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Published 2011

Co-operative Problem Solving: Pieces of the Puzzle Approach

What is the pieces of a puzzle approach.

You are responsible for your own work and behaviour
You must be willing to help any group member who asks
You may only ask the teacher for help if everyone in the group has the same question
Risk taking - pupils are more likely ask questions of each other and put forward ideas in a small group situation, particularly with Rule 2 in place.
Mathematical language development - usually the clues for the tasks are communicated with words. The group needs to negotiate their interpretation of the mathematical vocabulary. They also must talk to each other, listen to others and explain their ideas clearly.
Peer coaching - pupils are able to clarify their understanding of mathematical concepts, correct misconceptions and test out ideas during the process of finding a collective solution to the problem.
Teacher's role as a facilitator and observer - the independence of the groups gives the teacher freedom to move around the class, observe language and strategies, interact with groups as required and assess their progress.
Effective learning - the tasks generally incorporate the manipulation of physical objects to produce a final product, which promotes the linking of verbal knowledge with visual imagery.
Mixed ability class teaching - the features listed above combine to make this approach particularly suited to use with mixed ability classes. Every child should be able to make a contribution to the problem solving process, learn from the activity and have received attention from the teacher when needed.

Forming the Groups

There are, of course, many ways to organise children into groups. Unless the teacher has specific reasons for doing otherwise, a random mix method is best for this type of co-operative problem solving.

Random Mix by the Cards

Here is one way to achieve a random mix of pupils using a pack of ordinary playing cards. To form seven groups of four children, use all four card suits from one (Ace) to seven. Shuffle this pack and have each child choose a card. All the sevens form a group, all the sixes form a group and so on.

Diamonds - team manager - responsible for assisting teacher to get group's attention at specified signal and reminding the group of the 'rules';
Spades - equipment manager - responsible for collecting and returning materials, and ensuring all group members have access to the materials;
Hearts - recorder - noting significant information, steps in solution, or preparation of finished product (such as the model, drawing or chart);
Clubs - spokesperson - responsible for reporting the group's efforts and/or solutions

Lesson Structure

Introduction: This type of problem solving activity is well suited to developing and clarifying mathematical ideas that have already been introduced in other lessons. Therefore, in introducing the task to the class, the teacher can make links to previous work. If the mathematical vocabulary contained in the problem is of particular concern, then key terms should be revised.

Group work: The groups are formed and each child in a group is given one clue card. To maintain 'ownership' of the piece of information, the child may not physically give away the clue-card, but must be responsible for communicating the content to the group. Each pupil's role is now to work within his/her group to solve the puzzle, following the set of work rules. The teacher must also take care to follow these rules, and not take back responsibility for the task by interfering with the problem-solving processes or offering help before being asked by the whole group.

As always, it is advisable to have an extension question ready for a group that finishes before the others. It is also useful to have one or two 'extra' clues ready. These can be used to allow the inclusion of an extra group member, to give help to a group that is 'stuck', or to assist 'checking' when a group thinks it has finished the task.

Plenary - It is important for groups to report on their problem-solving processes as well as confirming the correctness of their end product. The teacher can use questions focus on particular issues and highlight points that have been observed during the session. For example:

Examples of Problems

(More than one answer is possible until Clues E & F are incorporated)

Stick Figures

Each group needs a handful of sticks, all of the same length - such as matches, ice-cream or lolly sticks, or drinking straws. The aim is to arrange some of the sticks to make either a single shape or shapes-combinations (depending on the level of complexity).

Fractured Shapes

The clues in this type of problem are non-verbal. In the example below, the squares are cut up by the teacher and each member of a group-of-four is given three pieces marked with the same letter. The aim is for the group to make four complete squares.

Each group needs a set of digit cards (two or three copies of the digits 0-9) and a template of the algorithm, in this example a two-column sum

Burns, M. (1992) About Teaching Mathematics , Maths Solution Publications: California Erickson, T. (1989) Get It Together, EQUALS: University of California.

Gould, P. (1993) Co-operative Problem Solving in Mathematics , Mathematical Association of N.S.W. Australia. ISBN 0-7310-1371-9 (Available through the Australian Association of Mathematics Teachers Catalogue code MAN466 - http://www.aamt.edu.au/ )

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Small Group Math Activities

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Math Stations

Discover small group math activities that promote student engagement and foster a love for math. This blog post explores 10 activities, including math games, hands-on manipulatives, real-world investigations, technology tools, problem solving activities, and more to help you transform your math stations into a dynamic learning environment.

I have a secret confession to make.

Teaching reading has never been my cup of tea.

Don’t get me wrong, I adore immersing my students in captivating books and opening their minds to new worlds.

But when it comes to reading workshop, let’s just say it didn’t exactly light a fire in my soul.

The never-ending cycle of reading from the textbook series and completing author’s purpose, inference, and comprehension worksheets felt mundane and, dare I say it, a bit dull. #yawn 🥱

Despite my best efforts, I struggled to make it truly exciting.

So, when the opportunity to introduce math workshop came knocking, I must admit, I wasn’t exactly jumping for joy.

It’s All About Engagement

Math stations are a powerful tool for promoting student engagement and deepening our students’ mathematical understanding.

By incorporating engaging activities into your math station rotations, you can create a dynamic learning environment that sparks excitement and curiosity in your students.

In this blog post, we will explore 10 engaging small group math activities that will captivate your students and inspire them to develop a love for math.

10 Small Group Math Activities for Any Math Station Rotation

$This is an example of 5 small group math activities.$

Activity 1: Math Games Galore

Math games are a fantastic way to make learning fun and interactive. These small group math activities provide opportunities for students to practice math skills while communicating mathematically with their peers. Here are a few examples of card and dice games that can be incorporated into your math station rotations:

War Games: This classic math game requires only a deck of cards. Partners each turn over a card and use their math skills to compare the numbers, such as whole numbers, fractions, decimals, or even simple expressions. The player with the higher value wins the round. Players continue playing until no cards are remaining.
Cover-Up Games: This simple board game requires two dice. In turn, each student rolls the dice and completes the problem associated with the dice sum. Then, they cover the solution with a marker in a grid trying to get four in a row, column, or diagonal.
Traditional Board Games: Pair a set of task cards with a traditional board game to create this math station activity. After correctly answering a question, students can roll a die or toss a coin to move along the path.

Activity 2: Hands-On Manipulatives

Hands-on manipulatives bring abstract math concepts to life, making them more concrete and tangible. These activities provide students with a visual and kinesthetic experience, enhancing their understanding of mathematical concepts. Consider incorporating the following manipulative-based activities into your math stations:

Pattern Block Puzzles: Provide students with pattern blocks and challenge them to create different shapes and designs, exploring concepts like symmetry, fractions, and geometry.
Base Ten Blocks: Use base ten blocks to reinforce place value concepts. Students can build and represent numbers and explore operations with whole numbers and decimals.
Data Analysis with Spinners: Use spinners with different sections labeled with numbers or categories. Students spin the spinner multiple times, record the results, and represent the data they collected by creating a frequency table, bar graph, or dot plot.

Want to use math manipulatives but need more resources? Try virtual manipulatives !

Activity 3: Puzzle Power

Puzzles are not only engaging but also promote critical thinking and problem solving skills. They challenge students to think creatively and persevere through complex tasks. Here are a few puzzle-based activities to include in your math stations:

Number Crossword: Create a crossword puzzle where students respond to math-related clues and fill in the corresponding numbers in the grid.
Logic Grids: Challenge students with logic puzzles that require them to use deductive reasoning and critical thinking skills to solve.
Sudoku: Provide students with Sudoku puzzles focusing on numbers, shapes, or mathematical operations, encouraging them to apply logical reasoning to complete the puzzles.

Activity 4: Real-World Math Investigations

Real-world math investigations allow students to apply their mathematical knowledge and skills to authentic situations. These activities promote problem-solving, critical thinking, and the ability to connect math and the real world. Consider the following examples for your math station rotations:

Recipe Conversions: Provide students with recipes that need to be converted to serve a different number of people. Students must adjust ingredient quantities using proportional reasoning and fractions.
Budgeting and Shopping: Give students a budget and a list of items with prices, such as a local grocery ad or restaurant menu. They must plan a shopping trip, choose items based on their budget, and calculate the total cost.
Measurement Scavenger Hunt: Create a list of objects in the classroom or nearby hallway students need to measure using various units of measurement. Students will use rulers, measuring tapes, or scales to gather the data and record their measurements.

Activity 5: Technology Tools

Incorporating technology into math stations can engage students and provide interactive learning experiences. Consider utilizing the following online resources and educational apps:

Online Math Games and Activities: Websites such as IXL Learning, Prodigy, and Math Playground provide opportunities to gamify the learning experience. Students can earn points and virtual rewards while building math skills.
Digital Activities: Activities designed for Google Classroom and Seesaw provide engaging opportunities for students to use digital tools to review math concepts and skills .
Digital Task Cards: Take task cards to the next level with digital task cards . Task cards created for use at Boom Learning or even with Google Forms can increase student engagement while students practice essential math skills.

Activity 6: Ready-Made Math Activities

In addition to creating your small group math activities, incorporating ready-made resources can provide a valuable and time-saving option for engaging your students. These pre-made activities offer an interactive and hands-on way to reinforce math skills and concepts.

Electronic Flashcard Games: Electronic flashcard games provide an exciting and interactive way for students to practice and reinforce math facts. These games often offer various difficulty levels and customizable options to cater to students’ needs. Math Whiz and Math Shark are two of my favorites!
VersaTiles: VersaTiles is a hands-on, puzzle-inspired activity with an interactive workbook system designed to reinforce math skills. Students use a unique answer case and answer tiles to complete activities and self-check their answers. It’s a favorite of my elementary and middle school students alike!
Marcy Cook Tiling Tasks: Marcy Cook Tiling Tasks are critical thinking activities that require students to use a set of tiles labeled 0-9 to complete math puzzles. These tasks promote problem-solving skills, logical reasoning, and mathematical thinking. Students arrange the tiles to fill in the blanks and create equations and solutions that satisfy the given conditions.

Activity 7: Math Task Cards

Math task cards offer various practice opportunities and allow students to work independently. They are also easy to make and readily available on teacher marketplaces across the web. Here are some examples of task card activities:

Showdown: Partners select one card and complete it individually. Then, students “showdown” and share their responses using math talk and supporting each other as necessary.
Math Game: Pair a set of task cards with a game board to gamify the learning experience! Students place their game markers at the start line. To move down the path, students must correctly respond to a task card, toss a die (or flip a coin), and move the number of spaces indicated on the die or based on the side of the coin visible after the coin toss (heads = 2 spaces, tails = one space).
Cover Up: To create a Cover Up game, program a 4 x 4 grid with the solutions to a set of task cards. Then, when students respond correctly, they can cover the answer with a board marker, such as centimeter cubes, color tiles, Bingo chips, or beans. The goal is to get four markers in a row, column, or diagonal. Note: This activity works best with multiple-choice questions, true or false questions, or questions with numerical answers.

$This is an example of how math picture books can be used to create small group math activities.$

Activity 8: Math Picture Books

Integrating math and literature activities enhances students’ mathematical understanding and develops their reading comprehension, critical thinking, and analytical skills. Consider incorporating the following math and literacy activities into your math stations:

Math Investigations: Use the storyline in a book to practice a skill. For example, use the Pigs Will Be Pigs book by Amy Axelrod to practice adding and subtracting decimals as the pigs find money hidden around their home and then spend it at a restaurant.
Story-based Problems: Use the book as a springboard to reinforce a specific skill. Either re-create scenarios from the book or create new problems based on the problems the characters faced in the story such as comparing the amounts in two different groups after reading Amanda Bean’s Amazing Dream by Cindy Neuschwander.
Famous Mathematicians Book Study: Create a set of questions to help students learn more about famous mathematicians, such as Katherine Johnson , and provide students with access to a physical or digital biography to read and use to respond to the questions.

This is an example of a calculator challenge.

Activity 9: Calculator Challenges

Incorporating calculator challenges into your math stations can allow upper elementary students to deepen their understanding of math concepts while developing their computational skills. Calculator activities engage students in hands-on exploration, problem-solving, and critical thinking while building their technology proficiency skillset.

These activities encourage students to use calculators to investigate, solve problems, and make connections. Consider incorporating the following calculator challenges into your math stations:

The Broken Calculator Challenge: In this challenge, students are shown an image of a calculator with only three or four working buttons. Students then determine how to use the remaining keys on the broken calculator to create specific values, such as using +, x, 2, and 3 to achieve a value of 8.
Calculator Corrections: This task requires students to determine how to correct a calculator mistake without clearing the calculator. Using the calculator, students determine how to fix a mistake, check the answer, and make adjustments as necessary. After completing the task, students can justify the changes they made. For example, Brandi wanted to enter the number 4265 into her calculator. By mistake, she typed 4165. Without clearing her calculator, how can she fix her mistake?
Target Number: For this task, students represent place value in numbers, determine what number to add or subtract to reach the target number, and use the calculator to check their process. For example, students are given the following directions: Start with 7,254. Find a number to subtract that will result in a 0 in the hundreds column.

Activity 10: Problem Solving and Critical Thinking

Problem-solving and critical thinking are essential life skills for students to develop. Engage your students in meaningful and challenging math experiences by incorporating problem solving and critical thinking activities into your small group math activities. Click here for a list of problem solving activities ; that encourage students to think critically, analyze situations, and apply their mathematical knowledge to real-world scenarios.

A Shift in Thinking

While I never found a way to make reading workshop exciting, math workshop was my students’ favorite part of the day.

Integrating various small group math activities into the rotation was the key to keeping students engaged in learning and wanting more.

If you’re new to math stations, the best way to get started is to choose 1-2 new activities to implement. Consider adding another activity after students are comfortable with the previous activities and staying engaged with minimal support.

Adding new small group math activities gradually will help maintain order during the rotation and save your sanity! If you’d like more tips and tools for managing math stations, download the Math Station Management Toolbox using the form at the bottom of this post.

Math station rotation boards are an excellent organizational tool for implementing the small group math activities above. This visual display helps students understand the structure of the math station rotation and enhances their independence and accountability.

The small group math activities shared above can be assigned to specific stations on the rotation board. Then, teachers can use the math station rotation board to effectively monitor student progress as they rotate through various math stations.

Experiment with these small group math activities and adapt them to meet the needs and interests of your students, ensuring math station time is an exciting and transformative experience for all.

What are your favorite small group math activities? Respond in the comments below.

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Team Work makes the Math Work

I don't need to tell you that the pandemic has had some significate affects in our students learning, especially in math. Analysis shows that on average students are 5 months behind in math learning and that number increases for historically disadvantaged students to as 7 months of learning loss. Now that students are back in the classroom one step we can take to increase math learning is to make math a group or team activity. Group work helps student improve their critical thinking and problem-solving skills; it helps them express their understanding in a safe atmosphere that is interactive supportive and efficient. Groupwork helps students use mathematical vocabulary and incorporate life experiences into their understanding of the math problem.

A few things to think about when doing group math work.

1. Grouping students: A group is a social unit that is comprised of two or more people who have a common goal. Here are three different way to group students and the pros and cons to each.

Student Choice –

i. Pros: positive attitudes towards each other – higher outcomes – less planning

ii. Cons: less diversity – some students not selected – off task talking

Random Grouping –

i. Pros: less planning – group diversity – builds communication skills

ii. Cons: negative attitude about selection – lower group cohesion

Educator Selected Academics –

i. Pros: organized based on needs, improves dept of learning

ii. Cons: widens achievement gaps, planning, labeling

Group roles: Students should know that they will not be able so succeed on their own unless the others will. Students should have roles to help in the solving of the problem, these roles should change as students form new groups.
Leader – keeps students on task, delegates
Recorder – writes out responses
Challenger – questions
Thinker – produces ideas
Supporter – eases tension and promotes people ideas
Math problems
Multi-step to encourage deeper thinking
Relatable so students understand the necessity of learning (if children are in the problem have the students change the names to their own)
Provide information on problem solving strategies so they can select the best way to find a solution.

Problem solving strategies

1. Guess and Check

2. Draw a picture

3. Act it out

4. Create a grid

5. Find a pattern

6. Use logic

7. Work backwards

8. Simplify problem

These steps will help student improve their math understanding quicker than any worksheet or web-game. Check out MANGO Math for fun hands-on math games that engage and educated students while they enjoy math.

MANGO Math Blog

14 Best Team Building Problem Solving Group Activities For 2024

The best teams see solutions where others see problems. A great company culture is built around a collaborative spirit and the type of unity it takes to find answers to the big business questions.

So how can you get team members working together?

How can you develop a mentality that will help them overcome obstacles they have yet to encounter?

One of the best ways to improve your teams’ problem solving skills is through team building problem solving activities .

“86% of employees and executives cite lack of collaboration or ineffective communication for workplace failures.” — Bit.AI

These activities can simulate true-to-life scenarios they’ll find themselves in, or the scenarios can call on your employees or coworkers to dig deep and get creative in a more general sense.

The truth is, on a day-to-day basis, you have to prepare for the unexpected. It just happens that team building activities help with that, but are so fun that they don’t have to feel like work ( consider how you don’t even feel like you’re working out when you’re playing your favorite sport or doing an exercise you actually enjoy! )

Team Building Problem Solving Group Activities

What are the benefits of group problem-solving activities?

The benefits of group problem-solving activities for team building include:

Better communication
Improved collaboration and teamwork
More flexible thinking
Faster problem-solving
Better proactivity and decision making

Without further ado, check out this list of the 14 best team-building problem-solving group activities for 2024!

Page Contents (Click To Jump)

2. Problem-Solving Templates

Problem-Solving Templates are popular problem-solving activities that involve a group of people working together to solve an issue. The challenge generally involves members of the team utilizing pre-made templates and creating solutions for a given problem with the help of visual aids.

This activity is great for teams that need assistance in getting started on their problem-solving journey.

Why this is a fun problem-solving activity: Problem-Solving Templates offer teams an easy and stress-free way to get the creative juices flowing. The visual aids that come with the templates help team members better understand the issue at hand and easily come up with solutions together.

This activity is great for teams that need assistance in getting started on their problem-solving journey, as it provides an easy and stress-free way to get the creative juices flowing.

Problem Solving Group Activities & Games For Team Building

3. coworker feud, “it’s all fun and games”.

Coworker Feud is a twist on the classic Family Feud game show! This multiple rapid round game keeps the action flowing and the questions going. You can choose from a variety of customizations, including picking the teams yourself, randomized teams, custom themes, and custom rounds.

Best for: Hybrid teams

Why this is an effective problem solving group activity: Coworker Feud comes with digital game materials, a digital buzzer, an expert host, and a zoom link to get the participants ready for action! Teams compete with each other to correctly answer the survey questions. At the end of the game, the team with the most competitive answers is declared the winner of the Feud.

How to get started:

Sign up for Coworker Feud
Break into teams of 4 to 10 people
Get the competitive juices flowing and let the games begin!

Learn more here: Coworker Feud

4. Crack The Case

“who’s a bad mamma jamma”.

Crack The Case is a classic WhoDoneIt game that forces employees to depend on their collective wit to stop a deadly murderer dead in his tracks! Remote employees and office commuters can join forces to end this crime spree.

Best for: Remote teams

Why this is an effective problem solving group activity: The Virtual Clue Murder Mystery is an online problem solving activity that uses a proprietary videoconferencing platform to offer the chance for employees and coworkers to study case files, analyze clues, and race to find the motive, the method, and the individual behind the murder of Neil Davidson.

Get a custom quote here
Download the app
Let the mystery-solving collaboration begin!

Learn more here: Crack The Case

5. Catch Meme If You Can

“can’t touch this”.

Purposefully created to enhance leadership skills and team bonding , Catch Meme If You Can is a hybrid between a scavenger hunt and an escape room . Teammates join together to search for clues, solve riddles, and get out — just in time!

Best for: Small teams

Why this is an effective problem solving group activity: Catch Meme If You Can is an adventure with a backstory. Each team has to submit their answer to the puzzle in order to continue to the next part of the sequence. May the best team escape!

The teams will be given instructions and the full storyline
Teams will be split into a handful of people each
The moderator will kick off the action!

Learn more here: Catch Meme If You Can

6. Puzzle Games

“just something to puzzle over”.

Puzzle Games is the fresh trivia game to test your employees and blow their minds with puzzles, jokes , and fun facts!

Best for: In-person teams

Why this is an effective problem solving group activity: Eight mini brain teaser and trivia style games include word puzzles, name that nonsense, name that tune, and much more. Plus, the points each team earns will go towards planting trees in the precious ecosystems and forests of Uganda

Get a free consultation for your team
Get a custom designed invitation for your members
Use the game link
Dedicated support will help your team enjoy Puzzle Games to the fullest!

Learn more here: Puzzle Games

7. Virtual Code Break

“for virtual teams”.

Virtual Code Break is a virtual team building activity designed for remote participants around the globe. Using a smart video conferencing solution, virtual teams compete against each other to complete challenges, answer trivia questions, and solve brain-busters!

Why this is an effective problem solving group activity: Virtual Code Break can be played by groups as small as 4 people all the way up to more than 1,000 people at once. However, every team will improve their communication and problem-solving skills as they race against the clock and depend on each other’s strengths to win!

Reach out for a free consultation to align the needs of your team
An event facilitator will be assigned to handle all of the set-up and logistics
They will also provide you with logins and a play-by-play of what to expect
Sign into the Outback video conferencing platform and join your pre-assigned team
Lastly, let the games begin!

Learn more here: Virtual Code Break

8. Stranded

“survivor: office edition”.

Stranded is the perfect scenario-based problem solving group activity. The doors of the office are locked and obviously your team can’t just knock them down or break the windows.

Why this is an effective problem solving group activity: Your team has less than half an hour to choose 10 items around the office that will help them survive. They then rank the items in order of importance. It’s a bit like the classic game of being lost at sea without a lifeboat.

Get everyone together in the office
Lock the doors
Let them start working together to plan their survival

Learn more here: Stranded

9. Letting Go Game

“for conscious healing”.

The Letting Go Game is a game of meditation and mindfulness training for helping teammates thrive under pressure and reduce stress in the process. The tasks of the Letting Go Game boost resiliency, attentiveness, and collaboration.

Why this is an effective problem solving group activity: Expert-guided activities and awareness exercises encourage team members to think altruistically and demonstrate acts of kindness. Between yoga, face painting, and fun photography, your employees or coworkers will have more than enough to keep them laughing and growing together with this mindfulness activity!

Reach out for a free consultation
A guide will then help lead the exercises
Let the funny videos, pictures, and playing begin!

Learn more here: Letting Go Game

10. Wild Goose Chase

“city time”.

Wild Goose Chase is the creative problem solving activity that will take teams all around your city and bring them together as a group! This scavenger hunt works for teams as small as 10 up to groups of over 5000 people.

Best for: Large teams

Why this is an effective group problem solving activity: As employees and group members are coming back to the office, there are going to be times that they’re itching to get outside. Wild Goose Chase is the perfect excuse to satisfy the desire to go out-of-office every now and then. Plus, having things to look at and see around the city will get employees talking in ways they never have before.

Download the Outback app to access the Wild Goose Chase
Take photos and videos from around the city
The most successful team at completing challenges on time is the champ!

Learn more here: Wild Goose Chase

11. Human Knot

“for a knotty good time”.

The Human Knot is one of the best icebreaker team building activities! In fact, there’s a decent chance you played it in grade school. It’s fun, silly, and best of all — free!

Why this is an effective group problem solving activity: Participants start in a circle and connect hands with two other people in the group to form a human knot. The team then has to work together and focus on clear communication to unravel the human knot by maneuvering their way out of this hands-on conundrum. But there’s a catch — they can’t let go of each other’s hands in this team building exercise.

Form a circle
Tell each person to grab a random hand until all hands are holding another
They can’t hold anyone’s hand who is directly next to them
Now they have to get to untangling
If the chain breaks before everyone is untangled, they have to start over again

Learn more here: Human Knot

12. What Would You Do?

“because it’s fun to imagine”.

What Would You Do? Is the hypothetical question game that gets your team talking and brainstorming about what they’d do in a variety of fun, intriguing, and sometimes, whacky scenarios.

Best for: Distributed teams

Why this is an effective group problem solving activity: After employees or coworkers start talking about their What Would You Do? responses, they won’t be able to stop. That’s what makes this such an incredible team building activity . For example, you could ask questions like “If you could live forever, what would you do with your time?” or “If you never had to sleep, what would you do?”

In addition to hypothetical questions, you could also give teammates some optional answers to get them started
After that, let them do the talking — then they’ll be laughing and thinking and dreaming, too!

13. Crossing The River

“quite the conundrum”.

Crossing The River is a river-crossing challenge with one correct answer. Your team gets five essential elements — a chicken, a fox, a rowboat, a woman, and a bag of corn. You see, the woman has a bit of a problem, you tell them. She has to get the fox, the bag of corn, and the chicken to the other side of the river as efficiently as possible.

Why this is an effective group problem solving activity: She has a rowboat, but it can only carry her and one other item at a time. She cannot leave the chicken and the fox alone — for obvious reasons. And she can’t leave the chicken with the corn because it will gobble it right up. So the question for your team is how does the woman get all five elements to the other side of the river safely in this fun activity?

Form teams of 2 to 5 people
Each team has to solve the imaginary riddle
Just make sure that each group understands that the rowboat can only carry one animal and one item at a time; the fox and chicken can’t be alone; and the bag of corn and the chicken cannot be left alone
Give the verbal instructions for getting everything over to the other side

14. End-Hunger Games

“philanthropic fun”.

Does anything bond people quite like acts of kindness and compassion? The End-Hunger Games will get your team to rally around solving the serious problem of hunger.

Best for: Medium-sized teams

Why this is an effective problem solving group activity: Teams join forces to complete challenges based around non-perishable food items in the End-Hunger Games. Groups can range in size from 25 to more than 2000 people, who will all work together to collect food for the local food bank.

Split into teams and compete to earn boxes and cans of non-perishable food
Each team attempts to build the most impressive food item construction
Donate all of the non-perishable foods to a local food bank

Learn more here: End-Hunger Games

Q: What kind of skills do group problem solving activities & games improve?

A: Group problem solving activities and games improve collaboration, leadership, and communication skills.

Q: What are problem solving based team building activities & games?

A: Problem solving based team building activities and games are activities that challenge teams to work together in order to complete them.

Q: What are some fun free problem solving games for groups?

A: Some fun free problem solving games for groups are kinesthetic puzzles like the human knot game, which you can read more about in this article. You can also use all sorts of random items like whiteboards, straws, building blocks, sticky notes, blindfolds, rubber bands, and legos to invent a game that will get the whole team involved.

Q: How do I choose the most effective problem solving exercise for my team?

A: The most effective problem solving exercise for your team is one that will challenge them to be their best selves and expand their creative thinking.

Q: How do I know if my group problem solving activity was successful?

A: In the short-term, you’ll know if your group problem solving activity was successful because your team will bond over it; however, that should also translate to more productivity in the mid to long-term.

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Original research article, mathematical problem-solving through cooperative learning—the importance of peer acceptance and friendships.

1 Department of Education, Uppsala University, Uppsala, Sweden
2 Department of Education, Culture and Communication, Malardalen University, Vasteras, Sweden
3 School of Natural Sciences, Technology and Environmental Studies, Sodertorn University, Huddinge, Sweden
4 Faculty of Education, Gothenburg University, Gothenburg, Sweden

Mathematical problem-solving constitutes an important area of mathematics instruction, and there is a need for research on instructional approaches supporting student learning in this area. This study aims to contribute to previous research by studying the effects of an instructional approach of cooperative learning on students’ mathematical problem-solving in heterogeneous classrooms in grade five, in which students with special needs are educated alongside with their peers. The intervention combined a cooperative learning approach with instruction in problem-solving strategies including mathematical models of multiplication/division, proportionality, and geometry. The teachers in the experimental group received training in cooperative learning and mathematical problem-solving, and implemented the intervention for 15 weeks. The teachers in the control group received training in mathematical problem-solving and provided instruction as they would usually. Students (269 in the intervention and 312 in the control group) participated in tests of mathematical problem-solving in the areas of multiplication/division, proportionality, and geometry before and after the intervention. The results revealed significant effects of the intervention on student performance in overall problem-solving and problem-solving in geometry. The students who received higher scores on social acceptance and friendships for the pre-test also received higher scores on the selected tests of mathematical problem-solving. Thus, the cooperative learning approach may lead to gains in mathematical problem-solving in heterogeneous classrooms, but social acceptance and friendships may also greatly impact students’ results.

Introduction

The research on instruction in mathematical problem-solving has progressed considerably during recent decades. Yet, there is still a need to advance our knowledge on how teachers can support their students in carrying out this complex activity ( Lester and Cai, 2016 ). Results from the Program for International Student Assessment (PISA) show that only 53% of students from the participating countries could solve problems requiring more than direct inference and using representations from different information sources ( OECD, 2019 ). In addition, OECD (2019) reported a large variation in achievement with regard to students’ diverse backgrounds. Thus, there is a need for instructional approaches to promote students’ problem-solving in mathematics, especially in heterogeneous classrooms in which students with diverse backgrounds and needs are educated together. Small group instructional approaches have been suggested as important to promote learning of low-achieving students and students with special needs ( Kunsch et al., 2007 ). One such approach is cooperative learning (CL), which involves structured collaboration in heterogeneous groups, guided by five principles to enhance group cohesion ( Johnson et al., 1993 ; Johnson et al., 2009 ; Gillies, 2016 ). While CL has been well-researched in whole classroom approaches ( Capar and Tarim, 2015 ), few studies of the approach exist with regard to students with special educational needs (SEN; McMaster and Fuchs, 2002 ). This study contributes to previous research by studying the effects of the CL approach on students’ mathematical problem-solving in heterogeneous classrooms, in which students with special needs are educated alongside with their peers.

Group collaboration through the CL approach is structured in accordance with five principles of collaboration: positive interdependence, individual accountability, explicit instruction in social skills, promotive interaction, and group processing ( Johnson et al., 1993 ). First, the group tasks need to be structured so that all group members feel dependent on each other in the completion of the task, thus promoting positive interdependence. Second, for individual accountability, the teacher needs to assure that each group member feels responsible for his or her share of work, by providing opportunities for individual reports or evaluations. Third, the students need explicit instruction in social skills that are necessary for collaboration. Fourth, the tasks and seat arrangements should be designed to promote interaction among group members. Fifth, time needs to be allocated to group processing, through which group members can evaluate their collaborative work to plan future actions. Using these principles for cooperation leads to gains in mathematics, according to Capar and Tarim (2015) , who conducted a meta-analysis on studies of cooperative learning and mathematics, and found an increase of .59 on students’ mathematics achievement scores in general. However, the number of reviewed studies was limited, and researchers suggested a need for more research. In the current study, we focused on the effect of CL approach in a specific area of mathematics: problem-solving.

Mathematical problem-solving is a central area of mathematics instruction, constituting an important part of preparing students to function in modern society ( Gravemeijer et al., 2017 ). In fact, problem-solving instruction creates opportunities for students to apply their knowledge of mathematical concepts, integrate and connect isolated pieces of mathematical knowledge, and attain a deeper conceptual understanding of mathematics as a subject ( Lester and Cai, 2016 ). Some researchers suggest that mathematics itself is a science of problem-solving and of developing theories and methods for problem-solving ( Hamilton, 2007 ; Davydov, 2008 ).

Problem-solving processes have been studied from different perspectives ( Lesh and Zawojewski, 2007 ). Problem-solving heuristics Pólya, (1948) has largely influenced our perceptions of problem-solving, including four principles: understanding the problem, devising a plan, carrying out the plan, and looking back and reflecting upon the suggested solution. Schoenfield, (2016) suggested the use of specific problem-solving strategies for different types of problems, which take into consideration metacognitive processes and students’ beliefs about problem-solving. Further, models and modelling perspectives on mathematics ( Lesh and Doerr, 2003 ; Lesh and Zawojewski, 2007 ) emphasize the importance of engaging students in model-eliciting activities in which problem situations are interpreted mathematically, as students make connections between problem information and knowledge of mathematical operations, patterns, and rules ( Mousoulides et al., 2010 ; Stohlmann and Albarracín, 2016 ).

Not all students, however, find it easy to solve complex mathematical problems. Students may experience difficulties in identifying solution-relevant elements in a problem or visualizing appropriate solution to a problem situation. Furthermore, students may need help recognizing the underlying model in problems. For example, in two studies by Degrande et al. (2016) , students in grades four to six were presented with mathematical problems in the context of proportional reasoning. The authors found that the students, when presented with a word problem, could not identify an underlying model, but rather focused on superficial characteristics of the problem. Although the students in the study showed more success when presented with a problem formulated in symbols, the authors pointed out a need for activities that help students distinguish between different proportional problem types. Furthermore, students exhibiting specific learning difficulties may need additional support in both general problem-solving strategies ( Lein et al., 2020 ; Montague et al., 2014 ) and specific strategies pertaining to underlying models in problems. The CL intervention in the present study focused on supporting students in problem-solving, through instruction in problem-solving principles ( Pólya, 1948 ), specifically applied to three models of mathematical problem-solving—multiplication/division, geometry, and proportionality.

Students’ problem-solving may be enhanced through participation in small group discussions. In a small group setting, all the students have the opportunity to explain their solutions, clarify their thinking, and enhance understanding of a problem at hand ( Yackel et al., 1991 ; Webb and Mastergeorge, 2003 ). In fact, small group instruction promotes students’ learning in mathematics by providing students with opportunities to use language for reasoning and conceptual understanding ( Mercer and Sams, 2006 ), to exchange different representations of the problem at hand ( Fujita et al., 2019 ), and to become aware of and understand groupmates’ perspectives in thinking ( Kazak et al., 2015 ). These opportunities for learning are created through dialogic spaces characterized by openness to each other’s perspectives and solutions to mathematical problems ( Wegerif, 2011 ).

However, group collaboration is not only associated with positive experiences. In fact, studies show that some students may not be given equal opportunities to voice their opinions, due to academic status differences ( Langer-Osuna, 2016 ). Indeed, problem-solvers struggling with complex tasks may experience negative emotions, leading to uncertainty of not knowing the definite answer, which places demands on peer support ( Jordan and McDaniel, 2014 ; Hannula, 2015 ). Thus, especially in heterogeneous groups, students may need additional support to promote group interaction. Therefore, in this study, we used a cooperative learning approach, which, in contrast to collaborative learning approaches, puts greater focus on supporting group cohesion through instruction in social skills and time for reflection on group work ( Davidson and Major, 2014 ).

Although cooperative learning approach is intended to promote cohesion and peer acceptance in heterogeneous groups ( Rzoska and Ward, 1991 ), previous studies indicate that challenges in group dynamics may lead to unequal participation ( Mulryan, 1992 ; Cohen, 1994 ). Peer-learning behaviours may impact students’ problem-solving ( Hwang and Hu, 2013 ) and working in groups with peers who are seen as friends may enhance students’ motivation to learn mathematics ( Deacon and Edwards, 2012 ). With the importance of peer support in mind, this study set out to investigate whether the results of the intervention using the CL approach are associated with students’ peer acceptance and friendships.

The Present Study

In previous research, the CL approach has shown to be a promising approach in teaching and learning mathematics ( Capar and Tarim, 2015 ), but fewer studies have been conducted in whole-class approaches in general and students with SEN in particular ( McMaster and Fuchs, 2002 ). This study aims to contribute to previous research by investigating the effect of CL intervention on students’ mathematical problem-solving in grade 5. With regard to the complexity of mathematical problem-solving ( Lesh and Zawojewski, 2007 ; Degrande et al., 2016 ; Stohlmann and Albarracín, 2016 ), the CL approach in this study was combined with problem-solving principles pertaining to three underlying models of problem-solving—multiplication/division, geometry, and proportionality. Furthermore, considering the importance of peer support in problem-solving in small groups ( Mulryan, 1992 ; Cohen, 1994 ; Hwang and Hu, 2013 ), the study investigated how peer acceptance and friendships were associated with the effect of the CL approach on students’ problem-solving abilities. The study aimed to find answers to the following research questions:

a) What is the effect of CL approach on students’ problem-solving in mathematics?

b) Are social acceptance and friendship associated with the effect of CL on students’ problem-solving in mathematics?

Participants

The participants were 958 students in grade 5 and their teachers. According to power analyses prior to the start of the study, 1,020 students and 51 classes were required, with an expected effect size of 0.30 and power of 80%, provided that there are 20 students per class and intraclass correlation is 0.10. An invitation to participate in the project was sent to teachers in five municipalities via e-mail. Furthermore, the information was posted on the website of Uppsala university and distributed via Facebook interest groups. As shown in Figure 1 , teachers of 1,165 students agreed to participate in the study, but informed consent was obtained only for 958 students (463 in the intervention and 495 in the control group). Further attrition occurred at pre- and post-measurement, resulting in 581 students’ tests as a basis for analyses (269 in the intervention and 312 in the control group). Fewer students (n = 493) were finally included in the analyses of the association of students’ social acceptance and friendships and the effect of CL on students’ mathematical problem-solving (219 in the intervention and 274 in the control group). The reasons for attrition included teacher drop out due to sick leave or personal circumstances (two teachers in the control group and five teachers in the intervention group). Furthermore, some students were sick on the day of data collection and some teachers did not send the test results to the researchers.

FIGURE 1 . Flow chart for participants included in data collection and data analysis.

As seen in Table 1 , classes in both intervention and control groups included 27 students on average. For 75% of the classes, there were 33–36% of students with SEN. In Sweden, no formal medical diagnosis is required for the identification of students with SEN. It is teachers and school welfare teams who decide students’ need for extra adaptations or special support ( Swedish National Educational Agency, 2014 ). The information on individual students’ type of SEN could not be obtained due to regulations on the protection of information about individuals ( SFS 2009 ). Therefore, the information on the number of students with SEN on class level was obtained through teacher reports.

TABLE 1 . Background characteristics of classes and teachers in intervention and control groups.

Intervention

The intervention using the CL approach lasted for 15 weeks and the teachers worked with the CL approach three to four lessons per week. First, the teachers participated in two-days training on the CL approach, using an especially elaborated CL manual ( Klang et al., 2018 ). The training focused on the five principles of the CL approach (positive interdependence, individual accountability, explicit instruction in social skills, promotive interaction, and group processing). Following the training, the teachers introduced the CL approach in their classes and focused on group-building activities for 7 weeks. Then, 2 days of training were provided to teachers, in which the CL approach was embedded in activities in mathematical problem-solving and reading comprehension. Educational materials containing mathematical problems in the areas of multiplication and division, geometry, and proportionality were distributed to the teachers ( Karlsson and Kilborn, 2018a ). In addition to the specific problems, adapted for the CL approach, the educational materials contained guidance for the teachers, in which problem-solving principles ( Pólya, 1948 ) were presented as steps in problem-solving. Following the training, the teachers applied the CL approach in mathematical problem-solving lessons for 8 weeks.

Solving a problem is a matter of goal-oriented reasoning, starting from the understanding of the problem to devising its solution by using known mathematical models. This presupposes that the current problem is chosen from a known context ( Stillman et al., 2008 ; Zawojewski, 2010 ). This differs from the problem-solving of the textbooks, which is based on an aim to train already known formulas and procedures ( Hamilton, 2007 ). Moreover, it is important that students learn modelling according to their current abilities and conditions ( Russel, 1991 ).

In order to create similar conditions in the experiment group and the control group, the teachers were supposed to use the same educational material ( Karlsson and Kilborn, 2018a ; Karlsson and Kilborn, 2018b ), written in light of the specified view of problem-solving. The educational material is divided into three areas—multiplication/division, geometry, and proportionality—and begins with a short teachers’ guide, where a view of problem solving is presented, which is based on the work of Polya (1948) and Lester and Cai (2016) . The tasks are constructed in such a way that conceptual knowledge was in focus, not formulas and procedural knowledge.

Implementation of the Intervention

To ensure the implementation of the intervention, the researchers visited each teachers’ classroom twice during the two phases of the intervention period, as described above. During each visit, the researchers observed the lesson, using a checklist comprising the five principles of the CL approach. After the lesson, the researchers gave written and oral feedback to each teacher. As seen in Table 1 , in 18 of the 23 classes, the teachers implemented the intervention in accordance with the principles of CL. In addition, the teachers were asked to report on the use of the CL approach in their teaching and the use of problem-solving activities embedding CL during the intervention period. As shown in Table 1 , teachers in only 11 of 23 classes reported using the CL approach and problem-solving activities embedded in the CL approach at least once a week.

Control Group

The teachers in the control group received 2 days of instruction in enhancing students’ problem-solving and reading comprehension. The teachers were also supported with educational materials including mathematical problems Karlsson and Kilborn (2018b) and problem-solving principles ( Pólya, 1948 ). However, none of the activities during training or in educational materials included the CL approach. As seen in Table 1 , only 10 of 25 teachers reported devoting at least one lesson per week to mathematical problem-solving.

Tests of Mathematical Problem-Solving

Tests of mathematical problem-solving were administered before and after the intervention, which lasted for 15 weeks. The tests were focused on the models of multiplication/division, geometry, and proportionality. The three models were chosen based on the syllabus of the subject of mathematics in grades 4 to 6 in the Swedish National Curriculum ( Swedish National Educational Agency, 2018 ). In addition, the intention was to create a variation of types of problems to solve. For each of these three models, there were two tests, a pre-test and a post-test. Each test contained three tasks with increasing difficulty ( Supplementary Appendix SA ).

The tests of multiplication and division (Ma1) were chosen from different contexts and began with a one-step problem, while the following two tasks were multi-step problems. Concerning multiplication, many students in grade 5 still understand multiplication as repeated addition, causing significant problems, as this conception is not applicable to multiplication beyond natural numbers ( Verschaffel et al., 2007 ). This might be a hindrance in developing multiplicative reasoning ( Barmby et al., 2009 ). The multi-step problems in this study were constructed to support the students in multiplicative reasoning.

Concerning the geometry tests (Ma2), it was important to consider a paradigm shift concerning geometry in education that occurred in the mid-20th century, when strict Euclidean geometry gave way to other aspects of geometry like symmetry, transformation, and patterns. van Hiele (1986) prepared a new taxonomy for geometry in five steps, from a visual to a logical level. Therefore, in the tests there was a focus on properties of quadrangles and triangles, and how to determine areas by reorganising figures into new patterns. This means that structure was more important than formulas.

The construction of tests of proportionality (M3) was more complicated. Firstly, tasks on proportionality can be found in many different contexts, such as prescriptions, scales, speeds, discounts, interest, etc. Secondly, the mathematical model is complex and requires good knowledge of rational numbers and ratios ( Lesh et al., 1988 ). It also requires a developed view of multiplication, useful in operations with real numbers, not only as repeated addition, an operation limited to natural numbers ( Lybeck, 1981 ; Degrande et al., 2016 ). A linear structure of multiplication as repeated addition leads to limitations in terms of generalization and development of the concept of multiplication. This became evident in a study carried out in a Swedish context ( Karlsson and Kilborn, 2018c ). Proportionality can be expressed as a/b = c/d or as a/b = k. The latter can also be expressed as a = b∙k, where k is a constant that determines the relationship between a and b. Common examples of k are speed (km/h), scale, and interest (%). An important pre-knowledge in order to deal with proportions is to master fractions as equivalence classes like 1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 6/18 = 7/21 = 8/24 … ( Karlsson and Kilborn, 2020 ). It was important to take all these aspects into account when constructing and assessing the solutions of the tasks.

The tests were graded by an experienced teacher of mathematics (4 th author) and two students in their final year of teacher training. Prior to grading, acceptable levels of inter-rater reliability were achieved by independent rating of students’ solutions and discussions in which differences between the graders were resolved. Each student response was to be assigned one point when it contained a correct answer and two points when the student provided argumentation for the correct answer and elaborated on explanation of his or her solution. The assessment was thus based on quality aspects with a focus on conceptual knowledge. As each subtest contained three questions, it generated three student solutions. So, scores for each subtest ranged from 0 to 6 points and for the total scores from 0 to 18 points. To ascertain that pre- and post-tests were equivalent in degree of difficulty, the tests were administered to an additional sample of 169 students in grade 5. Test for each model was conducted separately, as students participated in pre- and post-test for each model during the same lesson. The order of tests was switched for half of the students in order to avoid the effect of the order in which the pre- and post-tests were presented. Correlation between students’ performance on pre- and post-test was .39 ( p < 0.000) for tests of multiplication/division; .48 ( p < 0.000) for tests of geometry; and .56 ( p < 0.000) for tests of proportionality. Thus, the degree of difficulty may have differed between pre- and post-test.

Measures of Peer Acceptance and Friendships

To investigate students’ peer acceptance and friendships, peer nominations rated pre- and post-intervention were used. Students were asked to nominate peers who they preferred to work in groups with and who they preferred to be friends with. Negative peer nominations were avoided due to ethical considerations raised by teachers and parents ( Child and Nind, 2013 ). Unlimited nominations were used, as these are considered to have high ecological validity ( Cillessen and Marks, 2017 ). Peer nominations were used as a measure of social acceptance, and reciprocated nominations were used as a measure of friendship. The number of nominations for each student were aggregated and divided by the number of nominators to create a proportion of nominations for each student ( Velásquez et al., 2013 ).

Statistical Analyses

Multilevel regression analyses were conducted in R, lme4 package Bates et al. (2015) to account for nestedness in the data. Students’ classroom belonging was considered as a level 2 variable. First, we used a model in which students’ results on tests of problem-solving were studied as a function of time (pre- and post) and group belonging (intervention and control group). Second, the same model was applied to subgroups of students who performed above and below median at pre-test, to explore whether the CL intervention had a differential effect on student performance. In this second model, the results for subgroups of students could not be obtained for geometry tests for subgroup below median and for tests of proportionality for subgroup above median. A possible reason for this must have been the skewed distribution of the students in these subgroups. Therefore, another model was applied that investigated students’ performances in math at both pre- and post-test as a function of group belonging. Third, the students’ scores on social acceptance and friendships were added as an interaction term to the first model. In our previous study, students’ social acceptance changed as a result of the same CL intervention ( Klang et al., 2020 ).

The assumptions for the multilevel regression were assured during the analyses ( Snijders and Bosker, 2012 ). The assumption of normality of residuals were met, as controlled by visual inspection of quantile-quantile plots. For subgroups, however, the plotted residuals deviated somewhat from the straight line. The number of outliers, which had a studentized residual value greater than ±3, varied from 0 to 5, but none of the outliers had a Cook’s distance value larger than 1. The assumption of multicollinearity was met, as the variance inflation factors (VIF) did not exceed a value of 10. Before the analyses, the cases with missing data were deleted listwise.

What Is the Effect of the CL Approach on Students’ Problem-Solving in Mathematics?

As seen in the regression coefficients in Table 2 , the CL intervention had a significant effect on students’ mathematical problem-solving total scores and students’ scores in problem solving in geometry (Ma2). Judging by mean values, students in the intervention group appeared to have low scores on problem-solving in geometry but reached the levels of problem-solving of the control group by the end of the intervention. The intervention did not have a significant effect on students’ performance in problem-solving related to models of multiplication/division and proportionality.

TABLE 2 . Mean scores (standard deviation in parentheses) and unstandardized multilevel regression estimates for tests of mathematical problem-solving.

The question is, however, whether CL intervention affected students with different pre-test scores differently. Table 2 includes the regression coefficients for subgroups of students who performed below and above median at pre-test. As seen in the table, the CL approach did not have a significant effect on students’ problem-solving, when the sample was divided into these subgroups. A small negative effect was found for intervention group in comparison to control group, but confidence intervals (CI) for the effect indicate that it was not significant.

Is Social Acceptance and Friendships Associated With the Effect of CL on Students’ Problem-Solving in Mathematics?

As seen in Table 3 , students’ peer acceptance and friendship at pre-test were significantly associated with the effect of the CL approach on students’ mathematical problem-solving scores. Changes in students’ peer acceptance and friendships were not significantly associated with the effect of the CL approach on students’ mathematical problem-solving. Consequently, it can be concluded that being nominated by one’s peers and having friends at the start of the intervention may be an important factor when participation in group work, structured in accordance with the CL approach, leads to gains in mathematical problem-solving.

TABLE 3 . Mean scores (standard deviation in parentheses) and unstandardized multilevel regression estimates for tests of mathematical problem-solving, including scores of social acceptance and friendship in the model.

In light of the limited number of studies on the effects of CL on students’ problem-solving in whole classrooms ( Capar and Tarim, 2015 ), and for students with SEN in particular ( McMaster and Fuchs, 2002 ), this study sought to investigate whether the CL approach embedded in problem-solving activities has an effect on students’ problem-solving in heterogeneous classrooms. The need for the study was justified by the challenge of providing equitable mathematics instruction to heterogeneous student populations ( OECD, 2019 ). Small group instructional approaches as CL are considered as promising approaches in this regard ( Kunsch et al., 2007 ). The results showed a significant effect of the CL approach on students’ problem-solving in geometry and total problem-solving scores. In addition, with regard to the importance of peer support in problem-solving ( Deacon and Edwards, 2012 ; Hwang and Hu, 2013 ), the study explored whether the effect of CL on students’ problem-solving was associated with students’ social acceptance and friendships. The results showed that students’ peer acceptance and friendships at pre-test were significantly associated with the effect of the CL approach, while change in students’ peer acceptance and friendships from pre- to post-test was not.

The results of the study confirm previous research on the effect of the CL approach on students’ mathematical achievement ( Capar and Tarim, 2015 ). The specific contribution of the study is that it was conducted in classrooms, 75% of which were composed of 33–36% of students with SEN. Thus, while a previous review revealed inconclusive findings on the effects of CL on student achievement ( McMaster and Fuchs, 2002 ), the current study adds to the evidence of the effect of the CL approach in heterogeneous classrooms, in which students with special needs are educated alongside with their peers. In a small group setting, the students have opportunities to discuss their ideas of solutions to the problem at hand, providing explanations and clarifications, thus enhancing their understanding of problem-solving ( Yackel et al., 1991 ; Webb and Mastergeorge, 2003 ).

In this study, in accordance with previous research on mathematical problem-solving ( Lesh and Zawojewski, 2007 ; Degrande et al., 2016 ; Stohlmann and Albarracín, 2016 ), the CL approach was combined with training in problem-solving principles Pólya (1948) and educational materials, providing support in instruction in underlying mathematical models. The intention of the study was to provide evidence for the effectiveness of the CL approach above instruction in problem-solving, as problem-solving materials were accessible to teachers of both the intervention and control groups. However, due to implementation challenges, not all teachers in the intervention and control groups reported using educational materials and training as expected. Thus, it is not possible to draw conclusions of the effectiveness of the CL approach alone. However, in everyday classroom instruction it may be difficult to separate the content of instruction from the activities that are used to mediate this content ( Doerr and Tripp, 1999 ; Gravemeijer, 1999 ).

Furthermore, for successful instruction in mathematical problem-solving, scaffolding for content needs to be combined with scaffolding for dialogue ( Kazak et al., 2015 ). From a dialogical perspective ( Wegerif, 2011 ), students may need scaffolding in new ways of thinking, involving questioning their understandings and providing arguments for their solutions, in order to create dialogic spaces in which different solutions are voiced and negotiated. In this study, small group instruction through CL approach aimed to support discussions in small groups, but the study relies solely on quantitative measures of students’ mathematical performance. Video-recordings of students’ discussions may have yielded important insights into the dialogic relationships that arose in group discussions.

Despite the positive findings of the CL approach on students’ problem-solving, it is important to note that the intervention did not have an effect on students’ problem-solving pertaining to models of multiplication/division and proportionality. Although CL is assumed to be a promising instructional approach, the number of studies on its effect on students’ mathematical achievement is still limited ( Capar and Tarim, 2015 ). Thus, further research is needed on how CL intervention can be designed to promote students’ problem-solving in other areas of mathematics.

The results of this study show that the effect of the CL intervention on students’ problem-solving was associated with students’ initial scores of social acceptance and friendships. Thus, it is possible to assume that students who were popular among their classmates and had friends at the start of the intervention also made greater gains in mathematical problem-solving as a result of the CL intervention. This finding is in line with Deacon and Edwards’ study of the importance of friendships for students’ motivation to learn mathematics in small groups ( Deacon and Edwards, 2012 ). However, the effect of the CL intervention was not associated with change in students’ social acceptance and friendship scores. These results indicate that students who were nominated by a greater number of students and who received a greater number of friends did not benefit to a great extent from the CL intervention. With regard to previously reported inequalities in cooperation in heterogeneous groups ( Cohen, 1994 ; Mulryan, 1992 ; Langer Osuna, 2016 ) and the importance of peer behaviours for problem-solving ( Hwang and Hu, 2013 ), teachers should consider creating inclusive norms and supportive peer relationships when using the CL approach. The demands of solving complex problems may create negative emotions and uncertainty ( Hannula, 2015 ; Jordan and McDaniel, 2014 ), and peer support may be essential in such situations.

Limitations

The conclusions from the study must be interpreted with caution, due to a number of limitations. First, due to the regulation of protection of individuals ( SFS 2009 ), the researchers could not get information on type of SEN for individual students, which limited the possibilities of the study for investigating the effects of the CL approach for these students. Second, not all teachers in the intervention group implemented the CL approach embedded in problem-solving activities and not all teachers in the control group reported using educational materials on problem-solving. The insufficient levels of implementation pose a significant challenge to the internal validity of the study. Third, the additional investigation to explore the equivalence in difficulty between pre- and post-test, including 169 students, revealed weak to moderate correlation in students’ performance scores, which may indicate challenges to the internal validity of the study.

Implications

The results of the study have some implications for practice. Based on the results of the significant effect of the CL intervention on students’ problem-solving, the CL approach appears to be a promising instructional approach in promoting students’ problem-solving. However, as the results of the CL approach were not significant for all subtests of problem-solving, and due to insufficient levels of implementation, it is not possible to conclude on the importance of the CL intervention for students’ problem-solving. Furthermore, it appears to be important to create opportunities for peer contacts and friendships when the CL approach is used in mathematical problem-solving activities.

Data Availability Statement

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

Ethics Statement

The studies involving human participants were reviewed and approved by the Uppsala Ethical Regional Committee, Dnr. 2017/372. Written informed consent to participate in this study was provided by the participants’ legal guardian/next of kin.

Author Contributions

NiK was responsible for the project, and participated in data collection and data analyses. NaK and WK were responsible for intervention with special focus on the educational materials and tests in mathematical problem-solving. PE participated in the planning of the study and the data analyses, including coordinating analyses of students’ tests. MK participated in the designing and planning the study as well as data collection and data analyses.

The project was funded by the Swedish Research Council under Grant 2016-04,679.

Conflict of Interest

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

Publisher’s Note

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

Acknowledgments

We would like to express our gratitude to teachers who participated in the project.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feduc.2021.710296/full#supplementary-material

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Karlsson, N., and Kilborn, W. (2018c). It's enough if they understand it. A study of teachers 'and students' perceptions of multiplication and the multiplication table [Det räcker om de förstår den. En studie av lärares och elevers uppfattningar om multiplikation och multiplikationstabellen]. Södertörn Stud. Higher Educ. , 175.

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Keywords: cooperative learning, mathematical problem-solving, intervention, heterogeneous classrooms, hierarchical linear regression analysis

Citation: Klang N, Karlsson N, Kilborn W, Eriksson P and Karlberg M (2021) Mathematical Problem-Solving Through Cooperative Learning—The Importance of Peer Acceptance and Friendships. Front. Educ. 6:710296. doi: 10.3389/feduc.2021.710296

Received: 15 May 2021; Accepted: 09 August 2021; Published: 24 August 2021.

Reviewed by:

Copyright © 2021 Klang, Karlsson, Kilborn, Eriksson and Karlberg. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Nina Klang, [email protected]

Our Mission

Students working together in a small group of four, discussing and writing notes

Group Work That Works

Educators weigh in on solutions to the common pitfalls of group work.

Mention group work and you’re confronted with pointed questions and criticisms. The big problems, according to our audience: One or two students do all the work; it can be hard on introverts; and grading the group isn’t fair to the individuals.

But the research suggests that a certain amount of group work is beneficial.

“The most effective creative process alternates between time in groups, collaboration, interaction, and conversation... [and] times of solitude, where something different happens cognitively in your brain,” says Dr. Keith Sawyer, a researcher on creativity and collaboration, and author of Group Genius: The Creative Power of Collaboration .

So we looked through our archives and reached out to educators on Facebook to find out what solutions they’ve come up with for these common problems.

Making Sure Everyone Participates

“How many times have we put students in groups only to watch them interact with their laptops instead of each other? Or complain about a lazy teammate?” asks Mary Burns, a former French, Latin, and English middle and high school teacher who now offers professional development in technology integration.

Unequal participation is perhaps the most common complaint about group work. Still, a review of Edutopia’s archives—and the tens of thousands of insights we receive in comments and reactions to our articles—revealed a handful of practices that educators use to promote equal participation. These involve setting out clear expectations for group work, increasing accountability among participants, and nurturing a productive group work dynamic.

Norms: At Aptos Middle School in San Francisco, the first step for group work is establishing group norms. Taji Allen-Sanchez, a sixth- and seventh-grade science teacher, lists expectations on the whiteboard, such as “everyone contributes” and “help others do things for themselves.”

For ambitious projects, Mikel Grady Jones, a high school math teacher in Houston, takes it a step further, asking her students to sign a group contract in which they agree on how they’ll divide the tasks and on expectations like “we all promise to do our work on time.” Heather Wolpert-Gawron, an English middle school teacher in Los Angeles, suggests creating a classroom contract with your students at the start of the year, so that agreed-upon norms can be referenced each time a new group activity begins.

Group size: It’s a simple fix, but the size of the groups can help establish the right dynamics. Generally, smaller groups are better because students can’t get away with hiding while the work is completed by others.

“When there is less room to hide, nonparticipation is more difficult,” says Burns. She recommends groups of four to five students, while Brande Tucker Arthur, a 10th-grade biology teacher in Lynchburg, Virginia, recommends even smaller groups of two or three students.

Meaningful roles: Roles can play an important part in keeping students accountable, but not all roles are helpful. A role like materials manager, for example, won’t actively engage a student in contributing to a group problem; the roles must be both meaningful and interdependent.

At University Park Campus School , a grade 7–12 school in Worcester, Massachusetts, students take on highly interdependent roles like summarizer, questioner, and clarifier. In an ongoing project, the questioner asks probing questions about the problem and suggests a few ideas on how to solve it, while the clarifier attempts to clear up any confusion, restates the problem, and selects a possible strategy the group will use as they move forward.

A handout given to a student tasked with the role of clarifier

At Design 39, a K–8 school in San Diego, groups and roles are assigned randomly using Random Team Generator , but ClassDojo , Team Shake , and drawing students’ names from a container can also do the trick. In a practice called vertical learning, Design 39 students conduct group work publicly, writing out their thought processes on whiteboards to facilitate group feedback. The combination of randomizing teams and public sharing exposes students to a range of problem-solving approaches, gets them more comfortable with making mistakes, promotes teamwork, and allows kids to utilize different skill sets during each project.

Rich tasks: Making sure that a project is challenging and compelling is critical. A rich task is a problem that has multiple pathways to the solution and that one person would have difficulty solving on their own.

In an eighth-grade math class at Design 39, one recent rich task explored the concept of how monetary investments grow: Groups were tasked with solving exponential growth problems using simple and compound interest rates.

Rich tasks are not just for math class. When Dan St. Louis, the principal of University Park, was a teacher, he asked his English students to come up with a group definition of the word Orwellian . They did this through the jigsaw method, a type of grouping strategy that John Hattie’s study Visible Learning ranked as highly effective.

“Five groups of five students might each read a different news article about the modern world,” says St. Louis. “Then each student would join a new group of five where they need to explain their previous group’s article to each other and make connections to each. Using these connections, the group must then construct a definition of the word Orwellian .” For another example of the jigsaw approach, see this video from Cult of Pedagogy.

Supporting Introverts

Teachers worry about the impact of group work on introverts. Some of our educators suggest that giving introverts choice in who they’re grouped with can help them feel more comfortable.

“Even the quietest students are usually comfortable and confident when they are with peers with whom they connect,” says Shelly Kunkle, a veteran teacher at Wasawee Middle School in North Webster, Indiana. Wolpert-Gawron asks her students to list four peers they want to work with and then makes sure to pair them with one from their list.

Having defined roles within groups—like clarifier or questioner—also provides structure for students who may be less comfortable within complex social dynamics, and ensures that introverts don’t get overshadowed by their more extroverted peers.

Finally, be mindful that introverted students often simply need time to recharge. “Many introverts do not mind and even enjoy interacting in groups as long as they get some quiet time and solitude to recharge. It’s not about being shy or feeling unsafe in a large group,” says Barb Larochelle, a recently retired high school English teacher in Edmonton, Alberta, who taught for 29 years.

“I planned classes with some time to work quietly alone, some time to interact in smaller groups or as a whole class, and some time to get up and move around a little. A whole class of any one of those is going to be hard on one group, but a balance works well.”

Assessing Group Work

Grading group work is problematic. Often, you don’t have a clear understanding of what each student knows, and a single student’s lack of effort can torpedo the group grade. To some degree, strategies that assign meaningful roles or that require public presentations from groups provide a window in to each student’s knowledge and contributions.

But not all classwork needs to be graded. Suzanna Kruger, a high school science teacher in Seaside, Oregon, doesn’t grade group work—there are plenty of individual assignments that receive grades, and plenty of other opportunities for formative assessment.

John McCarthy, a former high school English and social studies teacher and current education consultant and adjunct professor at Madonna University for the graduate department for education, suggests using group presentations or group products as a non-graded review for a test. But if you want to grade group work, he recommends making all academic assessments within group work individual assessments. For example, instead of grading a group presentation, McCarthy grades each student on an essay, which the students then use to create their group presentation.

Students working together on a project with paper, tape, and scissors

Laura Moffit, a fifth-grade teacher in Wilmington, North Carolina, uses self and peer evaluations to shed light on how each student is contributing to group work—starting with a lesson on how to do an objective evaluation. “Just have students circle :), :|, or :( on three to five statements about each partner, anonymously,” Moffit commented on Facebook. “Then give the evaluations back to each group member. Finding out what people really think of your performance is a wake-up call.”

And Ted Malefyt, a middle school science teacher in Hamilton, Michigan, carries a clipboard with the class list formatted in a spreadsheet and walks around checking in on students while they do group work.

“Using this spreadsheet, you have your own record of which student is meeting your expectations and who needs extra help,” explains Malefyt. “As formative assessment takes place, quickly document with simple checkmarks.”

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COMMENTS

Co-operative Problem Solving: Pieces of the Puzzle Approach
Group work: The groups are formed and each child in a group is given one clue card. To maintain 'ownership' of the piece of information, the child may not physically give away the clue-card, but must be responsible for communicating the content to the group. ... Gould, P. (1993) Co-operative Problem Solving in Mathematics, Mathematical ...
Small Group Math Activities
Discover small group math activities that promote student engagement and foster a love for math. This blog post explores 10 activities, including math games, hands-on manipulatives, real-world investigations, technology tools, problem solving activities, and more to help you transform your math stations into a dynamic learning environment.
Good Group Work in Math
In addition, a four-year study of high school students in different types of math classes showed that the students who learned math in mixed-ability classrooms that emphasized cooperative group work, open problem-solving, and the use of multiple strategies-compared to those in traditional math classrooms, which were often ability-grouped and ...
Team Work makes the Math Work
Use logic. 7. Work backwards. 8. Simplify problem. These steps will help student improve their math understanding quicker than any worksheet or web-game. Check out MANGO Math for fun hands-on math games that engage and educated students while they enjoy math. ‍. Group work helps student improve their critical thinking and problem-solving ...
PDF OO ROUP WORK N MAT
In addition, a four-year study of high school students in different types of math classes showed that the students who learned math in mixed-ability classrooms that emphasized cooperative group work, open problem-solving, and the use of multiple strategies--compared to those in traditional math classrooms, which were often ability-
Small Group Elementary Math Instruction
Embed the targeted math concept into rigorous problem-solving to get a deep look into processing behaviors, organization strategies, and the math strategies used to solve the problem. Keep assessments for small group instruction focused on the most essential math skills that students need to master. Keep it short. Use only one or two questions ...
The cops model for collaborative problem-solving in mathematics
2.5 Collaborative problem-solving in mathematics. Group-work has been found to increase students' understanding of concepts within mathematics, aided by the requirement for discussion, rather than the rote-learning of material (Koçak, Bozan, and Iık Citation 2009; Sofroniou and Poutos Citation 2016).
Investigating the Effectiveness of Group Work in Mathematics
Group work permits students to develop a range of critical thinking, analytical and communication skills; effective team work; appreciation and respect for other views, techniques and problem-solving methods, all of which promote active learning and enhance student learning. This paper presents an evaluation of employing the didactic and pedagogical customs of group work in mathematics with ...
Building Collaborative Problem Solvers
In math classes, students frequently take group tests and can consult with one another on the answers, but the teacher chooses only one test at random to grade for the group. Because the group work is intentionally more difficult, this process keeps individual students accountable for full participation in group work.
Mathematical Learning in A Virtual Environment: the Role of Group Work
This study describes an online method of measuring individual students' collaborative problem-solving abilities using four interactive mathematics-based tasks, with students working in pairs.
5 steps to develop collaborative problem-solving in maths
1. Use low-threshold, high-ceiling activities. First and foremost is the importance of low-threshold, high-ceiling (LTHC) activities and resources. These enable all learners to get started on a problem while also offering sufficient challenge. One of NRICH's most popular LTHC activities is the Factors and Multiples Game, which challenges ...
Collaborative Problem-Solving in Math
Variation #1 - Students work in groups of 4. One problem-solving page per student. Each student in the group individually answers the problem or question on a sticky note (give a time limit for this). Students then place all their sticky notes on a common page and read through the answers. Taking the very best parts of each person's answer ...
The importance of group work in mathematics
Group work shows that students can improve their critical thinking and problem solving skills; furthermore, their way of expressing themselves becomes better. This method helps students learn interactively and efficiently. Â© 2009 Elsevier Ltd. Keywords: Education, group work; integrated approach; mathematics; mathematics education. 1.
Full article: Exploring the relationship between metacognitive and
Because the use of metacognition and effective group work skills in mathematical problem-solving rarely develop automatically (e.g. Sfard & Kieran, Citation 2001), it is important that researchers are able to understand the nature of group interactions, together with mediating factors. Research in the area of collaborative problem-solving ...
14 Brain-Boosting Problem Solving Group Activities For Teams
Jeopardy. Problem-solving activities such as Virtual Team Challenges offer a great way for teams to come together, collaborate, and develop creative solutions to complex problems. 2. Problem-Solving Templates. Problem-Solving Templates are popular problem-solving activities that involve a group of people working together to solve an issue.
PDF Investigating the Effectiveness of Group Work in Mathematics
through group work can address these problems and enhance students' progress and achievements [33]. Group work interaction helps all members learn concepts and problem solving strategies, improve self-conﬁdence and overcome the fear of mistakes [6,14,34]. Mathematics does offer opportunities
Frontiers
Mathematical problem-solving constitutes an important area of mathematics instruction, and there is a need for research on instructional approaches supporting student learning in this area. This study aims to contribute to previous research by studying the effects of an instructional approach of cooperative learning on students' mathematical problem-solving in heterogeneous classrooms in ...
PDF The importance of group work in mathematics
2.2. Importance of Group Work in Mathematics. The traditional education of mathematics teach students to be passive, not to participate in lessons ,to be dependent on teachers, to memorise and not ...
Investigating the Effectiveness of Group Work in Mathematics
Group work and problem-solving are useful for student learning and self-efficacy (Evans et al., 2020; Sofroniou & Poutos, 2016) and the workshops also place an emphasis on communicating ...
Group Work That Works
Norms: At Aptos Middle School in San Francisco, the first step for group work is establishing group norms. Taji Allen-Sanchez, a sixth- and seventh-grade science teacher, lists expectations on the whiteboard, such as "everyone contributes" and "help others do things for themselves.". For ambitious projects, Mikel Grady Jones, a high ...
Microsoft Math Solver
Online math solver with free step by step solutions to algebra, calculus, and other math problems. ... Try Math Solver. Type a math problem. Solve. Quadratic equation { x } ^ { 2 } - 4 x - 5 = 0. Trigonometry. 4 \sin \theta \cos \theta = 2 \sin \theta . Linear equation. y = 3x + 4 ... See how to solve problems and show your work—plus get ...

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Co-operative Problem Solving: Pieces of the Puzzle Approach

Forming the Groups

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It’s All About Engagement

10 Small Group Math Activities for Any Math Station Rotation

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Activity 6: Ready-Made Math Activities

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Activity 9: Calculator Challenges

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Introduction

The Present Study

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Intervention

Implementation of the Intervention

Control Group

Tests of Mathematical Problem-Solving

Measures of Peer Acceptance and Friendships

Statistical Analyses

What Is the Effect of the CL Approach on Students’ Problem-Solving in Mathematics?

Is Social Acceptance and Friendships Associated With the Effect of CL on Students’ Problem-Solving in Mathematics?

Limitations

Implications

Data Availability Statement

Ethics Statement

Author Contributions

Conflict of Interest

Publisher’s Note

Acknowledgments

Supplementary Material