what role does problem solving play in a mathematics classroom

💡 Research Spotlight: In one study, students’ problem-solving processes were qualitatively shown to be supported by engaging in metacognitive regulation — the active monitoring and controlling of cognitive processes (Jin & Kim, 2018). Students were able to help monitor and adjust each other’s thinking through their conversations. As students said things like, “This makes no sense” or “I don’t understand this,” other students would respond with, “Let’s try to think of this another way.” Desoete and De Craene (2019) noted that metacognitive skills were associated with mathematical accuracy. Reflection is also linked to social-emotional learning, as students can benefit from reflecting on the thoughts, feelings, and emotional aspects of what they have learned.

How can teachers encourage metacognitive strategies in the classroom?

Metacognitive strategies can be integrated into regular classroom instruction through:

💡 Research Spotlight : In one study, students were guided to use metacognitive questioning as part of the process of solving math problems. These metacognitive questions included comprehension, connection, strategic and reflection questions (Mevarech & Kramarski, 2003).

Metacognitive Strategies in Math

Why is metacognition important in the math classroom.

Metacognition is a critical skill in K-5 math education because engaging in metacognitive strategies can help students build a conceptual understanding of content and foster student agency.

💡 Research Spotlight : Desoete and De Craene (2019) found that metacognitive activities can help students with learning disabilities build computational accuracy and mathematical reasoning.

Helpful Metacognitive Strategies in Math

Here are just a few practical methods that students can use to reflect on their learning and engage in overall metacognition:

Verbalizing and writing the steps to solving a problem helps students reflect on, monitor, and evaluate their problem-solving abilities and strategies. This has been shown to increase conceptual understanding and provides students the opportunity to evaluate their learning (Gray, 1991; Martin, Polly, & Kissel, 2017).

Writing about their thinking contributes to their mathematical learning (Martin et al., 2017). For example, students may write math journal entries to think about what they learned and what they might not yet understand.

Answering prompts about concepts and encourages students to collaboratively reflect, justify their reasoning, and elaborate on their thought processes. Choose prompts that frame math as a as a set of problem-solving strategies instead of an end result.

Reflecting through formative assessment allows them to consider how well they understand the lesson content and engage in thinking about their own thinking and how they feel about their learning

These metacognitive strategies allow learners greater metacognitive insight into their own thinking — connecting intuition, modeling, and conceptual representation — and are at the very heart of the mathematical practices that foster deeper mathematical learning (Hattie, 2017, p. 136). Metacognition also empowers students to drive their own learning, building from the support of a teacher’s modeling and moving toward independent practice of skills and concepts. An added benefit to this approach is that when teachers use strong focusing questions, they are also modeling how to ask clarifying questions in a way that will serve students better in later phases of learning, when they ask themselves those clarifying questions.

For more on the importance of metacognition in mathematics, and how metacognition is practiced through specific instructional elements in Reveal Math K-5 , see the full Reveal Math K-5 Research Foundations .

About the Authors

Lanette Trowery , Ph.D. is the Senior Director of the McGraw Hill Learning Research and Strategy Team.

Lanette was in public education for more than 25 years, working as a university professor, site-based mathematics coach, elementary and middle school teacher, mathematics consultant, and a professional learning consultant, before coming to McGraw Hill in 2014. She earned her Master’s and Doctorate from the University of Pennsylvania.

Lanette’s team, Learning Research and Strategy, serves as the center of excellence for teaching and learning best practices. Her team conducts market, effectiveness, and efficacy research into products to provide insights and recommendations to product development. They collaborate across internal teams, external experts, and customers to establish guiding principles and frameworks to move from theory to practice.

Margaret Bowman is an Academic Designer in the Mathematics Department at McGraw Hill.

Margaret earned her Bachelor of Science in Education from Ashland University with a teaching license in Middle Grades Education, and her Master of Education from Tiffin University. She was a middle school Math and Language Arts teacher for six years before joining the middle school team at McGraw Hill in 2012, writing and designing print and digital curriculum.

Margaret is also a Research Associate in the Research Laboratory for Digital Learning at The Ohio State University. She is nearing completion of a PhD in Educational Studies with an emphasis in Learning Technologies. Her past research and journal publications have focused on teachers’ value for using technology in the classroom and technology’s impact on student learning. Her current research examines how students’ use of technology can improve the value they have for mathematics and their expectations that they can succeed.

Adie, L., Willis, J., and Van der Kleij, F. (2018). Diverse perspectives on student agency in classroom assessment. The Australian Educational Researcher. 45. 1–12. https://doi.org/10.1007/s13384-018-0262-2

Denton, D. (2011). Reflection and learning: Characteristics, obstacles, and implications. Educational Philosophy and Theory, 43 (8), 838–852.

Desoete, A. & De Craene, B. (2019.) Metacognition and mathematics education: an overview. ZDM Mathematics Education, 51 (4), 565.

Flavell, J. (1976). Metacognitive aspects of problem-solving. In L. B. Resnick (Ed.), The nature of intelligence . (pp. 231–236). Hillsdale, NJ: Erlbaum.

Gray, S. (1991). Ideas in practice: Metacognition and mathematical problem solving. Journal of Developmental Education, 14 (3), 24–26, 28.

Hattie, J. (2017). Visible learning for mathematics, grades K-12: What works best to optimize student learning . Thousand Oaks, CA: Corwin Mathematics.

Jin, Q., & Kim, M. (2018). Metacognitive regulation during elementary students’ collaborative group work. Interchange, 49 (2), 263–281.

Klemencic, M. (2015). What is student agency? An ontological exploration in the context of research on student engagement. In Klemencic, Bergan, and Primozic (eds.) Student engagement in Europe: society, higher education and student governance (pp. 11–29) . Council of Europe Higher Education Series №20. Strasbourg: Council of Europe Publishing.

Martin, C., Polly, D., Kissel, B. (2017). Exploring the impact of written reflections on learning in the elementary mathematics classroom. The Journal of Educational Research, 110 (5), 538–553.

Mevarech, Z. & Kramarski, B. (2003). The effects of metacognitive training versus worked-out examples on students’ mathematical reasoning. British Journal of Educational Psychology, 73 , 449–471.

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The Playful Approach to Math

Math doesn’t have to be serious. One teacher believes play is the key to math comprehension for all ages.

Pie graph made of different colored candies

The concept of play is often limited to younger students and less academic endeavors, but play can be a useful strategy in an unlikely discipline: math.

Mathematics is known as cold, logical, and rigorous, but the subject doesn’t get enough credit for its true mischievous spirit, which is well-hidden from the world. The K–12 mathematics curricula can involve time and space to play with concepts and ideas, even in the rush of required topics.

In my research for a 2017 talk I gave at TEDxKitchenerEd called “ Math Is Play ,” I found few materials on the joy of math in upper grades. Much of the literature on play as a learning approach is based on the early years, particularly kindergarten, where it is an accepted pedagogical mode.

Young children at play often reach a state that psychologist Mihaly Csikszentmihalyi calls “flow,” an elusive state of mind where time seems to disappear as they focus deeply on what they’re doing. Getting to this ideal state in the classroom requires more than the freedom to play—teachers must also react to students’ ideas and guide them through concepts like counting and numbers. This type of guided play requires decision-making about how and when to give direct instruction. Creating freedom while at the same time offering direction allows for productive play that opens students’ minds to better understand difficult mathematical concepts.

The amount of play in “serious” academic topics like mathematics is inversely proportional, it seems, to the age of students, but this does not have to be the case. A playful pedagogy of mathematics can be codified and made real, rigorous, and authentic.

Embrace and Incorporate Play

In my book Teaching Mathematics Through Problem-Solving in K–12 Classrooms , I wrote about the need to accept that humans are born to play. Play is irrepressibly human, and we can play to learn. Playing and thinking are not at odds with each other. Though play is usually associated with turning off thinking and giving oneself to a pleasurable activity, working on interesting problems can be a trigger for flow. There is a sweet spot, often about 30 minutes into working on an interesting problem, where ideas start to become solutions.

Create a culture where mathematical ideas are not just formulas on a page but instead are concepts to be discussed and reasoned through. Play moves math instruction beyond rote memorization to a more expansive understanding of mathematics. Encourage students to talk, think, reason, and wonder as they move through problems. Creating a sense of curiosity, even for simple concepts, engages students in a playful way.

Simple strategies like turn-and-talk can create opportunities for collaborative, playful learning. Using prompts as part of the daily classroom routine can make mathematical concepts fun. Sites like Visual Patterns , Fraction Talks , or Estimation180 offer easy, quick ways to make mathematical concepts entertaining.

Lean Into the Unknown

Math is full of surprises that can be interesting and fun. There is no single path or strategy to the solution in many problems. Be receptive to surprises in how your students think about and solve problems. An openness to the unexpected can foster a culture of playful curiosity in the classroom. A playful mathematics learner is hopeful and optimistic—elements of a mindset that helps students improve their understanding of complex concepts.

Embrace the mess of the problem-solving process. Thinking is messy. We don’t always get things right the first time. Course corrections, revisions, and even total transformations of the work are necessary.

Observe your students as they work. Where are the roadblocks? How are they adapting to specific challenges? Listen to your own self-talk while you work, and use your challenges to think through ways your students might be challenged. Solutions are important, but so is the process along the way. Listening and talking to your students while they work allows you to give good feedback and receive assessment data.

Play creates open spaces for thinking where teachers can guide students to engage with big and interesting ideas of mathematics.

Use Concrete Methods

Physical or digital manipulatives like snap cubes, pattern blocks, and relational rods are all tools that can help students bring mathematics into being—a process called representation. Teachers can use decks of cards, dice, or counting objects to help students practice their basic skills.

For example, younger students can practice multiplication facts up to 6 times 6 by rolling two dice and multiplying the results. Older students can use decks of cards to practice integer operations, where red suits are negative and black suits are positive. For young students learning basic number skills, designate one day a week for purposeful practice using games.

Visual presentation of mathematical ideas can be playful. For example, give students a can lid or other circular object, some string, and a measuring tape to try and find the relationship between circumference and diameter.

Using physical or digital elements creates space for students to play with more abstract concepts and ideas. The freedom of a playful environment creates opportunities for deeper engagement. As I said in my talk, “Let them play. Let them talk and think and conjecture and wonder. Let them play.”

$what role does problem solving play in a mathematics classroom$

Problem Solving Activities: 7 Strategies

Critical Thinking

Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough.

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies.

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy.

Genius right?

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name.

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong.

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom.

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students.

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom.

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it.

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

$This is an example of a math starter.$

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here !

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons .

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next.

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below.

Which of the problem solving activities will you try first? Respond in the comments below.

$what role does problem solving play in a mathematics classroom$

Shametria Routt Banks

$what role does problem solving play in a mathematics classroom$

2 Responses

This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

Privacy Overview

The Role of the Teacher Changes in a Problem-Solving Classroom

How can teachers help students develop problem-solving skills when they themselves, even though confronted with an array of problems every day, may need to become better problem solvers? Our experience leads us to conclude that there is an expertise in a certain kind of problem-solving that teachers possess but that broader problem-solving skills are sometimes wanting.There are a few reasons why this happens. One reason may be that teacher preparation programs remain focused on how to teach subjects and behavior management techniques. Another reason may be that professional development opportunities offered in schools are focused elsewhere. And, another reason could be that leaders still often fail to engage their faculties in solving substantive problems within the school community.

A recent issue of Education Leadership was dedicated to the topic, “Unleashing Problem Solvers”. One theme that ran through several of the articles was the changing role of the teacher. In a positive but traditional classroom, information is shared by the teacher and the students are asked to demonstrate application of that information. A problem-solving classroom is different. A problem-solving classroom requires extraordinary planning on the part of the teacher. For problems to have relevance, students are engaged in the identification of the problem. Teachers have to become experts at creating questions that require students to reach back to information and skills already attained, while figuring out what they need to learn next in order to solve the problem. Some of us are really good at asking these kinds of questions. Others are not.

Students have to become experts at reflecting on these questions as guides resulting in a gathering of new information and skills, and answers. Teachers have to be prepared to offer lessons that bridge the gaps between the skills and information already attained and those the performance of the students demonstrate remain needed. Often it involves teams of students and they are simultaneously learning collaboration and communication skills.

Problem-Based Classrooms Require Letting Go

Opportunities for teachers to work with each other, to learn from experts, to receive feedback from observers of their work, all allow for skill development. But at the same time, there is a more challenging effort required of the teacher. Problem-based classrooms require teachers to dare to let go of control of the learning and to take hold of the role of questioner, coach, supporter, and diagnostician. In addition to the lack of training teachers have in these skills, the leaders in charge of evaluating their work also have to know what problem-solving classrooms look like and how to capture that environment in an observation, how to give feedback on the teachers’ efforts. Of course, if problem- solving is a collaborative school community process, how does that change the leader’s role? Are leaders, themselves, ready to become facilitators of the process rather than the sole problem solver? Many talk about wanting that but most get rewarded for being the problem solver.

Questions are Essential

There is a place to begin and that place is the shared understanding of what problem-based learning actually is. Because teachers traditionally plan for a time for Q and A within classes, they and their leaders may think of questions as having a correct answer. In moving into a problem-based learning design, the questions also have to be more overarching, create cognitive dissonance, and provoke the learner to search for answers. Here is why it is important to come to an understanding about the types of questions to be asked and shifting the teaching and learning practices to be one of expecting more from the learner.

Students Need Problem-Solving Skills

Problem-based learning skills are skills that prepare for a changing environment in all fields. Current educators cannot imagine some of the careers our students will have over their lifetimes. We do know that change will be part of everyone’s work. Flexibility and problem-solving are key skills. Problem- solving involves collaboration, communication, critical thinking, empathy, and integrity. If we listen to the business world, we will hear that design thinking is the way of the future.

Tim Brown, CEO of IDEO says,

Design thinking is a human-centered approach to innovation that draws from the designer’s toolkit to integrate the needs of people, the possibilities of technology, and the requirements for business success.

The only way for educators to develop these skills in students is to build lessons and units that are interdisciplinary and demand these skills. If we begin from the earliest of grades and expect more as they ascend through the grades, students will have mastered not only their subjects, but the skills that will prepare them for the world of work. How do we best prepare our students? We think problem solving is key.

A nn Myers and Jill Berkowicz are the authors of The STEM Shift (2015, Corwin) a book about leading the shift into 21st century schools. Ann and Jill welcome connecting through Twitter & Email .

Photo courtesy of Pixabay

The opinions expressed in Leadership 360 are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.

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Published: 07 March 2023

Exploring the effects of role scripts and goal-orientation scripts in collaborative problem-solving learning

Education and Information Technologies ( 2023 ) Cite this article

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Collaborative problem-solving (CPS) learning is increasingly valued for its role in promoting higher-order thinking of learners. Despite the widespread application of role scripts in CPS, little is known about the mechanisms by which roles influence learners' cognition and the impact of goal orientation on roles. In this study, we designed role scripts and goal-orientation scripts to facilitate CPS. Then, a total of 32 postgraduate students participated in CPS and they were divided into 8 groups, among which two roles of analyst and commenter were assigned respectively. Through qualitative and quantitative analysis, this study explored the differences between the two roles in terms of discourse space rotation, types of cognitive activities and epistemic network structure, and the function played by goal orientation. Results showed that there was a general structure in CPS, that analysts and commenters have different functional biases, and that goal orientation influences the function of the roles. This study clarified the cognitive contribution of different roles, and the respective strength of different goal orientation. The findings may provide instructors with implications for designing scripts and organizing CPS in the classroom context.

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Andrews-Todd, & Forsyth, C. M. (2020). Exploring social and cognitive dimensions of collaborative problem solving in an open online simulation-based task. Computers in Human Behavior, 104 , 105759. https://doi.org/10.1016/j.chb.2018.10.025

Article Google Scholar

Avcı, Ü. (2020). Examining the role of sentence openers, role assignment scaffolds and self-determination in collaborative knowledge building. Educational Technology Research and Development, 68 (1), 109–135. https://doi.org/10.1007/s11423-019-09672-5

Article MathSciNet Google Scholar

Avry, S., Chanel, G., Bétrancourt, M., & Molinari, G. (2020). Achievement appraisals, emotions and socio-cognitive processes: How they interplay in collaborative problem-solving? Computers in Human Behavior, 107 , 106267. https://doi.org/10.1016/j.chb.2020.106267

Cai, H., & Gu, X. (2015). Design Research on Cognitive Development in Computer-supported Collaborative Learning Environment. Open Education Research, 21 (04), 81–88.

Google Scholar

Cai, H., & Gu, X. (2022). Factors that influence the different levels of individuals’ understanding after collaborative problem solving: The effects of shared representational guidance and prior knowledge. Interactive Learning Environments, 30 (4), 695–706. https://doi.org/10.1080/10494820.2019.1679841

Chen, C. M., & Kuo, C. H. (2019). An optimized group formation scheme to promote collaborative problem-based learning. Computers & Education, 133 (64), 94–115. https://doi.org/10.1016/j.compedu.2019.01.011

Chen, G., Lo, C. K., & Hu, L. (2020). Sustaining online academic discussions: Identifying the characteristics of messages that receive responses. Computers & Education, 156 , 103938.

Cohen, E. G., Lotan, R. A., Abram, P. L., Scarloss, B. A., & Schultz, S. E. (2002). Can Groups Learn? Teachers College Record, 104 (6), 1045–1068.

Crespo, S., & Harper, Fk. (2020). Learning to pose collaborative mathematics problems with secondary prospective teachers. International Journal of Educational Research, 102 , 101430.

Engle, R. A., Langer-Osuna, J. M., & McKinney de Royston, M. (2014). Toward a model of influence in persuasive discussions: Negotiating quality, authority, privilege, and access within a student-led argument. Journal of the Learning Sciences, 23 (2), 245–268. https://doi.org/10.1080/10508406.2014.883979

Ertl, B., Fischer, F., & Mandl, H. (2006). Conceptual and socio-cognitive support for collaborative learning in videoconferencing environments. Computers & Education, 47 (3), 298–315. https://doi.org/10.1016/j.compedu.2004.11.001

Fabbri, M. (2020). To assign or not to assign? Role Taking in Higher Education. Open and Interdisciplinary Journal of Technology., 15 (2), 105–120. https://doi.org/10.30557/QW000026

Fiore, S. M., Graesser, A. C., Greiff, S., Griffin, P., Gong, B., Kyllonen, P., Massey, C. S., O’Neil, H. F., Pellegrino, J., Rothman, R. A., Soulé, H., & Davier, A. A. (2017). Collaborative Problem Solving: Considerations for the National Assessment of Educational Progress . National Center for Education Statistics.

Fiore, S. M., Graesser, A., Greiff, S., Griffin, P., Gong, B., Kyllonen, P., & von Davier, A. (2017). Collaborative problem solving: Considerations for the national assessment of educational progress . Alexandria: National Center for Education Statistics.

Fiore, S. M., Graesser, A., & Greiff, S. (2018). Collaborative problem-solving education for the twenty-first-century workforce. Nature Human Behaviour, 2 (6), 367. https://doi.org/10.1038/s41562-018-0363-y

Fischer, F., Kollar, I., Stegmann, K., & Wecker, C. (2013). Toward a script theory of guidance in computersupported collaborative learning. Educational Psychologist, 48 (1), 56–66. https://doi.org/10.1080/00461520.2012.748005

Garrison, D. R., Anderson, T., & Archer, W. (2001). Critical thinking, cognitive presence, and computer conferencing in distance education. American Journal of Distance Education, 15 (1), 7–23. https://doi.org/10.1080/08923640109527071

Gervits, F., Eberhard, K., & Scheutz, M. (2016). Team communication as a collaborative process. Frontiers in Robotics and AI, 3 , 62. https://doi.org/10.3389/frobt.2016.00062

Gillies, R. M. (2019). Promoting academically productive student dialogue during collaborative learning. International Journal of Educational Research, 97 , 200–209. https://doi.org/10.1016/j.ijer.2017.07.014

Griffin, P., McGaw, B., & Care, E. (2012). Assessment and teaching of 21st century skills. Assessment and Teaching of 21st Century Skills, 9789400723245 , 1–345.

Gu, X., Shao, Y., Guo, X., & Lim, C. P. (2015). Designing a role structure to engage students in computer-supported collaborative learning. The Internet and Higher Education, 24 , 13–20. https://doi.org/10.1016/j.iheduc.2014.09.002

Hara, N., Bonk, C. J., & Angeli, C. (2000). Content Analysis of Online Discussion in an Applied Educational Psychology Course. Instructional Science, 28 (2), 115–152. https://doi.org/10.1023/A:1003764722829

Hare, A. P. (1994). Types of Roles in Small Groups: A Bit of History and a Current Perspective. Small Group Research, 25 (3), 433–448. https://doi.org/10.1177/1046496494253005

Heinimäki, O., Volet, S., Jones, C., Laakkonen, E., & Vauras, M. (2021). Student participatory role profiles in collaborative science learning: Relation of within-group configurations of role profiles and achievement. Learning Culture and Social Interaction, 30 , 100539. https://doi.org/10.1016/j.lcsi.2021.100539

Heppner, P., & Petersen, C. H. (1982). The development and implications of a personal problem-solving inventory. Journal of Counseling Psychology, 29 (1), 66–75. https://doi.org/10.1037/0022-0167.29.1.66

Honey, P., & Mumford, A. (2006). The Learning Styles Questionnaire 80-Item Version . Peter Honey Publications.

Hu, L. (2021). Conceptualization and operationalization of group thinking sustainability in dialogic collaborative problem solving. Thinking Skills and Creativity, 42 , 100964. https://doi.org/10.1016/j.tsc.2021.100964

Hu, L., & Chen, G. (2021). Exploring turn-taking patterns during dialogic collaborative problem solving. Instructional Science, 50 (1), 63–88. https://doi.org/10.1007/s11251-021-09565-2

Huang, C., Han, Z., Li, M., Jong, M. S., & Tsai, C. (2019). Investigating students’ interaction patterns and dynamic learning sentiments in online discussions. Computers and Education, 140 , 103589. https://doi.org/10.1016/j.compedu.2019.05.015

Kimmerle, J., & Cress, U. (2008). Group awareness and self-presentation in computer-supported information exchange. International. Journal of Computer-Supported Collaborative Learning, 3 (1), 85–97. https://doi.org/10.1007/s11412-007-9027-z

Kobbe, L., Weinberger, A., Dillenbourg, P., Harrer, A., Hämäläinen, R., Häkkinen, P., & Fischer, F. (2007). Specifying Computer-Supported Collaboration Scripts. International Journal of Computer-Supported Collaborative Learning, 2 (2–3), 211-3<211-224. https://doi.org/10.1007/s11412-007-9014-4

Kollar, I., Fischer, F., & Hesse, F. W. (2006). Collaboration scripts–a conceptual analysis. Educational Psychology Review, 18 (2), 159–185. https://doi.org/10.1007/s10648-006-9007-2

Levinson, S. C. (1983). Pragmatics . Cambridge University Press.

Book Google Scholar

Lin, C., Barrett, N. E., & Liu, G. (2021). English outside the academic sphere: A mobile-based context-aware comparison study on collaborative and individual learning. Journal of Computer Assisted Learning, 37 (3), 657–671. https://doi.org/10.1111/jcal.12514

Liu, L., Hao, J., von Davier, A. A., Kyllonen, P., & Zapata-Rivera, J.-D. (2015). A tough nut to crack: Measuring collaborative problem solving. In Y. Rosen, S. Ferrara, & M. Mosharraf (Eds.), Handbook of research on computational tools for real-world skill development. IGI-Global.

Looi, C., Chen, W., & Ng, F.-K. (2010). Collaborative activities enabled by GroupScribbles (GS): An exploratory study of learning effectiveness. Computers and Education, 54 (1), 14–26. https://doi.org/10.1016/j.compedu.2009.07.003

López-Fernández, M., González-García, F., & Franco-Mariscal, A. J. (2021). Should We Ban Single-Use Plastics? A Role-Playing Game to Argue and Make Decisions in a Grade-8 School Chemistry Class. Journal of Chemical Education, 98 (12), 3947–3956. https://doi.org/10.1021/acs.jchemed.1c00580

Mahardale, J. W., & Lee, C. B. (2013). Understanding how social and epistemic scripts perpetuate intersubjectivity through patterns of interactions. Interactive Learning Environments, 21 (1), 68–88. https://doi.org/10.1080/10494820.2010.547204

Marcos-Garcia, J.-A., Martinez-Mones, A., & Dimitriadis, Y. (2015). DESPRO: A method based on roles to provide collaboration analysis support adapted to the participants in CSCL situations. Computers & Education, 82 , 335–353. https://doi.org/10.1016/j.compedu.2014.10.027

Meij, V., Veldkamp, S., & Leemkuil, H. (2020). Effects of scripting on dialogues, motivation and learning outcomes in serious games. British Journal of Educational Technology, 51 (2), 459–472. https://doi.org/10.1111/bjet.12851

Mercer, N., Wegerif, R., & Major, L. (2019). The Routledge international handbook of research on dialogic education . Routledge.

Mogan, R., Bulbulia, J., & Fischer, R. (2019). Joint action enhances cohesion and positive affect, but suppresses aspects of creativity when combined with shared goals. Frontiers in Psychology, 9 , 2790. https://doi.org/10.3389/fpsyg.2018.02790

Morris, R., Hadwin, A. F., Gress, C. L. Z., Miller, M., Fior, M., Church, H., & Winne, P. H. (2010). Designing roles, scripts, and prompts to support CSCL in gStudy. Computers in Human Behavior, 26 (5), 815–824. https://doi.org/10.1016/j.chb.2008.12.001

Mujtaba, S. M., Reynolds, B. L., Parkash, R., & Singh, M. K. M. (2021). Individual and collaborative processing of written corrective feedback affects second language writing accuracy and revision. Assessing Writing, 50 , 100566. https://doi.org/10.1016/j.asw.2021.100566

Najjemba, J. L., & Cronjé, J. (2020). Engagement with and Participation in Online role play Collaborative Arguments: A Sociocultural Perspective. Electronic Journal of e-Learning, 18 (5), 436–448. https://doi.org/10.34190/JEL.18.5.006

Naykki, P., Isohatala, J., Jarvela, S., Poysa-Tarhonen, J., & Hakkinen, P. (2017). Facilitating socio-cognitive and socio-emotional monitoring in collaborative learning with a regulation macro script – an exploratory study. International Journal of Computer-Supported Collaborative Learning, 12 (3), 251–279. https://doi.org/10.1007/s11412-017-9259-5

O’Brien, G., & Bedford, S. B. (2012). Small group work in large chemistry classes: Workshops in first year chemistry. Aiming for excellence in STEM learning and teaching. Proceedings of STEM annual conference. London: Imperial College.

OECD [Organisation for Economic Co-operation and Development]. (2019). OECD learning compass 2030 concept note series, from https://www.oecd.org/education/2030-project/contact/ . Accessed 27 Feb 2023.

Ouyang, F., Chen, Z., Cheng, M., Tang, Z., & Su, C.-Y. (2021). Exploring the effect of three scaffoldings on the collaborative problem-solving processes in China’s higher education. International Journal of Educational Technology in Higher Education, 18 (1), 35–35. https://doi.org/10.1186/s41239-021-00273-y

Pruner, M., & Liljedahl, P. (2021). Collaborative problem solving in a choice-affluent environment. ZDM, 53 , 753–770. https://doi.org/10.1007/s11858-021-01232-7

Radkowitsch, A., Vogel, F., & Fischer, F. (2020). Good for learning, bad for motivation? A meta-analysis on the effects of computer-supported collaboration scripts. International Journal of Computer-Supported Collaborative Learning, 15 (1), 5–47. https://doi.org/10.1007/s11412-020-09316-4

Reddick, R., & Smith, D. L. (2020). Celebrity House Party, or the Networking Role-Playing Game: Using Theatre as a Tool to Increase Social Emotional Learning in Adults with a Focus on Building Success in the Business Sector. Teaching Artist Journal, 18 (1–2), 45–78. https://doi.org/10.1080/15411796.2020.1800326

Rojas, Nussbaum, M., Chiuminatto, P., Guerrero, O., Greiff, S., Krieger, F., & Van Der Westhuizen, L. (2021). Assessing collaborative problem-solving skills among elementary school students. Computers and Education, 175 , 104313. https://doi.org/10.1016/j.compedu.2021.104313

Sassenberg, L., Landkammer, F., & Jacoby, J. (2014). The influence of regulatory focus and group vs. individual goals on the evaluation bias in the context of group decision making. Journal of Experimental Social Psychology, 54 , 153–164. https://doi.org/10.1016/j.jesp.2014.05.009

Schellens, T., Van Keer, H., De Wever, B., & Valcke, M. (2007). Scripting by assigning roles: Does it improve knowledge construction in asynchronous discussion groups? International Journal of Computer-Supported Collaborative Learning, 2 (2–3), 225–246.

Scholl, A., Landkammer, F., & Sassenberg, K. (2019). When those who know do share: Group goals facilitate information sharing, but social power does not undermine it. PLoS ONE, 14 (3), e0213795–e0213795. https://doi.org/10.1371/journal.pone.0213795

Seo, K. K. (2007). Utilizing peer moderating in online discussions: Addressing the controversy between teacher moderation and nonmoderation. American Journal of Distance Education, 21 (1), 21–36.

Shaffer, D. W. (2017). Quantitative Ethnography . Cathcart Press.

Shaffer, D. W., Collier, W., & Ruis, A. R. (2016). A tutorial on epistemic network analysis: Analyzing the structure of connections in cognitive, social, and interaction data. Journal of Learning Analytics, 3 (3), 9–45. https://doi.org/10.18608/jla.2016.33.3

Stadler, M., Shubeck, K. T., Greiff, S., & Graesser, A. C. (2020). Some critical reflections on the special issue: Collaboration in the 21st century: The theory, assessment, and teaching of collaborative problem solving. Computers in Human Behavior, 104 , 106135. https://doi.org/10.1016/j.chb.2019.09.011

Stasser, G., & Titus, W. (1985). Pooling of Unshared Information in Group Decision Making: Biased Information Sampling During Discussion. Journal of Personality and Social Psychology, 48 (6), 1467–1478. https://doi.org/10.1037/0022-3514.48.6.1467

Strijbos, J.-W., & De, M. F. (2010). LaatDeveloping the role concept for computer-supported collaborative learning: An explorative synthesis. Computers in Human Behavior, 26 (4), 495–505. https://doi.org/10.1016/j.chb.2009.08.014

Tan, S. C., Wang, X., & Li, L. (2022). The Development Trajectory of Shared Epistemic Agency in Online Collaborative Learning: A Study Combing Network Analysis and Sequential Analysis. Journal of Educational Computing Research, 59 (8), 1655–1681. https://doi.org/10.1177/07356331211001562

Tawfik, A. A., Koehler, A. A., Gish-Lieberman, J. J., & Gatewood, J. (2021). Investigating the depth of problem-solving prompts in collaborative argumentation. Innovations in Education and Teaching International, 58 (5), 533–544. https://doi.org/10.1080/14703297.2021.1966821

Tempelaar, D. T., Wosnitza, M., Volet, S., Rienties, B., Giesbers, S. J., & Gijselaers, W. (2013). The role of self- and social directed goals in a problem-based, collaborative learning context. Higher Education, 66 (2), 253–267. https://doi.org/10.1007/s10734-012-9602-8

Thürmer, J. L., Wieber, F., & Gollwitzer, P. M. (2017). Planning and performance in small groups: Collective implementation intentions enhance group goal striving. Frontiers in Psychology, 19 (8), 603. https://doi.org/10.3389/fpsyg.2017.00603

Unal, E., & Cakir, H. (2021). The effect of technology-supported collaborative problem solving method on students’ achievement and engagement. Education and Information Technologies, 26 (4), 4127–4150. https://doi.org/10.1007/s10639-021-10463-w

van Dijk, A. M., Gijlers, H., & Weinberger, A. (2014). Scripted collaborative drawing in elementary science education. Instructional Science, 42 (3), 353–372. https://doi.org/10.1007/s11251-013-9286-1

Volet, S., Jones, C., & Vauras, M. (2019). Attitude-, group- and activity-related differences in the quality of preservice teacher students’ engagement in collaborative science learning. Learning and Individual Differences, 73 , 79–91. https://doi.org/10.1016/j.lindif.2019.05.002

Wang, S., Hou, H., & Wu, S. (2017). Analyzing the knowledge construction and cognitive patterns of blog-based instructional activities using four frequent interactive strategies (problem solving, peer assessment, role playing and peer tutoring): A preliminary study. Educational Technology Research & Development, 65 (2), 301–323. https://doi.org/10.1007/s11423-016-9471-4

Weinberger, A., Ertl, B., Fischer, F., & Mandl, H. (2005). Epistemic and Social Scripts in Computer-Supported Collaborative Learning. Instructional Science, 33 (1), 1–30. https://doi.org/10.1007/s11251-004-2322-4

Weinberger, A., Stegmann, K., & Fischer, F. (2007). Knowledge convergence in collaborative learning: Concepts and assessment. Learning and Instruction, 17 (4), 416–426. https://doi.org/10.1016/j.learninstruc.2007.03.007

Wittenbaum, G. M., Hollingshead, A. B., & Botero, I. C. (2004). From cooperative to motivated information sharing in groups: Moving beyond the hidden profile paradigm. Communication Monographs, 71 (3), 286–310. https://doi.org/10.1080/0363452042000299894

Wu, B., Wang, M., Spector, M., & Yang, S. (2013). Design of a dual-mapping learning approach for problem solving and knowledge construction in ill-structured domains. Educational Technology & Society, 16 (4), 71–84.

Wu, B., Hu, Y., Ruis, A. R., & Wang, M. (2019). Analysing computational thinking in collaborative programming: A quantitative ethnography approach. Journal of Computer Assisted Learning, 35 (3), 421–434. https://doi.org/10.1111/jcal.12348

Ye, J., & Zhou, J. (2022). Exploring the relationship between learning sentiments and cognitive processing in online collaborative learning: A network analytic approach. The Internet and Higher Education, 55 , 100875. https://doi.org/10.1016/j.iheduc.2022.100875

Yousef, D. (2019). Exploring the reliability and validity of the learning styles questionnaire (LSQ) in an Arab setting. Quality Assurance in Education, 27 (4), 446–464. https://doi.org/10.1108/QAE-10-2018-0113

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