) to assess Gf. In many of these tasks, the stimuli are a series of shapes and patterns that change according to rules. The objective of the task is to extract the rules and apply them. An example of a figural analogy problem is shown in Figure 1 .

Figural analogy example. Note. An example figural analogy item used in the current study. The answer to this item is B.

Specific attributes of the stimuli have been shown to increase the difficulty of the problems. These features include how many rules and transformations are included, as well as the number of objects or elements in the problem ( Bethell-Fox et al. 1984 ; Mulholland et al. 1980 ). The difficulty in the maintenance of these transformations and elements has been ascribed to individual differences in WMC, with storage limits and attentional control being a large barrier to maintaining and manipulating all of the necessary information in memory ( Bethell-Fox et al. 1984 ; Carpenter et al. 1990 ; Jarosz and Wiley 2012 ; Mulholland et al. 1980 ; Primi 2001 ).

Though there are currently many different theories that postulate different structures for working memory ( Baddeley 2000 ; Barrouillet et al. 2004 ; Cowan 2005 ; Oberauer et al. 2003 ; Unsworth 2016 ), Unsworth ( 2016 ) suggested three components that make up WMC: primary memory, attentional control, and retrieval from secondary memory. Each of these subcomponents may play an important role in the relationship between WMC and Gf ( Unsworth et al. 2014 ), and together explain virtually all of their shared variance. For example, the capacity account ( Carpenter et al. 1990 ) of the WMC and Gf relationship would argue that primary memory allows one to hold the various rules, objects, or goals and subgoals required in a temporary storage space during problem solving. According to the distraction account ( Jarosz and Wiley 2012 ; Wiley et al. 2011 ), attentional control provides the necessary resources to focus on desired information while ignoring irrelevant or distracting information coming from within or between problems. Retrieval from secondary memory is the process of retrieving previously learned information and can be useful in retrieving rules and transformations that correctly led to previous solutions, a key process in the learning account ( Verguts and De Boeck 2002 ). Each of these components explains unique variance in WMC ( Unsworth 2016 ; Unsworth et al. 2014 ; Unsworth and Spillers 2010 ) and appear to uniquely contribute to problem solving and reasoning ( Unsworth et al. 2014 ). However, although these subcomponents can fully explain WMC’s relationship with Gf, WMC does not account for all of the variability found in Gf tasks ( Ackerman et al. 2005 ; Kane et al. 2005 ; Oberauer et al. 2005 ).

Although the role of WMC has been heavily studied within reasoning tasks, the mechanistic role it plays during solution and how WMC processes differ from other cognitive processes involved in reasoning tasks remain unclear. Kovacs and Conway ( 2016 ) argue that Gf is unlikely to be a unitary construct and, rather, performance on Gf tasks reflects multiple basic processes that are necessary for most Gf tasks. Given that WMC is also comprised of more basic processes and that the shared processes between WMC and Gf do not account for all of the variability in Gf ( Ackerman et al. 2005 ; Kovacs and Conway 2016 ; Unsworth et al. 2014 ), other mechanisms must be considered to fully understand individual differences in reasoning and problem solving.

3. Individual Differences in Knowledge

The reasoning literature primarily focuses on tasks where the solver has no knowledge, but this is not entirely reflective of problem solving encountered in a real-world setting. In most cases, solvers will have some knowledge pertaining to the problem or will be able to look up information about the problem. Understanding when and how information from memory is used during problem solving is crucial to understanding problem solving as a whole.

3.1. Expertise and Representation

Several studies investigating the effects of expertise on problem solving have shown drastic differences in how experts solve problems in their field when compared to novices. The classic study by Chase and Simon ( 1973 ) demonstrated an extreme form of chunking, with chess experts recalling four times the information that novices did. Additional research indicated that WMC could help to compensate for a lack of knowledge ( Sohn and Doane 2003 , 2004 ), but also that expertise could compensate for a lower WMC, as knowledge becomes more proceduralized and automatic ( Patsenko and Altmann 2010 ).

In addition to having access to more information in memory, experts also show distinct differences from novices in how they represent that information in memory. Experts tend to focus on deeper, more semantically driven representations of problems, whereas novices are more likely to focus on surface features that may not actually be helpful in solving the problem ( Chi et al. 1981 ). Experts’ knowledge representations tend to be highly interconnected, which enables them to move quickly and freely between concepts that are related ( Kohl and Finkelstein 2008 ). Experts are also better at solving problems that are lacking in a clear goal or representation ( Simon 1977 ) by adding in constraints and elaborating on the problem, while novices simply start listing answers or responses to the problem ( Voss et al. 1983 ). Indeed, experts have been shown to create and use goals and subgoals when stuck, whereas novices engage more in exploration ( Hershey et al. 1990 ; Kohl and Finkelstein 2008 ). Experts’ ability to create goals, Hershey et al. ( 1990 ) argue, comes from having plan-like scripts or schemas to help direct them. These highly developed scripts for familiar problems function similarly to productions in the skill acquisition literature, where the scripts and plans increase automaticity. Taken together, this suggests that experts do not simply have more knowledge, but are creating interconnected, abstract representations that benefit them in future problems.

3.2. Analogical Transfer

The analogical transfer literature focuses on the ability to generalize previously learned information given in a source problem to a new target problem. Looking at how participants solve a target problem after being given a structurally identical source, multiple studies have found that participants are unlikely to spontaneously transfer solutions ( Gick and Holyoak 1980 , 1983 ; Holyoak and Koh 1987 ; Novick 1988 ), and even hints do not guarantee transfer ( Gick and Holyoak 1983 ). However, giving participants additional source problems, especially those presented in a spaced-out structure ( Gick and Holyoak 1983 ; Wharton et al. 1994 ), as well as giving participants a delay between problems ( Holyoak and Koh 1987 ), has been shown to be helpful in building better representations. Findings from the skill acquisition literature also replicate the positive effects of including additional source problems and presenting them in a spaced presentation ( Carlson and Yaure 1990 ). Creating a deeper and richer representation appears to be a key element in transferring knowledge.

Although the representation of the source is crucial for understanding structural similarities between analogs, surface similarities (i.e., how much the problems superficially resemble each other) between the source and the analog also contribute to analogical transfer ( Holyoak and Koh 1987 ) by acting as a cue that there is relevant information in memory. In the absence of surface similarities, solvers must rely on their own internal ability to retrieve a previously learned solution. If solvers represent the source based upon its surface features, then it is less likely that solvers will easily retrieve the source when given a dissimilar target. However, if solvers represent the source in a more general and abstract way (i.e., an emphasis on the deep structure of the source problem, and not surface features), then the target should be a sufficient cue to retrieve the source because the structure, rather than the surface features, is the focus point.

There is some evidence to suggest that the ability to generalize previously learned solutions may actually be driven by WMC or reasoning processes. Kubricht et al. ( 2017 ) indicated a positive relationship between analogical transfer and Gf, with additional aids (e.g., providing more source problems) benefitting low-Gf individuals, whereas high-Gf individuals performed well regardless of whether those aids were present. This suggests that high-Gf individuals can more easily form general and abstract representations of the source that can then be transferred more readily. Similar studies have demonstrated the role of diffuse attention in analogical transfer ( Cushen and Wiley 2018 ). Increased attentional resources stemming from WMC may cause fixation on irrelevant details that prevent an individual from noticing that a source and analog are related. In the absence of a more general representation, diffuse attention may help in noticing more remote relationships. Furthermore, the ability to access remote ideas may be helpful in generating more general representations. The results from a study by Cushen and Wiley ( 2018 ) demonstrate that performance on the Remote Associates Test does indeed predict analogical transfer, even after accounting for WMC. Furthermore, Remote Associates Test performance also predicted the completeness of someone’s representation (as measured by a summary of the source problem). However, these results are incongruent with Storm and Bui ( 2016 ), who found that the propensity to mind wander negatively predicted analogical transfer, even if hints were included. It is possible that performance on the Remote Associates Test taps into an ability to reach remote ideas that is not driven by diffuse attention, or that diffuse attention is only helpful for a portion of the analogical transfer process. Cushen and Wiley ( 2018 ) note that once a relationship has been established, the solver must still map the source to the analog. Thus, analogical transfer as a whole may require flexibility in the capacity to use multiple processes.

3.3. Learning on Novel Tasks

Despite the fact that many tasks used to study reasoning are intended to provide novel situations, that does not mean that learning cannot occur throughout the task. Several studies involving Gf tasks have demonstrated that participants learn the rules during the task and use them as they approach new problems ( Bors and Vigneau 2003 ; Harrison et al. 2015 ; Loesche et al. 2015 ; Verguts and De Boeck 2002 ). Although participants may be using this information to help them solve problems, the ability to learn these rules well and apply them is more complicated than simply solving a problem correctly. Loesche et al. ( 2015 ) provided participants with the rules before completing the RAPM, and although performance did improve, it did not increase to such a point that knowing the rules was sufficient for solving all problems on the RAPM. They noted that this finding was especially sensitive to how well participants initially learned the rules. This is consistent with previously discussed findings in both the skill acquisition literature ( Carlson and Yaure 1990 ; Cooper and Sweller 1987 ) as well as studies looking at analogical transfer ( Gick and Holyoak 1983 ; Kubricht et al. 2017 ; Wharton et al. 1994 ). Interestingly, increases in performance due to rule knowledge do not necessarily change the validity of the tests. Schneider et al. ( Schneider et al. 2020 ; Schneider and Sparfeldt 2021a , 2021b ) demonstrated that though learning the rules could increase test performance across several Gf tasks, this increase did not change those tasks’ correlations with other measures of intelligence. This further emphasizes the need to understand how, mechanistically, learning rules influences solution success.

Learning on the RAPM is also sensitive to feedback, as well as exposure to rules throughout the task ( Verguts and De Boeck 2002 ). Additionally, even if participants are given the same problems over multiple sessions, they are inconsistent in solving them. This is true even if they correctly solve the problem the first time ( Bors and Vigneau 2003 ). These results clearly demonstrate that learning and knowledge do play a role in reasoning tasks, but also that previously solving a problem is not a guarantee for solving the same or a similar problem again. An individual’s ability to recognize that previously learned information is relevant, as well as their ability to successfully retrieve the relevant information, are additional processes to consider in conjunction with problem solving or reasoning processes.

Problem solving is clearly a complex task that draws upon many different cognitive processes. Individual differences in WMC are a large contributing factor to problem solving success ( Ash and Wiley 2006 ; Carpenter et al. 1990 ; Sohn and Doane 2003 ; Unsworth et al. 2014 ), but there also appears to be room for other processes. Individual differences in knowledge also play a significant role in problem solving ( Bors and Vigneau 2003 ; Chi et al. 1981 ; Luchins 1942 ; Wiley 1998 ). This knowledge can come in the form of expertise or as information that was learned on a previous problem, depending on the task. There is, however, a more complex relationship between knowledge and problem solving. More knowledge does not necessarily mean improved performance ( Bors and Vigneau 2003 ; Gick and Holyoak 1980 ). Sometimes knowledge can lead to fixation ( Luchins 1942 ; Wiley 1998 ), sometimes knowledge is not necessary if an individual has high levels of other cognitive abilities, such as WMC ( Sohn and Doane 2003 , 2004 ), and sometimes knowledge cannot be used because the individual is unable to transfer it to another problem ( Gick and Holyoak 1983 ; Holyoak and Koh 1987 ; Kubricht et al. 2017 ). What seems to be generally beneficial is the production of a general, abstract representation. In addition, the roles of WMC and knowledge are not necessarily completely distinct, and they likely influence each other.

5. The Present Study

Although the combination of several literatures has provided information on how knowledge and WMC contribute to and interact during problem solving, there are several research questions that have remained unanswered. Of primary concern are the differential problem-solving processes accounted for by WMC and knowledge. WMC clearly contributes to problem solving, but the mechanisms through which it acts remain under debate ( Carpenter et al. 1990 ; Verguts and De Boeck 2002 ; Wiley et al. 2011 ). Because WMC may contribute to knowledge at the encoding stage as well as the retrieval stage, it is important to identify what is breaking down when a solver fails to find or transfer a solution.

To start to isolate knowledge-specific problem-solving processes from general cognitive processes (e.g., attention) in the present study, several changes were made to existing methods in the problem-solving domain. Concerns with analogical transfer stimuli (i.e., using a small sample of fairly difficult problems) were resolved by using a figural analogy task. This ensures that there are multiple target and source problems, as well as making it easier to create problem isomorphs. Additionally, a reasoning task contains more active problem solving than when solely using classical analogical transfer materials. This ensures that there is enough variability in the task that individual differences in problem-solving skill will still be measured.

To keep track of knowledge and transfer throughout the task, stimuli were constructed such that all problems could be decomposed into rules. For example, one problem may require two objects to swap locations, a rotation of those objects, as well as a size change. Another problem may only require a rotation and a size change. Problems were considered unique based upon the combination of rules. To test the effects of increased knowledge on problem solving and transfer, participants first learned a select set of individual rules during a training phase, then were tested on more complex problems involving multiple rules. Figure 2 provides an illustration of the general procedure.

Diagram of figural analogy procedure.

To avoid biasing participants towards a particular representation of the rule, participants were not given the rule explicitly. Rather, rules were learned by solving simple problems that contained only one of those rules, (e.g., a problem where the answer is a single size change). The single-rule problems were designed to be solved fairly easily, such that participants could induce the rule on their own. This was accomplished by only using one rule, reducing the visual complexity of items compared to the standard figural analogies task, and reducing the number of response options from five to four. Furthermore, two variations of each rule were shown during the training phase.

During the test portion, participants solved items that included at least two rules. Half of the test items were comprised of only the rules given in the training portion, and the other half were comprised of entirely new rules. If participants were able to successfully transfer the rules learned in the training portion, even in a context where multiple pieces of information must be used, then participants should have higher accuracy on the test items that were comprised of the trained rules when compared to the items that consist of new rules.

Both the expertise literature and the analogical transfer literature have demonstrated that knowledge representations are crucial to knowledge being used, with an emphasis on structure and less emphasis on surface features being particularly beneficial for transferring that knowledge. As such, the representation quality of the rules may be critically important. To measure this, participants were asked to rate numerically how similar they thought two problems were. Participants were shown only the A:B component of a problem rather than the full version with A:B :: C:? so that they could focus on the rule and not on problem solving. The A:B components they saw came from the rules shown in the initial training phase problems. This ensured that participants were making similarity judgements on items for which they had successfully induced the rule previously. Of primary interest was how closely the individual rated slightly different versions of the same rules compared to completely different rules. For example, did the solver rate a 90-degree rotation rule and a 45-degree rotation rule as equally different when compared to a rotation rule and a size-change rule, or did they treat the two versions of the rotation rule as equally similar as two different 90-degree rotation problems? Where participants fell on this spectrum was used to assess their representation, with participants ranging from more general representations (the 90-degree rotation and 45-degree rotation were very similar) to more item-specific, less general representations (the 90-degree rotation and 45-degree rotation were treated as completely separate rules).

If rule representations do indeed help to facilitate retrieval, then more general representations should correlate with higher accuracy on the trained-rule problems. Ratings on the rule representation measure may also correlate with performance on novel-rule problems because the processes that facilitate the generation of general representations may also play a role in other reasoning processes. However, it is expected that there would be a stronger relationship for the trained-rule problems because the novel-rule problems should not be drawing on retrieval processes as much.

The final set of factors to consider is the role of individual differences in WMC and reasoning. It is unclear whether WMC and/or Gf help to develop more general representations, but it is reasonable to expect that WMC and Gf will interact with the training. Because WMC may play a large role in initially learning the rules and then later facilitating the retrieval of those rules during problem solving, WMC should have a stronger relationship with accuracy for the trained items, and Gf should have a stronger relationship with accuracy for the novel items. Furthermore, relationships between the individual differences measures and the rule representation measures can be investigated. Specifically, one question is whether or not the rule representation measure can explain unique variability on the figural analogies task, or if WMC/Gf determine the quality of the representation. If the rule representation measure does uniquely explain performance on the figural analogies task after accounting for WMC and Gf, then this would provide a novel measure that could potentially explain solution transfer. If, however, the knowledge representation measure can be explained by WMC/Gf, then this would provide some further specificity on why WMC and/or Gf explain performance. Whether rule representations correlate or are predicted by WMC or Gf will also be investigated. This will help to further clarify if rule representations are truly unique, share some processes with WMC and/or Gf, or can be entirely explained by WMC and/or Gf.

6.1. Participants

The target sample size for the study, after accounting for participants who fail to complete the tasks correctly or outliers, was set at 200 participants. This was based on simulated analyses demonstrating that 200 participants would be sufficient for detecting moderate effect sizes within a regression model containing a continuous predictor variable, a binary predictor variable, and an interaction term between the two predictor variables. Furthermore, correlations ranging from .3 to .5 begin to stabilize (remain within a window of ±.1 at 80% confidence) at around 212 and 143 participants, respectively, indicating that 200 participants should be sufficient in detecting moderate correlation coefficients as well ( Schönbrodt and Perugini 2013 ). However, because the study was administered entirely online and previously collected online studies at this university have had attrition rates ranging from 40–50%, a new target of 400 participants was set. A total of 418 participants, collected from a pool of Mississippi State University students, completed all tasks in the study. Of those 418 participants, 173 participants failed to meet the inclusion criteria for one or more of the tasks. Twenty-five additional participants were removed for falling outside of 2.5 standard deviations away from the mean on at least one of the tasks or were multivariate outliers, according to Mahalanobis distance ( Ghorbani 2019 ). This resulted in a final sample of 220 participants.

6.2. Materials

6.2.1. modified figural analogies task.

The modified figural analogies task is based on the figural analogies test by Lohman and Hagen ( 2001 ; Form 6, Level H, Test 8 of the cognitive abilities test). Some of the items from the original task were used in the modified version, but most of the items were created specifically for this experiment. In the standard figural analogies task, participants are shown a set of objects in the form of A:B :: C:? Participants must induce the rule(s) governing the changes from A to B and then apply that rule to the analog, C. Participants select their answer from five response options. An example item is shown in Figure 1 .

The modified figural analogies task was split into three parts: a training portion, the Rule-Similarity Judgement Task (RSJT), and a test portion (see Figure 2 ). For the training portion, participants solved figural analogies items that consisted of only one rule. Thus, participants could learn the rule easily, but it was still through their own induction processes. Then, for the RSJT, participants saw the A:B portion of two figural analogy items and rated how similar they thought the two rules were. The RSJT only used rules that were present in the training portion. Lastly, participants solved a series of figural analogy test items that more closely resembled the items normally shown in the figural analogies task. The test items were comprised of two or three rules, with some items being comprised of rules seen in the training portion and other items being entirely novel. Participants solved both types of problems and the two sets were counterbalanced across participants so that each set of rules was used as the training set and as the novel set at some point.

Figural Analogies Training

The participants solved 14 problems in the training portion; 2 problems for each rule. The two problems for each rule were slightly different versions of the rule. For example, for the “size change” rule, one problem was a size change where the object increased in size and the other was a size change where the object decreased in size. This resulted in a total of 14 single-rule items to be used in the training portion for each set, and 28 different versions in total. Participants only solved one set of 14 problems (7 rules) in the training portion because the other set of 7 rules was used to make up the novel rules condition in the test portion.

Prior to data collection, a larger set of rules were piloted. Some of the rules originated from the original figural analogies task, whereas others were generated specifically for this study. Pilot data indicated that the final set of 14 rules were all treated as distinct by participants and that the expected interpretation of the rule matched with participants’ verbal descriptions of the rules. For example, many participants described a rule wherein an object duplicates as “double”, “duplicating”, “multiply by 2”, “copy shape” or some other variation. These types of responses were consistent for the other rules, wherein there was some variation in the words participants chose, but the overall explanation aligned with the expected interpretation. The full list of rules, and which set they belonged to, can be found in Appendix A . Participants were given an unlimited amount of time to solve the training items. Because the validity of the RSJT and the effect of training both depended on participants successfully inducing the rules, participants were removed from analyses if they missed more than 4 problems in the training portion. Of the 418 participants that completed all tasks, 89 failed to meet the inclusion criteria for the training portion.

Rule-Similarity Judgement Task (RSJT)

After solving the 14 training items, participants made similarity judgements on the rules using a scale that ranged from 0 to 100, in intervals of 5. They were shown all of the items in a random order and had unlimited time to make the judgement.

Participants were shown only the A:B portion of the problem so that they could focus on only the rule. The rules used in the similarity judgement portion were the same rules used in the training portion, so participants had already demonstrated their ability to induce the single rule, which is necessary for making a comparison. Each comparison could be categorized into three conditions: the exact same version of the same rule (“same-version comparison”), two different versions of the same rule (“different-version comparison”), and different versions of different rules (“different-rule comparison”). Examples of the stimuli are provided in Figure 3 . An example of the same-version comparison condition would be a comparison between two different 90-degree rotation items. An example of the different-version condition would be a 90-degree rotation item and a 45-degree rotation item comparison. An example of the different-rule condition would be a 90-degree rotation item being compared to an increase in size; the size-change rule.

RSJT comparison stimuli example. Note. The same version comparison example includes two swap rules, the different version comparison includes two slightly different swap rules, and the different rule comparison includes a swap rule and a size change rule.

Pilot analyses indicated that participants were responsive to the different types of comparisons, with the average rating for same-version comparison being the highest ( M = 82.33, SD = 28.55), and the average rating for different-version comparison ( M = 56.56, SD = 35.95) being between same-version and different-rule comparisons ( M = 18.32, SD = 25.06). Furthermore, there were almost no two rules that were treated as being too similar, except for three different-rule comparisons that had an average rating over 30. These rules, however, were separated into different groups to prevent any issues that might have been caused by their similarities. Finally, subtle differences in the types of rules (quantifiably different rules, such as rotation, vs. qualitatively different rules, such as color change) did not systematically contribute to participants’ similarity judgements.

In order to provide a sufficient number of comparisons, six A:B items were created for each rule, including three for each rule version (i.e., three 90-degree rotation items and three 45-degree rotation items). The six A:B items were drawn with enough variation that there were no isomorphs during the same-version comparisons. However, all items were drawn with most shapes being square-like to encourage participants to look at the rule and not simply make a similarity judgement based upon surface features. An example of the six items for the numeracy rule is shown in Figure 4 . With six items, six same-version comparisons were shown (three per rule), six different-version comparisons were shown (more combinations were technically possible, but six comparisons were randomly selected), and twelve different-rule comparisons per rule were shown. Although more combinations are possible, only two comparisons per rule (one per version) were selected to be matched with other rules. This resulted in a total of 126 comparisons: 42 same-version comparisons, 42 different-version comparisons, and 42 different-rule comparisons. All comparisons were shown in a random order across all participants. Prior to starting the similarity judgement portion, participants were given three practice trials, one per comparison type, so that they could adjust to the procedure and the types of comparisons they would be making.

Numeracy A:B items. Note. Examples of the RSJT items used for the numeracy rule.

To ensure that participants were completing the similarity judgement task appropriately and not simply selecting random responses, a t -test was calculated for each participant to determine if they were treating the same-version rule condition differently than the different-rule condition. Given that these fall on two extremes, participants should rate these differently, and thus this served as a manipulation check. Of the 418 participants that completed all tasks, 57 failed to meet the inclusion criteria for the RSJT.

Figural Analogies Test

For the test portion, participants completed a total of 30 figural analogy problems. Half of the problems were comprised entirely of rules used in the training portion and the other half were comprised of novel rules. However, what constituted trained rules or novel rules depended on which set of rules the participant received in the training portion, with the two set of rules counterbalanced across participants. Pilot analyses from a larger sample of figural analogy problems were used to create the sample of thirty problems to ensure that the two sets of problems were equal in difficulty. The figural analogies test problems consisted of two or three rules (seven two-rule problems for Set A and nine for Set B, with the remainder of the set being three-rule problems), with some problems consisting of entirely distinct rules, whereas other problems used two versions of the same rule in a problem (paired-rule items). The paired-rule items were introduced to increase the number of problems used in the figural analogies test portion while still ensuring that no two problems used the same combination of rules. Furthermore, the practice of using two rules conditional on some other factor (such as the size of the object) is a technique used in the RAPM ( Raven et al. 1962 ) and therefore has precedent for being used in a Gf task. The distinct-rule items could be comprised of two or three rules, but the rules were always unique (e.g., color change, size change, and rotation). The paired-rule items could also consist of two or three rules, but always included two rules that were actually two versions of the same rule. For example, one problem may have a 90-degree rotation for the larger object and a 45-degree rotation for the smaller object. If the paired-rule item consisted of three rules, then the third rule was an additional distinct rule. Pilot analyses indicated that the paired-rule items did not differ in difficulty when compared to the distinct-rule items. Set A did include more paired-rule items than Set B (nine and seven, respectively), but this was a result of prioritizing balanced difficulty across the two sets.

Participants were shown the 30 problems in a random order and were given a maximum of 60 s to solve the problem. If they had not selected a response after 60 s, they were moved to the next problem and that item was marked as incorrect. To encourage accurate performance on the task, a 20 s penalty screen appeared if participants selected a response in less than 5 s and it was incorrect. The screen notified the participant that they selected their response quickly and encouraged them to make sure that they were performing the task correctly. To serve as a manipulation check, the example figural analogies item shown in the instructions (A:a :: R : ?) was drawn to resemble the figural problems more closely (adding triangles and rectangles around the letters) and placed randomly in the figural analogies test portion. Participants that failed to solve the manipulation check item (52/418) were removed from analyses.

6.2.2. Working Memory Capacity

Automated operation span.

The automated operation span ( Unsworth et al. 2005 ) is a complex span working memory task that tests an individual’s ability to remember letters while solving simple math problems in between the presentation of the letters. For the math portion, participants were shown a simple math problem followed by a number. They had to determine if the number was the answer to the previous problem or not. They were then shown a letter that was to be recalled at a later time. After several iterations, participants were asked to recall the letters in the sequence that they saw them in. Participants completed 2 blocks, with each sequence length, ranging from 3 to 7 letters, being presented once per block. The task was scored using the partial scoring method, where a participant’s total is comprised of the total correct letters recalled in the correct position of the sequence. Participants completed a shortened version ( Foster et al. 2015 ) of the task (two blocks instead of three) to try and reduce fatigue because participants completed all tasks online. Participants were removed if they failed to score at least 80% accuracy on the math portion (40/418).

Automated Symmetry Span

The automated symmetry span is very similar to the automated operation span, but it uses visual stimuli rather than verbal stimuli ( Unsworth et al. 2009 ). Instead of math problems, participants determine if an image is symmetrical or not. Then, they are shown a 4 × 4 grid with a single red square filled in. After several iterations, of which range from 2 to 5 to be remembered red squares, participants recall the location of the red squares in the sequence they were presented. Participants completed two blocks ( Foster et al. 2015 ) and the task was scored using the partial scoring method. Participants were removed if they failed to score at least 80% accuracy on the symmetry portion (59/418).

6.2.3. Gf Measures

Paper folding task.

The paper folding task ( Ekstrom et al. 1976 ) shows participants a piece of paper that is then folded several times. A hole is then punched through the folder paper and participants must determine what the unfolded paper would look like. Participants were shown a total of 20 items, with 3 min to complete the first 10 and another 3 min to complete the second set of 10. An example item is shown in Figure 5 . Because it was easy to click through this task and the study was administered online, participants were excluded from all analyses if their average response time across all items was less than two seconds (25/418).

Example of paper folding item. Note. A paperfolding example from Ekstrom et al. ( 1976 ).

Letter Series

The letter series task ( Kotovsky and Simon 1973 ) requires participants to identify a pattern in a sequence of letters and provide what the next letter in the sequence would be according to that pattern. For example, participants might be given ‘ababababa’, with the correct answer being ‘b’. Participants solved 15 items with no time limit for the task. Similar to the figural analogies test portion, however, participants were shown a 20 s time penalty screen if they selected their response in less than 5 s and it was incorrect. To find participants that were clicking through the task, the problem “abcde” was added as the tenth item (changing the total to 16 items). However, after data collection was completed, it was realized that “abcde” could be solved with multiple answers, so instead participants were excluded from analyses if their accuracy was less than three. Three was chosen because the first two items of the letter series task are extremely easy and most participants did solve the “abcde” item correctly, suggesting that most participants genuinely doing the task should be able to solve at least three problems correctly. Of the 418 participants that completed all data, 66 failed to meet the inclusion criteria for the letter series task.

6.3. Procedure

Participants completed all tasks in a single session, entirely online. Participants were told prior to starting the study that they must complete the study in one sitting so they should only begin when they are ready. Participants were given a final warning screen before starting the study to not begin unless they were ready. Participants completed the modified figural analogies task first, followed by the automated operation span task, the symmetry span task, the paper folding task, and the letter series task. All tasks were completed in this order, with a short one-to-two-minute break provided between each task.

Composite scores were generated for the WMC and Gf measures by taking performance on the two tasks (operation span and symmetry span for WMC and paper folding and letter series for gf), z -transforming the scores, and then taking the average of the two tasks 1 . For the modified figural analogies task, three rule-representations scores were generated from the RSJT, one score for each type of comparison (i.e., the same rule and the same version of the rule, or “same version”; the same rule but a different version of the rule, or “different version”; or a different rule and different version, or “different rule”). These were calculated by first recentering all the scores for each participant such that their minimum score became −1 and their highest score became 1. The recentering was performed across all of their judgement scores and was not split by type of comparison. This was carried out to account for participants using the scale differently 2 . Next, the average score was taken for each type of comparison for each participant, producing three scores: their average same-version comparison score, different-version comparison score, and different-rule comparison score. The primary measure of focus was their average score for the different-version comparisons. If participants have a positive value for their different-version score from the RSJT, then this would indicate that they are treating the different-version items similar to the same-version items, suggesting their representation of that rule is more general and that they are not treating different versions as entirely different rules. Conversely, if their different-version score is negative, then this would indicate that they are treating the different-version rules as separate rules.

7.1. Summary Statistics and Correlations

All summary statistics are included in Table 1 and the correlations between all tasks are shown in Table 2 . The RSJT scores were split by the two stimulus sets in Table 1 so that reliability could be calculated for each set. Reliability was calculated using Cronbach’s alpha at the item level for the figural analogies test items, letter series, and the RSJT same-version and different-version scores (averaged across each rule, treating it as an item). Split-half reliability was used for paper folding and the RSJT different-rule scores. Split-half reliability was used for the RSJT different-rule scores because they could not be averaged by rule, as two rules were shown in the different-rule comparisons. Parallel-forms reliability was used for operation span and symmetry span.

Descriptive statistics.

Note . FA refers to figural analogies, SV refers to same version, DV refers to different version, and DR refers to different rule.

Task correlations.

Note. * p < .05. FA refers to figural analogies, SV refers to same version, DV refers to different version, and DR refers to different rule.

7.2. Predicting Figural Analogies Accuracy with Training, RSJT Scores, WMC, and Gf

The first set of analyses investigated whether accuracy on the figural analogies test items changed as a function of training, the participant’s rule representation as measured by the RSJT different-version scores, and the WMC and Gf measures. To determine this, generalized linear mixed-effects models (GLMM) were used to predict item accuracy on the test items with the fixed effects hierarchically introduced. A logit link function was used to predict the binary accuracy data. The maximum random effects structure included random intercepts for subject and item, with random slopes added for training for both subject and item. The general procedure for the models was to include all fixed effects and the maximum random effects structure initially and to then gradually reduce the complexity of the random effects structure if the model failed to converge or was singular ( Bates et al. 2015 ; Matuschek et al. 2017 ). The structure could be reduced by removing correlation parameters or removing random effects that failed to explain a significant portion of variance (i.e., if variance was not greater than zero at α = 0.20). All binary predictors were coded using sum contrast coding (−1, 1) and all continuous predictors were z -transformed.

The first model predicted figural analogy accuracy with fixed effects for the training (items comprised of previously seen or novel rules) and the participants’ RSJT different-version score with a test for an interaction between RSJT different-version scores and training. The results of the model, Model 1, are shown in Table 3 . There was a significant interaction between the training manipulation and RSJT different-version scores, shown in Figure 6 ; however, the relationship was in the opposite direction of what was predicted. The interaction illustrates a small relationship between RSJT different-version scores and accuracy, but only when participants are solving problems comprised of novel rules. The RSJT scores did not predict accuracy at all for the trained items. It is worth noting that only three participants fell outside of −1.7 standard deviations away from the mean for the RSJT different-version scores but were within −2.5 standard deviations. The removal of these participants did not change the results of the model.

Interaction between RSJT different-version scores and training. Note. The plot was generated using the predict function in R to generate log odds ratio accuracy data based upon Model 1 ( Table 3 ). The data points represent item level data for all participants and the linear slopes were generated with the geom_smooth function in ggplot. The circles represent trained-rule items and the squares represent novel-rule items.

Predicting figural analogy accuracy with RSJT different-version scores, WMC, and Gf.

Note. Training was coded with −1 for the novel-rules condition and 1 for the trained-rules condition. DV refers to different version.

The next analysis introduced the WMC and Gf composite measures into the GLMM. WMC and Gf were added into the models to determine if rule representations accounted for unique variance or if they could be explained by other processes. Both WMC and Gf measures were included because prior work investigating analogical transfer has shown that Gf may contribute to building representations ( Kubricht et al. 2017 ), but WMC was not accounted for in that study.

WMC and Gf were added on top of the RSJT different-version scores, with WMC and Gf also tested for interactions with training. Because the inclusion of interaction terms can make it difficult to interpret main effects, nonsignificant interactions were removed for the final model, Model 4. However, the WMC and Gf models with all interaction terms are also included. All models’ results are shown in Table 3 . For WMC, shown in Model 2, there was no significant interaction with training, though WMC did predict accuracy on the figural analogies task. For Gf, in Model 3, there was also no significant interaction, but Gf did predict accuracy on the figural analogies task. The interaction between RSJT different-version scores and training did remain significant after including both Gf and WMC, indicating that the RSJT scores were measuring something unique from Gf and WMC.

7.2.1. Interim Discussion: Task Learning

The interaction between RSJT different-version scores and training was in an unexpected direction. These results may indicate that processes that would normally be beneficial in solving figural analogies problems become less important or less likely to be used when participants have been trained on the rules. This is similar to findings in the expertise literature, where dependence on other cognitive processes, such as working memory, decreases as expertise increases. The lack of an interaction between WMC and training was also unexpected, given prior work showing that the relationship between performance on Gf tasks and WMC changes depending on whether items are comprised of novel or previously seen rules ( Harrison et al. 2015 ; Loesche et al. 2015 ; Wiley et al. 2011 ). However, it has also been noted that participants learn throughout a task, even if all of the rules are novel, and that the frequency of rules used can bias participants’ expectations and use of rules ( Verguts and De Boeck 2002 ). Therefore, a post hoc analysis was conducted to investigate the relationship of WMC and training on accuracy while also accounting for learning throughout the task.

7.2.2. Task Learning Post Hoc Analysis

Learning throughout the task was assessed using trial number, so a separate analysis tested for a three-way interaction between WMC, training, and trial number, while predicting accuracy on the figural analogies task. The results of the GLMM are shown in Table 4 . The three-way interaction was significant ( p = .003), as shown in Figure 7 . Post hoc comparisons demonstrated that WMC and trial continued to interact for the novel-rule items ( p = .021) but not for the trained-rule items ( p = .07). However, there was still a main effect of WMC ( p < .001) and trial ( p = .02) for the trained-rule items (even with the interaction term removed). The models for the post hoc comparisons can be found in Appendix A . The results of the three-way interaction and the post hoc comparisons suggest that high-WMC individuals improve on the novel-rule items over time whereas the low-WMC individuals do not. Although the interaction term between WMC and trial was not significant for the trained-rule items, the main effects of WMC and trial indicate that high-WMC individuals were more likely to solve trained-rule items, but both high and low-WMC individuals improved on the trained-rule items over time. Notably, there were no significant interactions with Gf for training and trial number, so these results appear to be unique to WMC.

Interaction between WMC, training, and trial. Note. The plot was generated using the predict function in R to generate log odds ratio accuracy data based upon the model in Table 4 . The data points represent item-level data for all participants and the linear slopes were generated with the geom_smooth function in ggplot. The model was analyzed with WMC as a continuous predictor but a tertiary split was used to plot the data. The circles represent trained-rule items and the squares represent novel-rule items.

Predicting figural analogy accuracy with WMC, training, and trial.

Note. Training was coded with −1 for the novel-rules condition and 1 for the trained-rules condition.

7.3. Predicting RSJT Different-Version Scores

After investigating the relationship between memory retrieval and accuracy, a closer look at the rule representation measure was conducted to determine if WMC and/or Gf could explain the ability to generate more general rule representations. The second analysis used a linear mixed-effects model (LMM) to predict the RSJT different-version scores for each rule, with the WMC and Gf measures used as predictors. The random effects structure included random intercepts for subject and rule. The p -values were generated using the lmertest package in R. The results of the model can be found in Table 5 . Neither Gf nor WMC predicted the RSJT different-version scores.

Predicting RSJT different-version scores.

7.3.1. Interim Discussion: Further Investigating the RSJT Scores

The lack of a relationship between RSJT different-version scores and figural analogies accuracy on trained items, as well as the fact that RSJT same-version scores appeared to better correlate with figural analogy accuracy, prompted a deeper inspection of the RSJT scores and what they may actually measure. The original intention with the RSJT was to use the different version comparison scores only, because it was assumed that most participants would rate the same-version comparisons as very close to 1 and the different-rule comparisons as very close to −1, reducing those measures to be at the ceiling or at the floor. Although same-version comparisons were rated the highest on average and the different-rule comparisons were rated the lowest on average, there were no ceiling or floor effects, thus making these other RSJT scores potentially meaningful.

It is also possible that different processes are beneficial when solving an item that has two very similar rules included in a single item. The two types of figural analogy items, distinct-rule items (items comprised of all unique rules) and paired-rule items (items where two versions of the same rule appear in the same item), were originally developed to help control for difficulty across the two sets and to allow for a larger set of items by repeating rules. This requires the solver to be open to different variations of a rule and to not be overly fixated on a single element of the rule. Yet, it also requires that the solver does not over-generalize such that they cannot distinguish between the two highly similar rules. As such, the following analyses explore both the other two RSJT measures and their impact on different types of items.

7.3.2. Further Investigating the RSJT Scores Post Hoc Analyses

The first analysis sought to determine if each of the three RSJT scores measure different constructs. The three measures were used as simultaneous predictors in a GLMM predicting figural analogies accuracy. The results are shown in Table 6 . The RSJT same-version and RSJT different-rule measures did uniquely predict accuracy, but the RSJT different-version did not predict accuracy, congruent with prior analyses.

Predicting figural analogy accuracy with all three RSJT measures.

Note. SV refers to same version, DV refers to different version, and DR refers to different rule.

The next analysis explored whether the type of figural analogy item being solved contributed to the predictiveness of the RSJT measures. To test if the type of problem mattered, three mixed-effects models were run, each with a different RSJT measure. The models tested for a three-way interaction between the RSJT measure, training, and the type of figural analogy item (distinct or paired) with random intercepts for subject and item, and random slopes for training for both subject and item. The final models are shown in Table 7 . The type of figural analogies item only interacted with the RSJT different-version measurements. Figure 8 shows the three-way interaction between RSJT different version, training, and type of figural analogy item. Post hoc comparisons specified that the significant differences in slopes were between the novel paired-rule items and the trained paired-rule items, as well as the novel paired-rule items and the novel distinct items. All the models for the post hoc comparisons can be found in Appendix A . The results indicate that how an individual rates different versions of the same rule does predict accuracy on the figural analogies task, but only for novel paired-rule items. Furthermore, this interaction was not significant with the RSJT same-version or different-rule measures, suggesting that this is particular to the different version measure. Notably, the results found with the three-way interaction likely explain the effect found in the first analysis, with RSJT different version interacting with training. Finally, the lack of a main effect of item type, as well as a two-way interaction between training (namely in the same version and different rule models that do not include the three-way interaction term), indicate that the type of item did not contribute to overall accuracy and is also not responsible for any of the training effects.

Interaction between RSJT different version scores, training, and item type. Note. The plot was generated using the predict function in R to generate log odds ratio accuracy data based upon the different-version model in Table 7 . The data points represent item-level data for all participants and the linear slopes were generated with the geom_smooth function in ggplot. The circles represent trained-rule items and the squares represent novel-rule items.

Predicting figural analogy accuracy with RSJT measures, training, and item type.

Note. Training was coded with −1 for the novel-rules condition and 1 for the trained-rules condition. Item type was coded with −1 for the paired-rule items and 1 for the distinct-rule items. SV refers to the same-version score, DV refers to the different-version score, and DR refers to the different-rule score.

7.3.3. Interim Discussion: Measuring Different Version Relative to Same Version and Different Rule

The original different-version measure represented an individual’s average score for the different-version comparisons after rescaling all of their scores from −1 to 1. Although this method also provides measures for same-version and different rule, it fails to account for participant and item effects, it does not take into account the spread of an individual’s ratings (only the average), and it does not provide any information on how an individual rates different-version comparisons relative to the same version or different rule. For example, some participants may rate different-version rule comparisons as similar, but they may also rate different-rule comparisons as similar, suggesting that they have a general propensity toward calling all rules similar. Alternatively, participants may view same-version rules as being equally as distinct as different-version rules. Although all participants included in the sample needed to have a significant difference between the same-version and different-rule conditions to be included, the current measures do not provide information on how large of a difference there exists between the same-version and different-version comparisons, as well as the different-version and different-rule comparisons.

7.3.4. Relative Rule Post Hoc Analysis

To better address ratings of different-version rules relative to the other two rule comparison types, new measures were generated using a mixed-effects model. The linear mixed- effect model predicted raw similarity judgement ratings with type of comparison (same version, different version, different rule) as a fixed effect. The random effects included random intercepts for item and participant, with random slopes for type of comparison for each participant. Type of comparison was dummy-coded as two variables, same version–different version and different rule–different version, with same version coded as 1 for the same version–different version measure and different rule coded as 1 for the different rule–different version measure, and everything else coded as 0. The random slopes for the same version–different version and different rule–different version measures for each participant were extracted and used as predictors in a series of analyses. The same version–different version and different rule–different version measures represented the difference between the two types of comparisons. Individuals with higher (positive) values for the same version–different version measure on average rated same-version comparisons as higher than different-version comparisons, whereas individuals with lower (negative) values rated different-version comparisons as being closer to same-version comparisons. For the different rule–different version measure, individuals with larger (positive) values rated different-version comparisons as closer to different-rule comparisons, whereas individuals with lower (negative) values rated different-version comparisons as different from different-rule comparisons. Because the new measures produced some outliers for those measures (beyond 2.5 standard deviations away from the mean), some participants were removed for subsequent analyses. This resulted in a final sample of 215 participants. The correlations between the new RSJT measures, the old RJST measures, figural analogies accuracy, WMC, and Gf are in included in Table 8 .

Correlations for new RSJT measures.

Note. * p < .05 FA refers to figural analogies, SV refers to same version, DV refers to different version, and DR refers to different rule. SV-DV refers to the same version–different version score and DR-DV refers to the different rule–different version score.

The first analysis used a GLMM to predict figural analogy accuracy as a function of the two new measures, the training manipulation, WMC, and Gf, with a test for an interaction between the two new measures and the training manipulation. The random effects structure was identical to previous analyses, with random intercepts for subject and item, with random slopes added for training for both subject and item. The same version–different version and different rule–different version measures were z -transformed prior to including them in the model. The final model is shown in Table 9 . There was a significant interaction between the same version–different version measure and training, but not for the different rule–different version measure. The interaction is shown in Figure 9 . The interaction indicated a positive relationship between the same version–different version measure and figural analogies accuracy for the trained items only. Thus, individuals that tend to rate different-version comparisons as different from same-version comparisons show improved accuracy for the trained-rule items. These results are the opposite of what was found previously when just using the RSJT different version measure. Although there was no significant interaction with the different rule–different version measure, it did predict figural analogy accuracy as a main effect, with a larger difference between different version and different rule scores corresponding with higher accuracy on the figural analogies test items.

Interaction between different rule–different version and the training manipulation. Note. The plot was generated using the predict function in R to generate log odds ratio accuracy data based upon the model in Table 9 . The data points represent item-level data for all participants and the linear slopes were generated with the geom_smooth function in ggplot. The circles represent trained-rule items and the squares represent novel-rule items.

Predicting figural analogy accuracy with same version–different version and different rule–different version measures and training.

Note. Training was coded with −1 for the novel-rules condition and 1 for the trained-rules condition. SV-DV refers to same version–different version and DR-DV refers to different rule–different version.

The next analysis tested for interactions between the two new RSJT measures, the training manipulation, and item type (distinct vs. paired rules). The final models are shown in Table 10 . There was a significant interaction between all three measures when different rule–different version was included, but not when same version–different version was included. The results of the interaction are shown in Figure 10 . Post hoc comparisons indicated that the only significant difference in slopes was between the novel paired-rule items and the trained paired-rule items. The full models for the post hoc comparisons are located in Appendix A . These results are largely congruent with previous results showing a significant three-way interaction between different-version scores, training, and item type. Compared to the previous analyses, the current model specifies that not only is it higher different-version scores that predict accuracy on novel paired-rule items, but that higher different-version scores relative to different-rule scores predict accuracy on novel paired-rule items.

Interaction between different rule–different version, training, and item type. Note. The plot was generated using the predict function in R to generate log odds ratio accuracy data based upon the different rule–different version model in Table 10 . The data points represent item-level data for all participants and the linear slopes were generated with the geom_smooth function in ggplot. The circles represent trained-rule items and the squares represent novel-rule items.

Predicting figural analogy accuracy with same version–different version and different rule–different version measures, training, and item type.

Note. Training was coded with −1 for the novel-rules condition and 1 for the trained-rules condition. Item type was coded with −1 for the paired-rule items and 1 for the distinct-rule items. SV-DV refers to same version–different version and DR-DV refers to different rule–different version.

8. Discussion

8.1. knowledge representations and transfer.

The present work examined the unique and interacting impact of processes driven by WMC and knowledge representations on success during reasoning. The potential for more thorough knowledge representations to better facilitate transfer is not a novel concept ( Anderson 1987 ; Gick and Holyoak 1983 ; Holyoak and Koh 1987 ; Wharton et al. 1994 ) and neither is the contribution of knowledge to performance on Gf tasks ( Bors and Vigneau 2003 ; Harrison et al. 2015 ; Loesche et al. 2015 ; Verguts and De Boeck 2002 ). Similarly, the role of WMC during reasoning has been explored previously ( Carpenter et al. 1990 ; Verguts and De Boeck 2002 ; Wiley et al. 2011 ). Where the present study breaks new ground is in looking at these mechanistically, during a Gf task.

Although both knowledge representations and WMC did predict success during the figural analogies task, the results did not align with a priori predictions. It was assumed that the presence of general rule representations would better facilitate transfer, as measured by the RSJT different-version scores. However, although RSJT different-version scores did interact with the training manipulation, they only predicted accuracy on novel items, not the trained items. This was opposite of what was expected. The original reasoning was that generalized rule representations would facilitate retrieval, but it is possible that the training or even the RSJT itself helped most participants conceptualize the rules in a way that was useful, thus leaving retrieval of the trained rules to depend on other processes, such as WMC. That being said, the analyses that included same version–different version measure did provide some support for rule representations facilitating retrieval. The same version–different version measure only predicted accuracy for the trained-rule items, not the novel-rule items. However, it also showed a positive relationship, suggesting that individuals who treat different-version comparisons as being less similar than the same-version comparisons had improved accuracy on the figural-analogy-trained items. This is also contrary to what was expected. Although these interactions differed from expectations, they did remain significant once WMC and Gf were introduced into the models. This indicates that the RSJT can uniquely explain variance on novel and trained figural analogies items beyond what Gf and WMC can explain.

The interaction between training and RSJT different-version scores also increased when accounting for the type of figural analogy item (distinct vs. paired rules). It is likely that the initial two-way interaction between training and RSJT different-version scores is driven by the three-way interaction with figural analogy items, and that in truth RSJT different-version scores really only predict novel paired-rule items. However, the relationship was positive, congruent with the initial hypotheses of the study. Mentally representing two versions of the same rule as closely similar, as opposed to treating them as distinct rules, corresponded with higher accuracy on novel problems where two versions of the same rule were included. Furthermore, the different rule–different version analyses indicated that it may be more important that individuals treat different-version comparisons as different from different rules than it is for different-version comparisons to be treated as similar to same-version comparisons. Notably, the fact that the RSJT different-version scores, as well the different rule–different version scores, only predicted novel items suggests that individuals with a propensity to treat different versions of the same rule as more similar, but still as separate rules, may have an easier time inducing related, but slightly different rules when they are exposed to them for the first time. It is likely that the training or the RSJT helped participants induce and develop representations to a point where individual differences in RSJT different-version scores no longer mattered for solving the trained-rule problems.

Unlike the RSJT different-version scores, WMC did appear to explain transfer, showing interactions with the training manipulation when accounting for learning across the task. Both high- and low-WMC individuals improved on trained rules over time, but high-WMC individuals were more likely to solve trained items correctly than low-WMC individuals. Furthermore, high-WMC individuals improved on the novel-rules items as they progressed, with performance increasing as they solved more items. Low-WMC individuals did not show this benefit, appearing to struggle on novel items throughout the task. It is possible that high-WMC individuals improved on the novel items by learning the rules and using them later in the task ( Harrison et al. 2015 ; Loesche et al. 2015 ; Verguts and De Boeck 2002 ), or they may have simply improved in solving novel problems, learning new strategies or becoming more comfortable with the task ( Klauer et al. 2002 ; Tomic 1995 ). The low-WMC individuals did not improve on the novel problems over time, suggesting that they struggled to induce the rules at all, or that they may need substantially more practice before they begin to benefit from learned rules.

These results are congruent with prior work in multiple ways. First, the fact that high-WMC individuals were able to benefit from trained rules more than low-WMC individuals indicates that WMC is important for retrieving previously learned information ( Loesche et al. 2015 ; Unsworth 2016 ). Second, only the high-WMC individuals improved on novel items over time, whereas both low- and high-WMC individuals improved on the trained items over time, indicating that WMC also contributes to learning throughout the task ( Harrison et al. 2015 ; Unsworth 2016 ). Finally, because the high-WMC individuals were generally better at solving novel items and low-Gf individuals did not improve at the novel items over time, WMC seems important for initially inducing the rules ( Carpenter et al. 1990 ). Although these results support several explanations for the role of WMC in Gf tasks, it is worth noting that the findings only became apparent after testing for the three-way interaction with trial number. Furthermore, these results fail to replicate studies showing a stronger relationship between WMC and repeated rules (items wherein the combination of rules has been seen previously) on the RAPM ( Loesche et al. 2015 ; Harrison et al. 2015 ) or studies showing the opposite, where WMC better predicts novel (unique combinations) RAPM items ( Wiley et al. 2011 ). Taking into consideration learning across the task, as well as accounting for individual rules rather than just unique combinations of rules, may explain the mixed findings on the role of WMC in Gf tasks.

Finally, it is worth noting that WMC may play a large role in how well the rules are initially learned. Previous work with analogical transfer has found that Gf may explain the ability to develop more general representations that are more easily transferred ( Kubricht et al. 2017 ). However, WMC and Gf are highly correlated and so it is possible that the high-Gf individuals in Kubricht et al.’s study did not benefit from the training manipulation because they were also high in WMC, thus learning the source problem better. This would explain why WMC is shown to explain transfer in the current study and not Gf. Yet, it is worth noting that Cushen and Wiley ( 2018 ) found that WMC only explained the completeness of an individual’s summary of the source problem when performance on the Remote Associates Test was not accounted for. Thus, although WMC may be important for retrieving learned rules, other processes may still be important in helping to generate more general representations, especially in cases of more complex learned information.

8.2. The Rule-Similarity Judgement Task

The original intention with the RSJT was to only use the different-version scores, but the same-version and different-rule scores ultimately did provide meaningful information, as did the difference-score measures, with each predicting figural analogies accuracy differently and uniquely. As many of these analyses were post hoc considerations, it is thus worth considering what processes these measures are tapping into. The RSJT same-version measure was the best predictor of figural analogies accuracy overall, even though it did not interact with any of the training manipulations. Because it was comparing two identical rules, it is possible that the measure is tapping into an individual’s propensity to let surface features of the items factor into their similarity judgements. For example, consider Figure 4 , which utilizes a numeracy rule. In this case, all of the items look slightly different. Some are just lines, some make a whole shape, and some include both aspects. Thus, even though they all increase an edge by two or lose an edge by one, some participants may have been accounting for surface features, with this potentially affecting their ability to solve figural analogy problems. Given that the same-version measure did predict accuracy and did also correlate with paperfolding and the Gf composite measure, it may be that a reliance on surface features is something that generally correlates with accuracy on Gf tasks. Furthermore, because the same version–different version measure did not correlate with figural analogy accuracy, Gf, WMC, or even the RSJT same version measure, but did correlate with the different-version and different-rule scores, it does appear that the RSJT same-version measure is tapping into something unique that happens when same-version comparisons are made.

The same version–different version and different rule–different version difference scores showed complementary as well as distinct findings from the RSJT same-version, different-version, and different-rule scores. The same version–different version measure was the only measure to predict trained-rule items and it predicted positively, indicating that representing different-version comparisons as less similar to same-version was beneficial, rather than what was originally hypothesized. The different rule–different version measure did support the initial findings with the RSJT different-version scores, but further specified that it was beneficial for accuracy on novel paired-rule items to represent different-version comparisons as more similar than different-rule comparisons. The same version–different version and different rule–different version measures indicate that generally treating the three comparisons as different is beneficial for accuracy. Although the same version–different version measures and the different rule–different version measures better target the difference between the three types of comparisons, it appears that all five measures produced by the RSJT measure slightly different propensities and further work will need to be conducted to better understand the differences and the similarities between all of the measures.

Although the RSJT did explain some transfer when using the same version–different version measure, it is possible that the RSJT did not explain transfer in the expected way because the measure was designed to look at the abstractness of the rule representations. Prior work has primarily looked at whether the representations include all the necessary information that is needed for transfer or mapping ( Cushen and Wiley 2018 ), rather than looking at the quality of a representation that includes all the necessary information. Lacking information may produce a more salient effect with transfer, whereas the quality of a whole representation may matter less. Ultimately, more information is needed on the three RSJT measures to ascertain what they are actually measuring and why they are distinct from WMC and Gf, in order to determine the role of rule representations in novel problem solving and transfer.

8.3. Conclusions

In conclusion, individual differences in knowledge representations and WMC play independent roles in reasoning performance. WMC appears to be important for both learning and retrieving rules, as well as contributing to novel problem solving. However, beyond WMC, individual differences in knowledge representations were able to explain some aspects of performance via retrieval as well as for novel problems. The results indicate that there may be a happy medium with knowledge representations, wherein an individual will want to recognize similarities when present while also understanding distinctions between rules. Furthermore, the propensity to develop a more general or stimuli-specific knowledge representation was not explained by WMC and Gf. Thus, understanding what prompts individuals to build better representations may be key to not only understanding novel reasoning but problem solving as a whole.

Figural analogy rules.

Post hoc comparisons: RSJT different-version × training × item type.

Note. Training was coded with −1 for the novel-rules condition and 1 for the trained-rules condition. Item type was coded with −1 for the paired-rule items and 1 for the distinct-rule items. DV refers to different version.

Post hoc comparisons: WMC × training × trial.

Post hoc comparisons: RSJT different-rule × Gf × training.

Note. Training was coded with −1 for the novel-rules condition and 1 for the trained-rules condition. DR refers to different rule.

Post hoc comparisons: different-rule–different-version × training × item type.

Note. Training was coded with −1 for the novel-rules condition and 1 for the trained-rules condition. Item type was coded with −1 for the paired-rule items and 1 for the distinct-rule items. DR-DV refers to different rule–different version.

Funding Statement

This research received no external funding.

Author Contributions

Conceptualization, M.J.R. and A.F.J.; methodology, M.J.R. and A.F.J.; software, M.J.R.; validation, M.J.R.; formal analysis, M.J.R.; investigation, M.J.R.; resources, A.F.J.; data curation, M.J.R.; writing—original draft preparation, M.J.R.; writing—review and editing, M.J.R. and A.F.J.; visualization, M.J.R.; supervision, M.J.R. and A.F.J.; project administration, M.J.R. and A.F.J. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

The study was conducted in accordance with the Declaration of Helsinki, and approved by the Institutional Review Board (or Ethics Committee) of Mississippi State University (IRB #21-342; approved 9/1/21).

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

Conflicts of interest.

The authors declare no conflict of interest.

1 To address concerns that composite variables for WMC and Gf may not be appropriate, several models were checked with each of the individual indicators for these variables, rather than the composite variables. In the WMC x Novel/Learned x Trial interaction, using Operation Span instead of the composite moved the p -value to p = .07, rather than being significant, while the interaction remained significant using only Symmetry Span. In the Representation Scores x Novel/Learning + WMC + Gf analysis, using the individual Gf tasks moved the main effect of DV representation scores from non-significant to significant. When predicting SV-DV training, changes from composites to individual measures changed nothing. As these are minor differences, composites were used throughout the paper for analyses.

2 Only 3 participants failed to use the highest marking on the scale (100) for any of their scores; all 3 instead used 95 as their top score. A total of 29 participants put their lowest raw score as something other than 0. For 2, the lowest score was 25, for 2 others it was 20, and for 4 it was 15. All of the rest used 5 or 10 as their lowest number. Because 86% of the sample used the full scale, it is not anticipated that this caused substantial changes to the analyses.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

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New Model for Solving Novel Problems Uses Mental Map

• by Andy Fell
• September 02, 2021

How do we make decisions about a situation we have not encountered before? New work from the Center for Mind and Brain at the University of California, Davis, shows that we can solve abstract problems in the same way that we can find a novel route between two known locations — by using an internal cognitive map. The work is published Aug. 31 in the journal Nature Neuroscience .

Humans and animals have a great ability to solve novel problems by generalizing from existing knowledge and inferring new solutions from limited data. This is much harder to achieve with artificial intelligence.

Animals (including humans) navigate by creating a representative map of the outside world in their head as they move around. Once we know two locations are close to each other, we can infer that there is a shortcut between them even if we haven’t been there. These maps make use of a network of “grid cells” and “place cells” in parts of the brain.

In earlier work , Professor Erie Boorman, postdoctoral researcher Seongmin (Alex) Park, Douglas Miller and colleagues showed that human volunteers could construct a similar cognitive map for abstract information. The volunteers were given limited information about people in a two-dimensional social network, ranked by relative competence and popularity. The researchers found that the volunteers could mentally reconstruct this network, represented as a grid, without seeing the original.

The new work takes the research further by testing if people can actually use such a map to find the answers to novel problems.

Matchmaking entrepreneurs

As before, volunteers learned about 16 people they were told were entrepreneurs, ranked on axes of competence and popularity. They never saw the complete grid, only comparisons between pairs.

They were then asked to select business partners for individual entrepreneurs that would maximize growth potential for a business they started together. The assumption was that an entrepreneur scoring high in competence but low on popularity would be complemented by one with a higher popularity score. 

“For example, would Mark Zuckerberg be better off collaborating with Bill Gates or Richard Branson?” Boorman said. (The actual experiment did not use real people.)

While the volunteers were performing the decision task, the researchers scanned their brains with functional magnetic resonance imaging, or fMRI. 

If the volunteers were using the grid cells inside their head to infer the answer, that should be measurable with a tailored analysis approach applied to the fMRI signal, Boorman said.

“It turns out the system in the brain does show the signature of these trajectories being computed on the fly,” he said. “It looks like they are leveraging the cognitive map.”

Computing solutions on the fly

In other words, we can take in loosely connected or fragmentary information, assemble it into a mental map, and use it to infer solutions to new problems.  

Scientists have considered that the brain makes decisions by computing the value of each choice into a common currency, which allows them to be compared in a single dimension, Park said. For example, people might typically choose wine A over wine B based on price, but we know that our preference can be changed by the food you will pair with the wine.

“Our study suggests that the human brain does not have a wine list with fixed values, but locates wines in an abstract multidimensional space, which allows for computing new decision values flexibly according to the current demand,” he said.

The cognitive map allows for computation on the fly with limited information, Boorman said.

“It’s useful when the decisions are novel,” he said. “It’s a totally new framework for understanding decision making.”

The navigational map in rodents is located in the entorhinal cortex, an “early” part of the brain. The cognitive map in humans expands into other parts of the brain including the prefrontal cortex and posterior medial cortex. These brain areas are part of the default mode network, a large “always on” brain network involved in autobiographical memory, imagination, planning and the theory of mind.

The work was supported by the National Science Foundation and National Institutes of Health. 

Media Resources

Read the paper

Media Contacts:

• Seongmin Park, Center for Mind and Brain, [email protected]
• Erie Boorman, Center for Mind and Brain and Department of Psychology, [email protected]
• Andy Fell, News and Media Relations, 530-304-8888, [email protected]

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35 problem-solving techniques and methods for solving complex problems

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All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

• Tips for more effective problem-solving

Complete problem-solving methods

• Problem-solving techniques to identify and analyze problems
• Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

• Six Thinking Hats
• Lightning Decision Jam
• Problem Definition Process
• Discovery & Action Dialogue

Design Sprint 2.0

• Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

• The Creativity Dice
• Fishbone Analysis
• Problem Tree
• SWOT Analysis
• Agreement-Certainty Matrix
• The Journalistic Six
• LEGO Challenge
• What, So What, Now What?
• Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

• Improved Solutions
• Four-Step Sketch
• 15% Solutions
• How-Now-Wow matrix
• Impact Effort Matrix

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

• Check-in/Check-out
• Doodling Together
• Show and Tell
• Constellations
• Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

• One Breath Feedback
• Who What When Matrix
• Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

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Interview Questions

Comprehensive Interview Guide: 60+ Professions Explored in Detail

26 Good Examples of Problem Solving (Interview Answers)

By Biron Clark

Published: November 15, 2023

Employers like to hire people who can solve problems and work well under pressure. A job rarely goes 100% according to plan, so hiring managers will be more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical in your approach.

But how do they measure this?

They’re going to ask you interview questions about these problem solving skills, and they might also look for examples of problem solving on your resume and cover letter. So coming up, I’m going to share a list of examples of problem solving, whether you’re an experienced job seeker or recent graduate.

Then I’ll share sample interview answers to, “Give an example of a time you used logic to solve a problem?”

Problem-Solving Defined

It is the ability to identify the problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation. 

Problem-solving also involves critical thinking, communication, listening, creativity, research, data gathering, risk assessment, continuous learning, decision-making, and other soft and technical skills.

Solving problems not only prevent losses or damages but also boosts self-confidence and reputation when you successfully execute it. The spotlight shines on you when people see you handle issues with ease and savvy despite the challenges. Your ability and potential to be a future leader that can take on more significant roles and tackle bigger setbacks shine through. Problem-solving is a skill you can master by learning from others and acquiring wisdom from their and your own experiences. 

It takes a village to come up with solutions, but a good problem solver can steer the team towards the best choice and implement it to achieve the desired result.

Watch: 26 Good Examples of Problem Solving

Examples of problem solving scenarios in the workplace.

• Correcting a mistake at work, whether it was made by you or someone else
• Overcoming a delay at work through problem solving and communication
• Resolving an issue with a difficult or upset customer
• Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
• Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
• Troubleshooting and resolving technical issues
• Handling and resolving a conflict with a coworker
• Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
• Taking initiative when another team member overlooked or missed something important
• Taking initiative to meet with your superior to discuss a problem before it became potentially worse
• Solving a safety issue at work or reporting the issue to those who could solve it
• Using problem solving abilities to reduce/eliminate a company expense
• Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
• Changing how a process, team, or task is organized to make it more efficient
• Using creative thinking to come up with a solution that the company hasn’t used before
• Performing research to collect data and information to find a new solution to a problem
• Boosting a company or team’s performance by improving some aspect of communication among employees
• Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem Solving Examples for Recent Grads/Entry Level Job Seekers

• Coordinating work between team members in a class project
• Reassigning a missing team member’s work to other group members in a class project
• Adjusting your workflow on a project to accommodate a tight deadline
• Speaking to your professor to get help when you were struggling or unsure about a project
• Asking classmates, peers, or professors for help in an area of struggle
• Talking to your academic advisor to brainstorm solutions to a problem you were facing
• Researching solutions to an academic problem online, via Google or other methods
• Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

You can share all of the examples above when you’re asked questions about problem solving in your interview. As you can see, even if you have no professional work experience, it’s possible to think back to problems and unexpected challenges that you faced in your studies and discuss how you solved them.

Interview Answers to “Give an Example of an Occasion When You Used Logic to Solve a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” since you’re likely to hear this interview question in all sorts of industries.

Example Answer 1:

At my current job, I recently solved a problem where a client was upset about our software pricing. They had misunderstood the sales representative who explained pricing originally, and when their package renewed for its second month, they called to complain about the invoice. I apologized for the confusion and then spoke to our billing team to see what type of solution we could come up with. We decided that the best course of action was to offer a long-term pricing package that would provide a discount. This not only solved the problem but got the customer to agree to a longer-term contract, which means we’ll keep their business for at least one year now, and they’re happy with the pricing. I feel I got the best possible outcome and the way I chose to solve the problem was effective.

Example Answer 2:

In my last job, I had to do quite a bit of problem solving related to our shift scheduling. We had four people quit within a week and the department was severely understaffed. I coordinated a ramp-up of our hiring efforts, I got approval from the department head to offer bonuses for overtime work, and then I found eight employees who were willing to do overtime this month. I think the key problem solving skills here were taking initiative, communicating clearly, and reacting quickly to solve this problem before it became an even bigger issue.

Example Answer 3:

In my current marketing role, my manager asked me to come up with a solution to our declining social media engagement. I assessed our current strategy and recent results, analyzed what some of our top competitors were doing, and then came up with an exact blueprint we could follow this year to emulate our best competitors but also stand out and develop a unique voice as a brand. I feel this is a good example of using logic to solve a problem because it was based on analysis and observation of competitors, rather than guessing or quickly reacting to the situation without reliable data. I always use logic and data to solve problems when possible. The project turned out to be a success and we increased our social media engagement by an average of 82% by the end of the year.

Answering Questions About Problem Solving with the STAR Method

When you answer interview questions about problem solving scenarios, or if you decide to demonstrate your problem solving skills in a cover letter (which is a good idea any time the job description mention problem solving as a necessary skill), I recommend using the STAR method to tell your story.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them. So before jumping in and talking about the problem that needed solving, make sure to describe the general situation. What job/company were you working at? When was this? Then, you can describe the task at hand and the problem that needed solving. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact.

Finally, describe a positive result you got.

Whether you’re answering interview questions about problem solving or writing a cover letter, you should only choose examples where you got a positive result and successfully solved the issue.

Example answer:

Situation : We had an irate client who was a social media influencer and had impossible delivery time demands we could not meet. She spoke negatively about us in her vlog and asked her followers to boycott our products. (Task : To develop an official statement to explain our company’s side, clarify the issue, and prevent it from getting out of hand). Action : I drafted a statement that balanced empathy, understanding, and utmost customer service with facts, logic, and fairness. It was direct, simple, succinct, and phrased to highlight our brand values while addressing the issue in a logical yet sensitive way.   We also tapped our influencer partners to subtly and indirectly share their positive experiences with our brand so we could counter the negative content being shared online.  Result : We got the results we worked for through proper communication and a positive and strategic campaign. The irate client agreed to have a dialogue with us. She apologized to us, and we reaffirmed our commitment to delivering quality service to all. We assured her that she can reach out to us anytime regarding her purchases and that we’d gladly accommodate her requests whenever possible. She also retracted her negative statements in her vlog and urged her followers to keep supporting our brand.

What Are Good Outcomes of Problem Solving?

Whenever you answer interview questions about problem solving or share examples of problem solving in a cover letter, you want to be sure you’re sharing a positive outcome.

Below are good outcomes of problem solving:

• Saving the company time or money
• Making the company money
• Pleasing/keeping a customer
• Obtaining new customers
• Solving a safety issue
• Solving a staffing/scheduling issue
• Solving a logistical issue
• Solving a company hiring issue
• Solving a technical/software issue
• Making a process more efficient and faster for the company
• Creating a new business process to make the company more profitable
• Improving the company’s brand/image/reputation
• Getting the company positive reviews from customers/clients

Every employer wants to make more money, save money, and save time. If you can assess your problem solving experience and think about how you’ve helped past employers in those three areas, then that’s a great start. That’s where I recommend you begin looking for stories of times you had to solve problems.

Tips to Improve Your Problem Solving Skills

Throughout your career, you’re going to get hired for better jobs and earn more money if you can show employers that you’re a problem solver. So to improve your problem solving skills, I recommend always analyzing a problem and situation before acting. When discussing problem solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Next, to get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t. Think about how you can get better at researching and analyzing a situation, but also how you can get better at communicating, deciding the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem solving ability.

If you practice the tips above, you’ll be ready to share detailed, impressive stories and problem solving examples that will make hiring managers want to offer you the job. Every employer appreciates a problem solver, whether solving problems is a requirement listed on the job description or not. And you never know which hiring manager or interviewer will ask you about a time you solved a problem, so you should always be ready to discuss this when applying for a job.

Related interview questions & answers:

• How do you handle stress?
• How do you handle conflict?
• Tell me about a time when you failed

About the Author

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15 Divergent Thinking Examples

Divergent thinking is problem-solving that involves generating unusual or unconventional solutions to problems. This is a type of thinking that is flexible, adaptive, and novel.

By looking at a situation from a unique perspective we may experience a “light-bulb” moment that inspires a unique solution. It is the opposite of convergent thinking, which involves finding one solution that is usually based on logic and linear thinking.

This can lead to amazing inventions such as the mobile phone or a simple fix to a simple problem like using a coin to tighten a screw.   

Definition of Divergent Thinking

The term divergent thinking was first coined by J.P. Guilford in 1956. In many ways, divergent thinking is synonymous with creative problem-solving .

Guilford was interested in testing for divergent thinking skills, so he designed the Alternative Uses Task , sometimes also called Guilford’s Test of Divergent Thinking .

The test is quite simple. Present a person with a normal, everyday object, and ask them to generate as many uses for that object as possible within a certain period of time. Although the testing process is fairly straightforward, the scoring is more complicated. Each answer is awarded points on four dimensions: fluency, flexibility, originality, and elaboration.

Examples of Divergent Thinking

1. using a coin as a flathead screwdriver.

Sometimes we might not have the right size screwdriver to tighten the screw of a shelf or cupboard door. We could call a neighbor and ask to borrow one of their tools, or we could just reach into our pocket and pull out some coins. One of them is bound to work.

This is an example of using a coin in an unusual and creative way. That fits the definition of divergent thinking quite well. It may not seem like the most profound example of creativity , but it does the trick. It solves the problem in a unique way and that’s the very definition of divergent thinking.   

2. Digging with a Fork

A fork is used to eat. However, if you were to think of new ways to use it, you would be engaging in divergent thinking.

One alternative way you might use a fork is to dig a hole. By using the fork as a shovel, you have found a creative solution to your lack of a shovel. Another person might get the fork and decide to use it as an engraving tool and start writing words into the side of a tree. Here, again, they have used divergent thinking.

Teachers will often use everyday implements like this and ask students to think of as many ways as they can to use the implements. By doing this task, teachers are encouraging students to think creatively and avoid the trap of functional fixedness .

3. Influencer Marketing

Central to divergent thinking is brainstorming . This is the process through which you come to new solutions to old problems.

For example, a brainstorming session might lead someone in a workplace to come up with a new way to market their old product. Instead of using traditional marketing techniques, they might go against the grain by giving their product to influencers and ask influencers to show the product to their Instagram or Tik Tok audience.

In fact, marketing is a job that requires divergent thinking all the time. Marketing is a saturated field with every company wanting to get their products in front of your eyes. If you can come up with a new type of television ad or marketing method that stands out from the crowd, you’ve probably been a very successful divergent thinker.

4. The Folding Bike

In 1887, the folding bike was invented by Emmit Latta as a way to make bikes more mobile.

While bicycles are great for getting us from Point A to Point B quickly, what do we do once we have arrived? They are quite clunky, can’t be taken onto public transport, and take up a lot of space when they’re stored.

Latta’s intelligent invention solved a lot of the problems we have with storing and moving bikes around. Now, there are even bikes you can carry on your back then unpack when it’s time to speed from Point A to Point B!

5. The Little Black Dress

Is there a woman alive today in the Western world that does not have an LBD? It is a black evening or cocktail dress made with a simple cut and is usually a bit short. The creator of the little black dress is none other than Coco Channel (Steele, 1988).

Although today it is considered an essential part of any walk-in closet, there was a time when it took the fashion world by storm. Back in the 1920s, Coco wanted to create something that was versatile and affordable to all. Those were concepts in the fashion world that were completely unheard of, and hence, represented divergent thinking at its finest.

Divergent thinking doesn’t have to involve complexity or high-tech inventions; a nice fabric, cut the right way, will do just fine.

6. Synectics  

Synectics may sound like an odd term, but it is actually a very useful way of fostering divergent thinking. The procedure is quite simple. Select a page on the internet at random. It doesn’t matter what type of website it is, just as long as it has a fair amount of text.

Then, close your eyes, take your index finger, move it in a circle a few times and then point it to a spot on the page. Write down the word your finger lands on. Repeat the process from the beginning one more time so that you end up with two words.

Now, try to think of things that could be described by those two words. Or, put them together to form a new word. For instance, if you have “purveyor” and “exception”, what objects or concepts could have connections to both? If you formed a new word, what could it mean?

7. The Smartphone

Although most people think the smartphone was invented by Steve Jobs, that would be incorrect. The first iteration of the smartphone was by IBM in 1994. It was huge and bulky, but it had a touchscreen and even a few apps.

Since then, the smartphone has evolved into an amazing device that can do just about anything: it can take photos, be used to play games with incredible graphics, track your movements wherever you go, and soon, be able to conduct various medical diagnostic tests. Oh, and it can make phone calls as well.

Each of those features represent another milestone in the smartphone’s evolution and another example of divergent thinking.

8. Brainstorming

Brainstorming just may be the most frequently exercised form of divergent thinking. The basic idea is to gather a group of people together, pencil and paper in hand, and for everyone to just write down as many ideas as they can related to a specific topic.

No one is to speak out loud for a few minutes until time is up. Everyone is instructed to just write whatever comes to mind, without fear of sounding foolish or having their ideas rejected by others.

It has become a common practice in most R&D departments of corporations around the world. It is so vital to the creation of new products and inventions, that there is a small niche market of boutique consulting enterprises that specialize in helping companies utilize divergent thinking to their advantage.

9. Children’s Creative Play

Watching young children at play is like witnessing a continuous flow of divergent thinking. A cardboard box is a house, a plane, a bulldozer and a cave where you can hide from dinosaurs.

Simply following a young child throughout their day will provide plenty more examples of children’s amazing abilities to imagine and create. They’re thinking is not constrained by reality and the narrowly defined functions of the objects they encounter. Any thing can become anything.

There is no doubt about it, children are the masters of divergent thinking. And then, they grow up. Surprisingly, some research indicates that developing executive control, a sign of cognitive development, actually inhibits divergent thinking (Vaisarova & Carlson, 2021).

10. Coffee Coke

There is probably no industry that attempts divergent thinking more than the modern-day beverage industry. For decades, there were basically a handful of carbonated beverages to choose from: Coke, Pepsi, and a few others.

However, today, if you go to the refrigerated section of a supermarket or convenience store, you will literally see a hundred different options. There are juices, teas, coffees, sodas, caffeine-infused drinks, vitamin-infused drinks, caffeine drinks infused with vitamins, and the list goes on, and on. The number of choices can be overwhelming.  

Maybe one of the most unique iterations of the cold-beverage offerings is Coffee Coke. It’s a can of cold coke infused with Brazilian coffee. So, if the caffeine from Coke isn’t enough, you can add a jolt of coffee too.

11. Thinking of Ways to Make Money  

If a teenager asks their parents to buy them a car, one response they might get is “to get a job”. Learning to be independent is a goal that most parents have for their children; nothing wrong with that.

One obvious solution that represents convergent thinking is to start applying at local stores and restaurants. Nothing wrong with that either. However, if the teenager is a bit creative then they may think of other, less conventional methods to raise cash.

Brainstorming other ways to make money could lead to starting a small lawn-care business, washing and waxing cars, pressure-washing patios, or editing videos for your friends’ vlogs and Tik Tok posts.  

12. Using a Hot Glue Stick

Believe it or not, a glue stick is a very handy household tool. It can fix a variety of problems that may crop up from time to time. For example, after a while, the rubber insulation that lines the inside of the refrigerator’s doors may come loose. This means the doors won’t close properly and all of your favorite cold-storage foods will spoil.

No need to throw away the frig and buy a new one. Just break-out the trusty hot glue stick and apply the hot glue between the door and rubber lining. Hold the lining firmly in place for 30-seconds, and mission accomplished.  

13. Internalizing Pluralism

If you spend the first 30 years of your life in one country, most likely you will adopt the customs and ways of thinking of that culture. It’s natural. We live around people that think and act in certain ways, so we do too. There’s nothing wrong with that.

But, of course, there is more than one perspective on life out there. If you move to another country that has a completely different culture, in a way, it’s like entering an entire world of divergent thinking.

To illustrate this point, consider the words of Bruce Lee: “The American life is like an Oak tree—he stands firm against the wind. If the wind is strong, he cracks. The Oriental stands like bamboo, bending with the wind and springing back when the wind ceases, stronger than ever before” (Little, 2017, p. 25).  

This is an example of divergent thinking by internalizing a different culture.

See Also: Pluralism in Sociological Theory

14. Children’s Play

From about the age of 4, children start engaging in divergent thinking during playtime. They come up with creative storylines and plots that embrace fantasy and magic. During this playtime, children use the things around them and utilize them in ways entirely unexpected by adults.

For example, a child might use a block of wood and push it along the floor, pretending it’s a car. Here, a child found something that isn’t generally thought of as a toy, and turned it into a toy in order to entertain themselves. They used this block of wood in a way divergent from the norm to enhance their play!

Children can be particularly good at divergent thinking because social norms are not as solidified in their minds yet. They don’t see things as having clear-cut purposes until they have been socialized into it later in life.

15. Survival of the Fittest

Developing a unique and profound insight into the evolution of all living organisms must surely be considered an example of divergent thinking. The concept of survival of the fittest postulates that the living creature that is most capable of adapting to environmental demands has the highest likelihood of propagating the species.

Although made famous by Charles Darwin (1869), Herbert Spencer was the first to actually use the term survival of the fittest . He stated, “This survival of the fittest, which I have here sought to express in mechanical terms, is that which Mr. Darwin has called ‘natural selection’, or the preservation of favoured races in the struggle for life” (Spencer, 1864, pp. 444-445).

Divergent vs Convergent Thinking

Divergent thinking and convergent thinking are opposites. They represent two different types of thinking that are each valuable in different situations.

Divergent thinking is all about finding new ideas. The term ‘divergent’ comes from ‘diverge’, meaning to separate from the norm. It involves brainstorming, thinking outside of the norm, and thinking creatively to find solutions to problems. It also often involves finding new ways to tackle existing problems and use existing tools.

Convergent thinking is about gathering facts to come up with an answer or solution. It’s seen as the opposite of divergent thinking because you’re gathering information together to come up with one single solution rather than searching around and comparing multiple different solutions.

While convergent thinking is primarily analytical, divergent thinking is primarily creative.

Divergent thinking means generating a novel solution and avoiding simplistic or binary thinking on an issue. It is usually creative and unconventional because it does not conform to linear thinking processes. This can mean using an object in an usual way or seeing how two unrelated concepts can be combined to create something never before considered.

History is full of examples of divergent thinking, such as the numerous iterations of the smartphone that included adding a screen, Apps, internet access, and a camera. Other examples can be found in the world of fashion or observed in a children’s playroom and a magical cardboard box.

Human beings really are an amazing species. Now, if we could only invent something to ensure world peace.

Clapham, M. M. (2003). The development of innovative ideas through creativity training. In Shavinina, L.V. (Ed.). The International Handbook on Innovation (pp. 366-376). doi: https://doi.org/10.1016/B978-008044198-6/50025-5

Darwin, C. (1869). On the Origin of Species by Means of Natural Selection: or The Preservation of Favoured Races in the Struggle for Life . London: J. Murray, Fifth edition.

Guilford, J. P. (1956). The structure of intellect. Psychological Bulletin , 53 (4), 267. doi: http://dx.doi.org/10.1037/h0040755

Little, J. (Ed.). (2017). Words of the dragon: Interviews, 1958-1973 . Tuttle Publishing.

Lee, B. (2018). Bruce Lee artist of life: Inspiration and insights from the world’s greatest martial artist (Vol. 6). Tuttle Publishing.

Runco, M. A., & Acar, S. (2019). Divergent thinking. In J. C. Kaufman & R. J. Sternberg (Eds.), The Cambridge handbook of creativity (pp. 224–254). Cambridge University Press. doi: https://doi.org/10.1017/9781316979839.013

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Steele, V. (1988). Paris fashion: A cultural history. Oxford University Press. Vaisarova, J., & Carlson, S. M. (2021). When a spoon is not a spoon: Examining the role of executive function in young children’s divergent thinking. Trends in Neuroscience and Education , 25 , 100161. doi: https://doi.org/10.1016/j.tine.2021.100161

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Dr. Cornell has worked in education for more than 20 years. His work has involved designing teacher certification for Trinity College in London and in-service training for state governments in the United States. He has trained kindergarten teachers in 8 countries and helped businessmen and women open baby centers and kindergartens in 3 countries.

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Functional Fixedness (Definition + Examples)

If you're here, you are probably researching functional fixedness to help you solve a problem or write a paper. Have no fear since this page aims to give you everything you need to know, including a few functional fixedness examples!

What is Functional Fixedness?

Functional fixedness is a mental obstacle that makes us see objects exclusively functioning traditionally. We cannot get past these fixed functions of objects or tools. This stunts our creativity and may hold us back from seeing an object's full potential.

Why Do We Experience Functional Fixedness?

Functional fixedness, like other biases and heuristics, streamlines our cognitive processes, aiding us in rapidly understanding the world around us. By learning from previous knowledge and experiences, we can navigate situations more efficiently. For instance, consider the teacup you encounter every morning. Instead of pondering its potential uses each day, you intuitively recognize it as a vessel for your tea. This immediate association, a sort of "mental shortcut," ensures you don't waste precious morning minutes deliberating its function.

These mental shortcuts, termed heuristics in psychology, are invaluable. They save time and effort by enabling us to know how to interact with familiar objects instantly. However, herein lies a double-edged sword. While it's undoubtedly helpful to identify a teacup primarily for tea drinking, being trapped within this singular perspective can be limiting. Recognizing an object's primary purpose is vital, but an inability to think beyond that predefined context can pose distinct disadvantages.

Heuristics and Functional Fixedness: Cognitive Pathways in Decision-Making

In cognitive psychology, understanding how humans make decisions and solve problems is central to comprehending the complex nature of the human mind. Heuristics and functional fixedness are two concepts that illustrate the shortcuts and potential pitfalls our minds take in this process. Let's delve into these concepts and explore their relationship.

Heuristics: Mental Shortcuts to Quicker Decisions

Heuristics are mental shortcuts that our brain uses to simplify complex decision-making processes. Instead of analyzing all available data when deciding, the brain uses heuristics to quickly arrive at a solution based on patterns and previous experiences. While these shortcuts can be incredibly efficient, they can sometimes lead to errors or biases.

For instance, the availability heuristic suggests that people base the likelihood of an event on how easily they can recall similar events from memory. This might lead someone to overestimate the risk of shark attacks after seeing a news story on one, even if such events are rare statistically.

Functional Fixedness: Stuck in Established Patterns

On the other hand, functional fixedness is a cognitive bias that limits our ability to see alternative uses for objects or methods beyond their traditional or known functions. It is the tendency to be "fixed" in our understanding of how something should function, based largely on prior experiences and knowledge.

For example, viewing a newspaper strictly as a medium for reading news might prevent someone from considering its use as a tool for cleaning windows, packing material, or even craftwork.

Comparing the Two

While both heuristics and functional fixedness relate to cognitive shortcuts and biases, they manifest differently:

• Nature of the Process : Heuristics are general decision-making shortcuts that can apply to various situations and help us navigate the world more efficiently. In contrast, functional fixedness is about seeing objects or methods in a limited scope based on their familiar functions.
• Outcome : Heuristics can often lead to reasonably accurate outcomes due to their basis in frequent experiences. However, they can also result in cognitive biases and errors. Functional fixedness, meanwhile, typically leads to limited problem-solving abilities and curtails creativity.
• Advantages & Pitfalls : Heuristics help speed up decision-making in a world brimming with information. They're essential for daily function. However, their reliance on past patterns can sometimes misguide us. On the other hand, functional fixedness primarily presents as an obstacle to innovative thinking and creative problem-solving.

Interrelation in Cognitive Processes

Despite their differences, heuristics and functional fixedness can sometimes intersect. For instance, one might use a heuristic to quickly decide how to use an object based on its most familiar function, leading to functional fixedness. Conversely, functional fixedness might cause someone to default to a heuristic way of problem-solving, relying on established patterns rather than seeking innovative solutions.

While both heuristics and functional fixedness highlight the brain's propensity for simplification and efficiency, they also underscore the importance of awareness in our cognitive processes. We can foster more thoughtful, creative, and informed decision-making by recognizing when we might be relying too heavily on mental shortcuts or getting stuck in established patterns.

Examples of Functional Fixedness Holding Us Back

Say you have a blunt kitchen knife that you need to sharpen. However, you don’t own a knife sharpener. Would you think of using the unglazed ring around the bottom of your teacup? After all, it has the same surface as a sharpening stone. Coming up with this alternative use for a teacup would quickly solve your problem. Otherwise, you would have to look for a “real” knife sharpener while using your cup only for drinking tea.

The moment we see an object, the motor cortex in our brains activates in anticipation of using it in a standard way. That means we don’t need to hesitate about reaching for a teacup when we feel like having tea. But that also means when you're looking for a knife sharpener, you're likely to glaze over that teacup because you don't take a mental shortcut from teacups to knife sharpeners. (Well, now you might!)

Being aware of functional fixedness is important because overcoming it could be the key to solving a problem.

Schemas, Prior Knowledge, and Functional Fixedness in Psychology

In the vast landscape of cognitive psychology, understanding how humans process information and navigate their world is paramount. Schemas and prior knowledge play pivotal roles in shaping our perceptions and responses to various situations, and their influence on cognitive biases like functional fixedness cannot be understated.

Schemas: Blueprint of Our Understanding

A schema is a mental framework or structure that organizes and interprets information in our brains. It's like a blueprint for categorizing and understanding the world around us. Schemas are created from accumulated experiences, cultural background, and learned knowledge. For instance, we have schemas about what constitutes a typical "bird" or how a usual "restaurant" operates. When we encounter information or experiences that fit into our existing schemas, it reinforces them. Conversely, when we encounter anomalies, we adjust our schema (accommodation) or try to fit this new information into our existing schemas (assimilation), as posited by Jean Piaget, a renowned developmental psychologist.

The Role of Prior Knowledge

Our past experiences significantly shape our present and future actions. Prior knowledge serves as a foundation upon which we build new knowledge. When faced with a situation, our brain quickly taps into the repository of prior experiences to find a suitable response or solution. This prior knowledge is a guidepost, helping us navigate familiar situations swiftly and efficiently.

Linking to Functional Fixedness

However, the reliance on schemas and prior knowledge can sometimes limit our cognitive flexibility, leading to functional fixedness. When too deeply entrenched in our pre-existing understanding of an object's function, we can become "fixed" in our approach, hindering our ability to see alternative uses or solutions. Our brain defaults to follow the well-trodden path of past experiences and established schemas. This is where functional fixedness comes into play. For example, if our schema of a "book" is strictly an object for reading, we might overlook its potential use as a doorstop or a makeshift monitor stand.

Functional fixedness, in many ways, is a byproduct of reliance on schemas and prior knowledge. While these cognitive structures help us process information efficiently, they can sometimes act as blinders, narrowing our field of vision and restricting creative problem-solving.

In the Broader Context of Cognitive Psychology

In psychology, schemas, prior knowledge, and functional fixedness are intertwined. They are all part of the broader cognitive structures and processes that dictate how we perceive, think, and act. Recognizing their interconnectedness can help us understand why we sometimes get stuck in particular patterns of thought and how we can potentially break free to foster innovation and creativity. By challenging our established schemas and being open to new experiences, we can mitigate the effects of functional fixedness and open the doors to a more flexible and adaptive way of thinking.

Examples of Overcoming Functional Fixedness in Everyday Life

You might identify these examples as "life hacks," but they are all forms of pushing past functional fixedness and seeing uses for everyday objects in new lights.

• Want to keep your door open? Tie a rubber band around it!
• Need to prop up your phone? Use upside-down sunglasses.
• Place a pool noodle under your child's fitted sheet to prevent them from rolling out of bed.
• Worried about your gear stick getting too hot in your car? Put a koozie over it!
• Need a last-minute speaker? Cups (plastic and glass) and toilet paper rolls are great alternatives.
• Preparing to serve condiments at a party but don't want to waste dishes? Place your condiments or sauces in a cupcake tin!
• Use a shoe rack to hang cleaning supplies.
• Clothespins are a great way to hold onto nails before you start hammering!
• Did your flip-flop fall apart because the hole is too big? Use a bread clip to keep the strap in place. (Bread clips are also a great way to organize and separate cords.)
• Looking for tiny things within your carpet? Roll some pantyhose or spandex over your vacuum to attract them without sucking them into your vacuum!
• Use your seat warmer to keep food warm after you pick it up from a restaurant!
• Hair straighteners make great collar irons in a pinch.
•  Don't have a juicer? Use tongs to get everything out of lemons or limes!

See how much you might have been missing out on? If all these hacks are within our grasp, what other uses could you consider for everyday items?

Who Discovered Functional Fixedness?

The term “functional fixedness” was coined in 1935 by German Gestalt therapist Karl Duncker who contributed to psychology with his extensive work on understanding cognition and problem-solving.

Duncker’s Candle Experiment

Duncker conducted a famous cognitive bias experiment that measured the influence of functional fixedness on our problem-solving abilities.

He handed the participants a box of thumbtacks, a candle, and matches. He then asked them to find a way to attach the lit candle to a wall so the wax wouldn’t drip on the floor. The solution consisted of removing the tacks from the box, tacking the box to the wall, and placing the candle upright in the box.

Pretty simple, right?

But most participants couldn’t solve this problem. They saw the box only as something that was used for holding tacks. Duncker observed a "mental block against using an object in a new way that is required to solve a problem" in these participants. To find a solution, they would first need to overcome the tendency towards the psychological obstacle holding them back—functional fixedness.

Functional Fixedness and Problem Solving

Functional fixedness is practical in everyday life and crucial in building expertise and specialization in fields where it’s important to come up with quick solutions. But as we saw in Duncker’s experiment, this cognitive constraint is the enemy of creativity. Functional fixedness stops us from seeing alternative solutions and makes problem-solving more difficult. 

Functional fixedness can become a genuine problem among professionals. Research shows that functional fixedness is one of large organizations' most significant barriers to innovation. If your job is to produce innovative solutions, being able to think “outside the box” is a must.

So why do we become limited when it comes to using objects?

Children, especially those under 5, are not as biased as adults. As we know only too well, toddlers won’t hesitate to turn a wall into a blank canvas for their works of art. But because they are constantly being corrected, children become more functionally fixed over time. Eventually, they realize that paper is the only acceptable support to draw on.

As we gain more experience and knowledge, we become increasingly fixated on the predetermined use of objects and tools. And the more we practice using them in certain ways, the harder it is to see other alternatives.

Knowledge and experience replace imagination and our ability to see an object for anything other than its original purpose.

How to Overcome Functional Fixedness?

The good news is that functional fixedness is not a psychological disorder that needs therapeutic intervention. We can train our minds to overcome the mental set, a problem-solving approach based on past experiences.

There are a few methods that can help break down functional fixedness and develop creative thinking:

Practicing creative thinking

The more often you try to see novel uses for everyday objects, the easier the process will eventually become. Let’s go back to the teacup. What other usages except for drinking tea (and sharpening knives) can you think of? With a bit of imagination, the same cup can become a paperweight, candle holder, cookie-cutter, bird feeder, and even a phone sound amplifier.

Practicing helps develop our ability to think creatively. It encourages something called divergent thinking, a term defined in 1967 by the American psychologist J. P. Guilford.

Contrary to convergent thinking , which focuses on finding a single solution, divergent thinking is a creative process where a problem is solved using strategies that deviate from commonly used ones.

Changing the context

Getting a fresh perspective is often useful when considering alternate approaches to a task. In a professional setting, this can mean brainstorming in a group or involving individuals from other disciplines to share their points of view.

Considering a problem from a different angle prompts us to think creatively.

Focusing on features instead of function

Another way of breaking away from habitual ways of looking at objects is to consider what they are made of instead of concentrating on their function. List an item's different characteristics, and you might come up with its alternative uses. A teacup is made of ceramic, which can be broken down into pieces to create a mosaic.

This approach helps combat functional fixedness by focusing on the object itself while distancing ourselves from the mechanics of its intended use.

Other Biases and Heuristics That Hold Us Back

Functional fixedness is not the only "mental shortcut" holding us back. If we allow ourselves to think beyond what appears to be the "obvious answer," we may do more than we could have ever imagined!

Bandwagon Effect

It's easy to agree with what other people think. Meetings go much faster when everyone agrees right away. Plus, if one person likes the idea, it's probably not so bad, right? Well, this isn't always the case. Sometimes, the bandwagon effect encourages us to go along with what everyone else is doing. (It's easy for us to "hop on the bandwagon," as they say." Will you and your colleagues find a better solution if you debate a few more options? Are you just agreeing to something because everyone else is?

Dunning-Kruger Effect

Think you know a lot about a subject? Think again. The Dunning-Kruger Effect suggests that the less we know about a subject, the more confident we are in our abilities. Let's say you go to a rock climbing gym for the first time. You look at the wall and think, "I can get the hang of this quickly!" After a few sessions, you learn that there are different grips and ways of moving your body that you would have never thought of before! The initial false sense of confidence is a result of the Dunning-Kruger Effect.

Confirmation Bias

Once we decide, we will likely search for "evidence" confirming that we are right. If you have decided to vote for a certain political candidate, for example, you may only seek out news articles and information that confirms that they are the best candidate for the job. If you decide to leave your job, you may start focusing on the worst parts of the job. Don't let the confirmation bias prevent you from seeing all sides of an argument!

Not all biases are inherently bad, but they can hold us back. When approaching a big decision or trying to solve a problem, evaluate how biases could influence your thinking. Can you push past them? Can you try something new and unexpected?

Related posts:

• Jean Piaget’s Theory of Cognitive Development
• The Psychology of Long Distance Relationships
• Operant Conditioning (Examples + Research)
• Beck’s Depression Inventory (BDI Test)
• Variable Interval Reinforcement Schedule (Examples)

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Improving examples to improve transfer to novel problems

• Published: September 1994
• Volume 22 , pages 606–615, ( 1994 )

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People often memorize a set of steps for solving problems when they study worked-out examples in domains such as math and physics without learning what domain-relevant subgoals or subtasks these steps achieve. As a result, they have trouble solving novel problems that contain the same structural elements but require different, lower-level steps. In three experiments, subjects who studied example solutions that emphasized a needed subgoal were more likely to solve novel problems that required a new approach for achieving this subgoal than were subjects who did not learn this subgoal. This result suggests that research aimed at determining the factors that influence subgoal learning may be valuable in improving transfer from examples to novel problems.

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Catrambone, R. Improving examples to improve transfer to novel problems. Memory & Cognition 22 , 606–615 (1994). https://doi.org/10.3758/BF03198399

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12 Best Problem Solving Books to Read in 2024

You found our list of top problem solving books .

Problem solving books are guides that improve critical thinking capability and the ability to resolve issues in the workplace. These works cover topics like bias and logical fallacies, problem prevention, and prioritizing. The purpose of these books is to help workers remain calm under pressure and come up with solutions more quickly.

These guides are similar to decision making books , negotiation books , and conflict resolution books . To improve competency in this area, one can also play problem solving games .

This list includes:

• problem solving books for adults
• creative problem solving books
• business problem solving books
• problem solving books for programmers

Here we go!

List of problem solving books

Here is a list of books to improve problem solving skills in the workplace.

1. Fixed: How to Perfect the Fine Art of Problem Solving by Amy E Herman

Fixed is one of the most useful new books on problem solving. The book calls for problem solvers to look beyond instinctual and obvious answers and provides a framework for more creative thinking. While most folks think about problem solving in terms of logic, reason, and disciplines like math and science, this book shows the role that art and imagination play in the process. Amy Herman consulted on leadership training with Silicon Valley companies and military organizations and brings this expertise into the text to train readers on how to adopt a more innovative critical thinking approach.

Notable Quote: “Working through problems is critical for productivity, profit, and peace. Our problem-solving skills, however, have been short-circuited by our complicated, technology-reliant world.”

Read Fixed .

2. Cracked it!: How to solve big problems and sell solutions like top strategy consultants by Bernard Garrette, Corey Phelps, and Olivier Sibony

Cracked it! is one of the best creative problem solving books. Drawing inspiration from the tactics of consultants, this guide is a practical playbook for approaching business problems. The authors outline a “4S” method– State – Structure – Solve – Sell– to tackle obstacles and get support from stakeholders. While many problem solving books simply focus on how to think through issues, this guide also demonstrates how to gain approval for ideas and get others onboard with the solution. The book explains how to best use these techniques, and presents case studies that show the theories in action. Cracked it! is a handy reference for any professional that faces tough challenges on the regular.

Notable Quote: “If you want to know how a lion hunts, don’t go to a zoo. Go to the jungle.”

Read Cracked it!

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3. Upstream: The Quest to Solve Problems Before They Happen by Dan Heath

Upstream takes a proactive approach to problem solving. The book urges readers to not only be responsive to issues, but also try to prevent obstacles from occurring. The guide opens with an exploration of “problem blindness,” and the psychological factors that cause folks to be oblivious to issues, along with a reminder that many problems are more controllable and avoidable than first assumed. The pages that follow outline a series of questions leaders can ask to fine-tune the system and steer clear of major headaches, for instance, “How Will You Unite the Right People?” and “How Will You Avoid Doing Harm?” Upstream is full of real world examples of how minor tweaks achieved major results and allowed organizations to sidestep serious holdups.

Notable Quote: “The postmortem for a problem can be the preamble to a solution.”

Read Upstream .

4. Problem Solving 101: A Simple Book for Smart People by Ken Watanabe

Problem Solving 101 is one of the most fun problem solving books for adults. Written by Ken Watanabe, the guide draws on Japanese philosophy as well as the author’s experience as a consultant at McKinsey to help readers understand and approach problems in productive ways. The pages provide blueprints for problem-solving methods such as logic trees and matrixes, and include scenarios and illustrations that help readers visualize the process more clearly. Problem Solving 101 breaks down the problem solving procedure into the most basic parts and lays out step-by-step instructions for choosing the best action in any situation.

Notable Quote: “When you do take action, every result is an opportunity to reflect and learn valuable lessons. Even if what you take away from your assessment seems to be of small consequence, all of these small improvements taken together make a huge difference in the long term.”

Read Problem Solving 101 .

5. What’s Your Problem?: To Solve Your Toughest Problems, Change the Problems You Solve by Thomas Wedell-Wedellsborg

What’s Your Problem? insists that the most important step in the problem solving process is to start by honing in on the correct problem. The root of much frustration and wasted efforts is that professionals often pick the wrong points to focus on. This book teaches readers how to reframe and approach issues from a different perspective. The guide outlines a repeatable three step process “Frame, Reframe, and Move Forward” to ensure that workers prioritize effectively and stay on track to achieve desired results. What’s Your Problem? teaches professionals of all levels how to be less rigid and more results-focused and adopt a more agile approach to fixing issues.

Notable Quote: “The problems we’re trained on in school are often quite different from the ones we encounter in real life.”

Read What’s Your Problem?

6. Sprint: How to Solve Big Problems and Test New Ideas in Just Five Days by Jake Knapp, John Zeratsky, et al

Sprint is one of the best problem solving books for programmers. The authors are the creators of the five-day-process at Google. This guide describes best practices for conducting sprints and solving problems in limited timeframes. The book provides a day-by-day breakdown of tasks for each day of the workweek, with the final steps being designing a prototype and a plan for implementation. Though this idea originated in the tech world and is most widely used in the software industry, this problem-solving and product design approach can be useful for any position that needs to find fixes in a time crunch.

Notable Quote: “We’ve found that magic happens when we use big whiteboards to solve problems. As humans, our short-term memory is not all that good, but our spatial memory is awesome. A sprint room, plastered with notes, diagrams, printouts, and more, takes advantage of that spatial memory. The room itself becomes a sort of shared brain for the team.”

Read Sprint , and check out this guide to virtual hackathons and this list of product design books .

7. Think Like a Rocket Scientist: Simple Strategies You Can Use to Make Giant Leaps in Work and Life by Ozan Varol

Think Like a Rocket Scientist lays out formulas and instructions for thinking more strategically. The guide reveals common problem solving approaches used by rocket scientists when exploring the unknown and testing new technology. The book is split into three sections– launch, accelerate, and achieve– with deep dives into concepts such as moonshot thinking and overcoming failure. The anecdotes revolve around space exploration and rocket science yet the methods can be applied to more commonplace and less complex problems as well. Think Like a Rocket Scientist proves that one does not need to be a genius to be a genius problem solver and lets readers learn tricks from one of the most complex professions on the planet.

Notable Quote: “Critical thinking and creativity don’t come naturally to us. We’re hesitant to think big, reluctant to dance with uncertainty, and afraid of failure. These were necessary during the Paleolithic Period, keeping us safe from poisonous foods and predators. But here in the information age, they’re bugs.”

Read Think Like a Rocket Scientist .

8. Bulletproof Problem Solving: The One Skill That Changes Everything by Charles Conn and Robert McLean

Bulletproof Problem Solving is one of the best business problem solving books. This workbook-style-guide breaks down a “bulletproof” method of problem solving favored by consultants at McKinsey. The authors distill the process into seven simple steps–define the problem, disaggregate, prioritize, workplan, analyze, synthesize, and communicate– and give numerous examples of how to follow this cycle with different dilemmas. The chapters explore each stage in depth and outline the importance and finer points of each phase. The book also provides practical tools for readers to build skills, including an appendix with exercise worksheets.

Notable Quote: “Problem solving doesn’t stop at the point of reaching conclusions from individual analyses. Findings have to be assembled into a logical structure to test validity and then synthesized in a way that convinces others that you have a good solution. Great team processes are also important at this stage.”

Read Bulletproof Problem Solving .

9. Think Like a Programmer: An Introduction to Creative Problem Solving by by V. Anton Spraul

Think Like a Programmer is one of the top problem solving books for programmers. The guide lays out methods for finding and fixing bugs and creating clean, workable code. The text emphasizes that programming is not merely a matter of being competent in the language, but also knowing how to troubleshoot and respond to unexpected occurrences. The chapters present examples of problems and puzzles and work through the answers to help strengthen professional competencies. The book provides an introductory crash course and practical toolkit for beginning coders, with a focus on C++. Yet since the text outlines general theory and approach, the book is also helpful for dealing with other programming languages, or for solving problems in non-tech industries as well. The point of the text is to provide a proper mindset and attitude for reacting to these developments, and the book can be a benefit for folks in any field.

Notable Quote: “Don’t Get Frustrated The final technique isn’t so much a technique, but a maxim: Don’t get frustrated. When you are frustrated, you won’t think as clearly, you won’t work as efficiently, and everything will take longer and seem harder. Even worse, frustration tends to feed on itself, so that what begins as mild irritation ends as outright anger.”

Read Think Like a Programmer .

10. The Founder’s Dilemmas: Anticipating and Avoiding the Pitfalls That Can Sink a Startup by by Noam Wasserman

The Founder’s Dilemmas lays out the most common problems entrepreneurs face and gives advice on how to avoid or solve these issues. The book tackles topics such as managing relationships, hiring, and rewarding or correcting employees. The chapters outline the mistakes inexperienced leaders often make and offer strategies for handling these tough situations with more smarts and skill. By reading this book, founders can learn from predecessors and avoid making obvious and avoidable errors in judgment. The Founder’s Dilemmas is a problem-solving resource for startup leaders and team members who lack more traditional guidance.

Notable Quote: “Ideas are cheap; execution is dear.”

Read The Founder’s Dilemmas , and check out more entrepreneurial books .

11. The Scout Mindset: Why Some People See Things Clearly and Others Don’t by Julia Galef

The Scout Mindset challenges readers to move beyond gut reactions and preconceptions and rethink problems. The book offers instructions for overcoming bias and central beliefs to gather more objective data. Julia Galef encourages readers to act more like scouts than soldiers and gather information without judging to make more informed decisions. The text outlines the common reasons folks jump to conclusions and offers advice on how to avoid incorrect assumptions and conduct level-headed analyses. The Scout Mindset is a call to action for objectivity and an instruction manual for breaking away from unhelpful mental patterns that can lead to poor choices.

Notable Quote: “Discovering you were wrong is an update, not a failure, and your worldview is a living document meant to be revised.”

Read The Scout Mindset .

12. Super Thinking: The Big Book of Mental Models by Gabriel Weinberg and Lauren McCann

Super Thinking is a comprehensive resource that explains various mental models for problem solving. The book identifies logical fallacies and shows readers how to avoid these pitfalls. The pages also lay out appropriate strategies, tools, techniques to use in different situations, such as matrices, pointed questions, and philosophies. The point of the guide is to teach readers how to evaluate information and make quick yet accurate judgements. The guide helps readers decide the best approach to use for each circumstance. Though packed with information, the pages also contain images and humor that prevent the material from getting too dry. Super Thinking is the ultimate cheat sheet for thinking rationally and acting with intention.

Notable Quote: “Unfortunately, people often make the mistake of doing way too much work before testing assumptions in the real world.”

Read Super Thinking .

Final Thoughts

Problem solving is one of the most essential skills for modern industry. With the breakneck pace at which the current business world changes, there is no shortage of new developments that professionals must contend with on a daily basis. Operating the same way for years at a time is impossible, and it is almost guaranteed that workers at every level will have issues to unravel at some point in their careers.

Books about problem solving help professionals predict, prevent, and overcome issues and find more viable and sustainable solutions. These guides not only provide skills, but also methods for survival in a highly competitive business landscape. These texts show workers that they are more capable than may first appear and that sometimes, seemingly insurmountable obstacles are beatable with a combination of creativity, teamwork, and proper process.

For more ways to beat the odds, check out this list of books on innovation and this list of books on business strategy .

We also have a list of the best communication books .

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FAQ: Problem solving books

Here are answers to common questions about problem solving books.

What are problem solving books?

Problem solving books are guides that teach critical thinking skills and strategies for resolving issues. The purpose of these works is to help professionals be more creative and strategic in problem solving approaches.

What are some good problem solving books for work?

Some good problem solving books for work include Sprint by Jake Knapp, John Zeratsky, et al, Upstream by Dan Heath, and Think Like a Rocket Scientist by Ozan Varol.

Author: Angela Robinson

Marketing Coordinator at teambuilding.com. Team building content expert. Angela has a Master of Fine Arts in Creative Writing and worked as a community manager with Yelp to plan events for businesses.

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What Does “Novelty” Mean?

Something you’ve never experienced may nonetheless be familiar to you.

Posted June 21, 2010

Intelligence is correlated with openness to novel experience. But what does “novel experience” mean?

Research in personality psychology has repeatedly shown that one of the Five-Factor Model personality factors – openness to experience – is significantly positively (albeit moderately) correlated with intelligence. More intelligent individuals are more open to novel experiences. The similarly and overlap between intelligence and openness are apparent from the fact that some researchers call this personality factor “intellect” rather than “openness.”

The Hypothesis can provide one explanation for why more intelligent individuals are more open to novel experiences and are therefore more prone to seek novelty. General intelligence evolved as a domain-specific adaptation to deal with and solve evolutionarily novel problems , so it makes perfect sense that more intelligent individuals, who are better able to solve such problems, are more open to novel entities and concepts that might potentially lead to the solution of such problems.

At the same time, the Hypothesis suggests a possible need to refine the concept of novelty and to distinguish between evolutionary novelty (entities and situations that did not exist in the ancestral environment) and experiential novelty (entities and situations that individuals have not personally experienced in their own lifetime). While the Five-Factor Model does not specify the type of novelty that open – and thus more intelligent – individuals are more likely to seek, the Hypothesis suggests that more intelligent individuals are more likely to seek only evolutionary novelty, not necessarily experiential novelty.

For example, everybody who is alive in the United States today has lived their entire lives in a strictly monogamous society, and, despite occasional exceptions which make the news, very few contemporary Americans have any personal experiences with polygyny. Therefore, monogamy is experientially familiar for most Americans whereas polygyny is experientially novel. The Five-Factor Model may therefore predict that more intelligent individuals are more likely to be open to polygyny as an experientially novel idea or lifestyle.

In contrast, humans are naturally polygynous . Comparative evidence suggests that our ancestors have practiced mild polygyny throughout human evolutionary history. Socially imposed monogamy that we have today in most western societies is a relatively recent historical phenomenon. Polygyny is therefore evolutionarily familiar whereas monogamy is evolutionarily novel. The Hypothesis would thus predict that more intelligent individuals are more likely to be open to monogamy and less open to polygyny. In fact, the evidence suggests that more intelligent men are more likely to value sexual exclusivity than less intelligent men .

As another example, for most contemporary Americans, traditional names derived from the Bible, such as John and Mary, are experientially more familiar than untraditional names like OrangeJello and LemonJello. So the Five-Factor Model may predict that more intelligent individuals are more likely to name their children untraditional names like OrangeJello and LemonJello than less intelligent individuals. From the perspective of the Hypothesis , however, both John and OrangeJello are equally evolutionarily novel, because the Bible itself and all the traditional names derived from it are evolutionarily novel. So it would not predict that more intelligent individuals are more likely to name their children untraditional names. In fact, there is no evidence at all that more intelligent individuals are more likely to prefer untraditional names for their children. Giving one’s children unusual names may indeed be a sign of lower intelligence.

The Hypothesis underscores the need to distinguish between evolutionary novelty and experiential novelty. It can potentially explain why more intelligent individuals are more likely to seek evolutionary novelty, but not necessarily experiential novelty. It further suggests that the established correlation between openness and intelligence may be limited to the domain of evolutionary novelty, not necessarily experiential novelty, but the current measures of openness do not adequately address this proposal.

Satoshi Kanazawa is an evolutionary psychologist at LSE and the coauthor (with the late Alan S. Miller) of Why Beautiful People Have More Daughters .

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21 Good Picture Books to Teach Problem and Solution

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Read mentor text picture books to teach problem and solution text structure. Understanding the problem and solution story structures improves comprehension and helps readers make informed predictions. (As well as helping children see the creative possibilities in problem-solving!)

Of course, almost all stories have a problem and a solution –with the exception of a concept book. So really, you can search out problem and solution examples in any book, whether it’s fiction or nonfiction.

When children learn what to expect in a problem and solution story, not only will they be able to predict solutions, but they will also be better able to write their own problem-solution stories. I started teaching this early to my young kids, well before they were school-age because we want our children to become problem solvers. That is an important life skill!

While many picture books model the narrative story structure of problem and solution, these are my favorites to use with kids both at home and in the classroom.

PRINTABLE LIST

Mentor Text Picture Books to Teach Problem and Solution

Problem Solved! by Jan Thomas When Rabbit sees his messy room, he learns that he has HIS OWN PROBLEM SOLVING PORCUPINE! Which seems good at first. But, it turns into a disaster. Because to clean up the blocks, the porcupine flushes them down the toilet. And to clean up his shirts, he feeds them to the goldfish. How can Rabbit get rid of his not-very-helpful problem-solving porcupine?

A House in the Woods  by Inga Moore Little Pig’s den becomes filled with friends, but once Moose arrives, the den collapses. Oh, no! Problem. What will they do to find a solution? Together, the animals build a new house in the woods big enough to fit all the friends.

Enigma  by Graeme Base Bertie needs to find the missing magic show props that have disappeared from his grandpa’s retirement home. Each performer tells him what’s missing. Readers help find the items in the illustrations so that Bertie can find the culprit. Like all his books, Base excels in his detailed illustrations.

7 Ate 9: The Untold Story  by Tara Lazar, illustrated by Ross MacDonald 6 bangs on Private I’s door for help! Because there’s a rumor that 7 is eating other numbers because apparently, 7 ate 9. YIKES! But did 7 really eat 9? Pitch perfect tongue-in-cheek number and word humor will crack you up throughout this suspenseful, funny problem and solution story. (Also on:  Best Picture Book Mysteries .)

The Brownstone  by Paula Scher, illustrated by Stan Mack The Bear family is ready for hibernation but first, they need to figure out what to do about the noise problem. Their solution? All the animals work together to shift apartments so that everyone finds the best apartment for their specific needs. You’ll love the message and illustrations.

Pigeon P.I.  by Meg McLaren What a unique and delightful mystery story! A little canary asks Pigeon P.I. (private investigator) to help her find her missing friends. Then the canary goes missing, too. It’s up to Pigeon to solve the missing bird mystery. The author writes in the style of the old detective shows– punchy with short sentences. The illustrator captures the details, giving kids clues to notice as they read.

One Word from Sophia  by Jim Averbeck, illustrated by Yasmeen Ismail This picture book is a great way to teach kids summarizing and word choice as well as a problem-solution text structure! Sophia really wants a pet giraffe for her birthday. As a result, she sets out to convince her family, starting with her mother, a judge. However, Mother says that Sophia’s argument is too verbose. As a result, Sophie tries fewer words with Father. But he says her presentation is too effusive. Sophia continues with each family member until she reaches her last-ditch attempt and says the one word that works: PLEASE.

No Boring Stories!  by Julie Falatko, illustrated by Charles Santoso When a cute little bunny tries to join a group of animal storytellers (mole, weevil, crab, and babirusa), the group doesn’t want to add her to their brainstorming group. As the animals continue their story plans with relatable characters, an inciting incident, rising action, climax, and…. Only the group gets stuck with the ending. That’s when bunny reveals that she likes making up weird (not boring) stories. The group realizes that the bunny has the perfect ending idea. Reluctantly, they agree that she can be part of the group. At least until a “ bunch of adorable frogs and puppies show up next week… ” This book shows plotting as well as the creative strengths of writers working together.

That Fruit Is Mine!  by Anuska Allepuz This is a charming problem and solution story about learning to share and the power of working together. You’ll crack up watching the elephants’ many failed attempts to get delicious-looking fruit off a tree while simultaneously watching a tiny group of mice work together to get the yummy fruit, too. The problem is getting the fruit but only one animal group succeeds in a solution. Who do you think it will be? Great for prediction! (Also on:  Picture Books That Teach Cooperation .)

Great, Now We’ve Got Barbarians!   by Jason Carter Eaton, illustrated by Mark Fearing Mom says that if the boy doesn’t clean his room, he’ll get pests . . . which the boy thinks aren’t all that bad, right? However, things go downhill when barbarian “pests” start arriving. Because they eat everything, use his toys to clean out their ears, and steal blankets and pillows. So there is only one thing to do — CLEAN up his room. It’s a predictable but funny solution with the perfect forgot-to-clean-up twist at the end.

Walrus in the Bathtub  by Deborah Underwood, illustrated by Matt Hunt The worst thing about this family’s new home is the walrus in the bathtub. And walrus songs are very, very loud. It’s a big problem. The family tries lots of clever things to get the walrus to leave the bathtub but with no success. So they decide to move. Again. That’s when the walrus shows them his list — “ How to Make Your New Family Feel Welcome ” — which, surprisingly, includes all the things that annoy the family. It turns out the walrus was just trying to be nice. As a result, the family stays with a few *new* rules. This story will make you want your own walrus in a bathtub.

The Thingity-Jig by Kathleen Doherty, illustrated by Kristyna Litten Wordplay, problem-solving, and persistence! One day Bear finds a Thingity-Jig (aka. a couch), which he thinks is wonderful as a sit-on-it, jump-on-it thing.  He asks his friends to help him carry it home but they’re too fast asleep, so Bear figures out some ideas to do it himself. He makes a Rolly-Rumpity! Which is a pack-it-up, heap-it-up, load-it-up thing. That isn’t enough to move the Thingit-Jig so Bear makes something else — a Lifty-Uppity. And then, a Pushy-Poppity. And at daybreak, he arrives back at home where his friends are waking up, with his special Thingity-Jig. Bingity…Bing…Boing…Bear falls asleep.

Someday is Now: Clara Luper and the 1958 Oklahoma City Sit-Ins  by Olugbemisola Rhuday-Perkovich Clara advocated for justice and equality during a time when Black people weren’t permitted the same rights as white people. As a teacher, she inspired her students to believe that change was possible. Clara and her students went to the Katz drugstore and asked to be served — even though the store didn’t serve black people. She and her students returned day after day despite people yelling and throwing food. Eventually, the Katz store relented and started to serve people of all races. Clara and her students finally could enjoy a Coke and a burger without trouble.

Wangari’s Trees of Peace  by Jeannette Winter Based on the true story of Wangari Maathai, winner of the Nobel Peace Prize, read how Wangari helped her country of Kenya whose forests were all but destroyed. She started planting trees which started a movement motivating other people to plant trees as well. This is an example of how narrative nonfiction book can also teach the plot structure of problem and solution .

Battle Bunny   by Jon Scieszka and Mac Barnett, illustrated by Matt Myers When Alex gets a silly, sappy picture book called Birthday Bunny, he picks up a pencil and turns it into something he’d like to read: Battle Bunny. An adorable rabbit’s journey through the forest becomes a secret mission to unleash an evil plan–a plan that only Alex can stop. Not only does this mentor text model problem and solution, but also voice and revision.

When Pigs Fly  by James Burke One day, an exuberant pig declares that he will fly. His sister observes with disbelief and horror as one attempt after another fails. The brother pig is so disappointed that he decides to give up. That’s when his sister comes up with an idea — something he hasn’t tried before that will help her brother fly — a pretend airplane. The pigs’ expressive illustrations are absolutely perfect as is the message of persistence despite failure.

Piper and Purpa Forever!  by Susan Lendroth, illustrated by Olivia Feng Most stories have a  problem and a solution  but this story is a great example showing a little girl’s ability to creatively  problem solve  with a beautiful solution to her problem. Piper loves her beloved purple sweater, Purpa, and is so sad when she grows out of it. Will she be able to keep her sweater somehow?

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Melissa Taylor, MA, is the creator of Imagination Soup. She's a mother, former teacher & literacy trainer, and freelance education writer. She writes Imagination Soup and freelances for publications online and in print, including Penguin Random House's Brightly website, USA Today Health, Adobe Education, Colorado Parent, and Parenting. She is passionate about matching kids with books that they'll love.

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My grandson loves cars, RC cars, sports cars but I don’t find any books about cars, racing, car features, etc. It would be a ‘hook’ to get him to read more. Any suggestions appreciated.

Here is a list of vehicle books. https://imaginationsoup.net/picture-books-vehicle-loving-kids/ . My recommendation for car books is Professor Wooford McPaw’s History of Cars by Elliot Kruszynski.

More From Forbes

5 keys to solving the right problems in your business.

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Two multi-ethnic workers working in a plastics factory, standing on the factory floor, looking at ... [+] the control panel of one of the machines. The African-American man is pointing to the panel. His coworker, an Hispanic woman, is holding a digital tablet.

There is no doubt that today’s business challenges are more complex and global than ever, but I still see my peers and business leaders using the same strategies that worked for them years ago. Aspiring new business owners often sink millions into innovations and marketing plans that never get off the ground, and overlook simple details that cost them time, energy, and success.

For example, many businesses are currently struggling with getting their employees back to the office for work, to improve business productivity, accountability, and customer satisfaction. In fact, this challenge clearly has personal team considerations, as well as business implications. Many people prefer the flexibility and comfort of working from home, outweighing results and growth.

I’m not sure if the real problem here is business process or people management, or both, but there is certainly much room for error on both sides. As a consultant, I found some good strategies for not solving the wrong problem in a recent book, “ Solve the Real Problem ,” by Roger L. Firestien, PhD., from Buffalo State University, Innovation Resources, and other roles.

He has real credentials in academia, as well as problem-solving and innovation experiences with many businesses around the world. He offers some key recommendations that I also espouse for how to zero in on the root challenge and not waste large amounts of time and money you cannot afford:

1. Creative questions are key to problem definition. Focus on chains of fact-finding questions and judgement or decision questions to bring out solution ideas. In all cases, defer judgment and avoid excuses like “I don’t have time.” One good question can generate whole new fields of inquiry and can prompt changes in entrenched thinking.

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Creative questions are also useful for exploring new business ideas. Just remember that solving customer problems is the challenge here, rather than internal problems. The process and the results are the same – starting with creative questions to find the real opportunity.

2. Adopt a more effective problem-solving mindset. Analyze your habitual approach to problem solving and be prepared to challenge your own assumptions. Avoid settling for symptoms as the problem or jumping to conclusions based on poor information or your own biases. Sometimes we get in our own way and end up working on the wrong thing.

This strategy also applies to new opportunities for customer growth as well as organizational problems. I still see too many technologists whose mindset is focused on the beauty of their innovation, rather than the problem it solves for customers.

3. Don’t trust or act on your first impression. We all make wrong judgments on first impressions, especially with recurring problems or with people who are of a different nationality, race, and ethnicity. First impressions are usually wrong, especially if they are made in an emotional environment, under time constraints, or with too little information.

4. Get an outside perspective with no agenda. The best way to get an outside perspective is to tap into people who run in circles different from your own. Look for “creative catalysts” who can provide a fresh perspective on the problem and potential solutions. Beware of experts in the relevant technology who may have their own biases.

5. Look for the bigger picture, not minutiae. Make sure that you don’t become unable to see the “forest for the trees” by looking only at a few details of the problem. Consciously step back and take a broader view of the challenge ahead. This approach also builds alignment with related perspectives and issues, and results in better long-term solutions.

In the real world, my experience is that none of these strategies will work without conscientious business leadership, committed team members, a positive business model, and a viable customer opportunity. Your team also needs the creativity skills and training to properly diagnose problems and challenges, generate solutions, and put these solutions into action.

I encourage all of you to recognize that every business in today’s world will encounter challenges and world-class problems. Thus it behooves all of us to continuously update our business problem-solving strategies, support a culture of innovation, and keep moving forward in your quest to make the world a better place, and enjoy the journey to get there.

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Improving examples to improve transfer to novel problems

Affiliation.

• 1 School of Psychology, Georgia Institute of Technology, Atlanta 30332.
• PMID: 7968556
• DOI: 10.3758/bf03198399

People often memorize a set of steps for solving problems when they study worked-out examples in domains such as math and physics without learning what domain-relevant subgoals or subtasks these steps achieve. As a result, they have trouble solving novel problems that contain the same structural elements but require different, lower-level steps. In three experiments, subjects who studied example solutions that emphasized a needed subgoal were more likely to solve novel problems that required a new approach for achieving this subgoal than were subjects who did not learn this subgoal. This result suggests that research aimed at determining the factors that influence subgoal learning may be valuable in improving transfer from examples to novel problems.

Publication types

• Research Support, U.S. Gov't, Non-P.H.S.
• Knowledge of Results, Psychological
• Mental Recall*
• Probability Learning
• Problem Solving*
• Transfer, Psychology*