problem solving in primary education

Next available on Monday 9 a.m.–5 p.m.

Additional Options

• smartphone Call / Text
• voice_chat Consultation Appointment
• place Visit
• email Email

Chat with a Specific library

• Business Library Business Library Chat is Offline
• College Library (Undergraduate) College Library Chat is Offline
• Ebling Library (Health Sciences) Ebling Library Chat is Offline
• Gender and Women's Studies Librarian GWS Library Chat is Offline
• Information School Library (Information Studies) iSchool Library Chat is Offline
• Law Library (Law) Law Library Chat is Offline
• Memorial Library (Humanities & Social Sciences) Memorial Library Chat is Offline
• MERIT Library (Education) MERIT Library Chat is Offline
• Steenbock Library (Agricultural & Life Sciences, Engineering) Steenbock Library Chat is Offline
• Ask a Librarian Hours & Policy
• Library Research Tutorials

Search the for Website expand_more Articles Find articles in journals, magazines, newspapers, and more Catalog Explore books, music, movies, and more Databases Locate databases by title and description Journals Find journal titles UWDC Discover digital collections, images, sound recordings, and more Website Find information on spaces, staff, services, and more

Language website search.

Find information on spaces, staff, and services.

• ASK a Librarian
• Library by Appointment
• Locations & Hours
• Resources by Subject

book Catalog Search

Search the physical and online collections at UW-Madison, UW System libraries, and the Wisconsin Historical Society.

• Available Online
• Print/Physical Items
• Limit to UW-Madison
• Advanced Search
• Browse by...

collections_bookmark Database Search

Find databases subscribed to by UW-Madison Libraries, searchable by title and description.

• Browse by Subject/Type
• Introductory Databases
• Top 10 Databases

article Journal Search

Find journal titles available online and in print.

• Browse by Subject / Title
• Citation Search

description Article Search

Find articles in journals, magazines, newspapers, and more.

• Scholarly (peer-reviewed)
• Open Access
• Library Databases

collections UW Digital Collections Search

Discover digital objects and collections curated by the UW Digital Collections Center .

• Browse Collections
• Browse UWDC Items
• University of Wisconsin–Madison
• Email/Calendar
• Google Apps
• Loans & Requests
• Poster Printing
• Account Details
• Archives and Special Collections Requests
• Library Room Reservations

Search the UW-Madison Libraries

Article search, creative problem solving in primary education: exploring the role of fact finding, problem finding, and solution finding across tasks.

• • Fact finding, problem finding and solution finding were included in creative problem solving tasks • Fact finding and problem finding were positively associated with fluency and originality • Problem finding seemed to help in finding complete ideas, fact finding did not. • Primary school students were able to identify their most creative ideas • Students did not undervalue certain aspects of creativity when applying solution finding Interest in fostering creative problem solving (CPS) from primary education onwards is growing. However, embedding CPS in Education seems to be a challenge. One problem is that generating creative ideas (idea finding) is often taught in isolation, rather than also including processes such as exploring knowledge (fact finding), defining the problem (problem finding) and comparing ideas to identify the most creative ones (solution finding). In the current study, we prepared CPS tasks for primary education that represent this more complete CPS model and studied whether successful fact finding and problem finding were positively associated with the creativity of the ideas found. Additionally, we studied whether solution finding is doable for these young students and how they select the most creative ideas. Bayesian analyses indicated a positive association of fact finding and problem finding with the number of ideas generated and the originality of these ideas. In addition, problem finding seemed to be positively associated with the completeness of ideas, whereas fact finding seemed not. We also found that primary school students were able to identify their most creative ideas. Students did not seem to undervalue certain aspects of creativity when applying solution finding. Our results indicate that when aiming for more and original solutions, teachers could embed fact finding and problem finding in their CPS teaching practices. Our results also indicate primary school students are able to recognize creativity.

Having Trouble?

If you are having trouble accessing the article, report a problem.

Physical Copies

Publication details.

• Elsevier SD Complete Freedom Collection [SCCMFC]
• Web of Science - Social Sciences Citation Index – 2020
• Bayesian statistics
• Creative Problem Solving
• Education & Educational Research
• fact finding
• primary education
• problem finding
• Social Sciences
• solution finding

Additional Information

Library staff details, keyboard shortcuts, available anywhere, available in search results.

Teaching Problem-Solving Skills

Many instructors design opportunities for students to solve “problems”. But are their students solving true problems or merely participating in practice exercises? The former stresses critical thinking and decision­ making skills whereas the latter requires only the application of previously learned procedures.

Problem solving is often broadly defined as "the ability to understand the environment, identify complex problems, review related information to develop, evaluate strategies and implement solutions to build the desired outcome" (Fissore, C. et al, 2021). True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.

Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.

Principles for teaching problem solving

• Model a useful problem-solving method . Problem solving can be difficult and sometimes tedious. Show students how to be patient and persistent, and how to follow a structured method, such as Woods’ model described below. Articulate your method as you use it so students see the connections.
• Teach within a specific context . Teach problem-solving skills in the context in which they will be used by students (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
• Help students understand the problem . In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
• Take enough time . When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal (both individually and as a class); dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
• Ask questions and make suggestions . Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
• Link errors to misconceptions . Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.

Woods’ problem-solving model

Define the problem.

• The system . Have students identify the system under study (e.g., a metal bridge subject to certain forces) by interpreting the information provided in the problem statement. Drawing a diagram is a great way to do this.
• Known(s) and concepts . List what is known about the problem, and identify the knowledge needed to understand (and eventually) solve it.
• Unknown(s) . Once you have a list of knowns, identifying the unknown(s) becomes simpler. One unknown is generally the answer to the problem, but there may be other unknowns. Be sure that students understand what they are expected to find.
• Units and symbols . One key aspect in problem solving is teaching students how to select, interpret, and use units and symbols. Emphasize the use of units whenever applicable. Develop a habit of using appropriate units and symbols yourself at all times.
• Constraints . All problems have some stated or implied constraints. Teach students to look for the words "only", "must", "neglect", or "assume" to help identify the constraints.
• Criteria for success . Help students consider, from the beginning, what a logical type of answer would be. What characteristics will it possess? For example, a quantitative problem will require an answer in some form of numerical units (e.g., $/kg product, square cm, etc.) while an optimization problem requires an answer in the form of either a numerical maximum or minimum.

Think about it

• “Let it simmer”.  Use this stage to ponder the problem. Ideally, students will develop a mental image of the problem at hand during this stage.
• Identify specific pieces of knowledge . Students need to determine by themselves the required background knowledge from illustrations, examples and problems covered in the course.
• Collect information . Encourage students to collect pertinent information such as conversion factors, constants, and tables needed to solve the problem.

Plan a solution

• Consider possible strategies . Often, the type of solution will be determined by the type of problem. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards.
• Choose the best strategy . Help students to choose the best strategy by reminding them again what they are required to find or calculate.

Carry out the plan

• Be patient . Most problems are not solved quickly or on the first attempt. In other cases, executing the solution may be the easiest step.
• Be persistent . If a plan does not work immediately, do not let students get discouraged. Encourage them to try a different strategy and keep trying.

Encourage students to reflect. Once a solution has been reached, students should ask themselves the following questions:

• Does the answer make sense?
• Does it fit with the criteria established in step 1?
• Did I answer the question(s)?
• What did I learn by doing this?
• Could I have done the problem another way?

If you would like support applying these tips to your own teaching, CTE staff members are here to help.  View the  CTE Support  page to find the most relevant staff member to contact. 

• Fissore, C., Marchisio, M., Roman, F., & Sacchet, M. (2021). Development of problem solving skills with Maple in higher education. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_15
• Foshay, R., & Kirkley, J. (1998). Principles for Teaching Problem Solving. TRO Learning Inc., Edina MN.  (PDF) Principles for Teaching Problem Solving (researchgate.net)
• Hayes, J.R. (1989). The Complete Problem Solver. 2nd Edition. Hillsdale, NJ: Lawrence Erlbaum Associates.
• Woods, D.R., Wright, J.D., Hoffman, T.W., Swartman, R.K., Doig, I.D. (1975). Teaching Problem solving Skills.
• Engineering Education. Vol 1, No. 1. p. 238. Washington, DC: The American Society for Engineering Education.

Catalog search

Teaching tip categories.

• Assessment and feedback
• Blended Learning and Educational Technologies
• Career Development
• Course Design
• Course Implementation
• Inclusive Teaching and Learning
• Learning activities
• Support for Student Learning
• Support for TAs
• Learning activities ,

Teaching problem solving: Let students get ‘stuck’ and ‘unstuck’

Subscribe to the center for universal education bulletin, kate mills and km kate mills literacy interventionist - red bank primary school helyn kim helyn kim former brookings expert @helyn_kim.

October 31, 2017

This is the second in a six-part  blog series  on  teaching 21st century skills , including  problem solving ,  metacognition , critical thinking , and collaboration , in classrooms.

In the real world, students encounter problems that are complex, not well defined, and lack a clear solution and approach. They need to be able to identify and apply different strategies to solve these problems. However, problem solving skills do not necessarily develop naturally; they need to be explicitly taught in a way that can be transferred across multiple settings and contexts.

Here’s what Kate Mills, who taught 4 th grade for 10 years at Knollwood School in New Jersey and is now a Literacy Interventionist at Red Bank Primary School, has to say about creating a classroom culture of problem solvers:

Helping my students grow to be people who will be successful outside of the classroom is equally as important as teaching the curriculum. From the first day of school, I intentionally choose language and activities that help to create a classroom culture of problem solvers. I want to produce students who are able to think about achieving a particular goal and manage their mental processes . This is known as metacognition , and research shows that metacognitive skills help students become better problem solvers.

I begin by “normalizing trouble” in the classroom. Peter H. Johnston teaches the importance of normalizing struggle , of naming it, acknowledging it, and calling it what it is: a sign that we’re growing. The goal is for the students to accept challenge and failure as a chance to grow and do better.

I look for every chance to share problems and highlight how the students— not the teachers— worked through those problems. There is, of course, coaching along the way. For example, a science class that is arguing over whose turn it is to build a vehicle will most likely need a teacher to help them find a way to the balance the work in an equitable way. Afterwards, I make it a point to turn it back to the class and say, “Do you see how you …” By naming what it is they did to solve the problem , students can be more independent and productive as they apply and adapt their thinking when engaging in future complex tasks.

After a few weeks, most of the class understands that the teachers aren’t there to solve problems for the students, but to support them in solving the problems themselves. With that important part of our classroom culture established, we can move to focusing on the strategies that students might need.

Here’s one way I do this in the classroom:

I show the broken escalator video to the class. Since my students are fourth graders, they think it’s hilarious and immediately start exclaiming, “Just get off! Walk!”

When the video is over, I say, “Many of us, probably all of us, are like the man in the video yelling for help when we get stuck. When we get stuck, we stop and immediately say ‘Help!’ instead of embracing the challenge and trying new ways to work through it.” I often introduce this lesson during math class, but it can apply to any area of our lives, and I can refer to the experience and conversation we had during any part of our day.

Research shows that just because students know the strategies does not mean they will engage in the appropriate strategies. Therefore, I try to provide opportunities where students can explicitly practice learning how, when, and why to use which strategies effectively  so that they can become self-directed learners.

For example, I give students a math problem that will make many of them feel “stuck”. I will say, “Your job is to get yourselves stuck—or to allow yourselves to get stuck on this problem—and then work through it, being mindful of how you’re getting yourselves unstuck.” As students work, I check-in to help them name their process: “How did you get yourself unstuck?” or “What was your first step? What are you doing now? What might you try next?” As students talk about their process, I’ll add to a list of strategies that students are using and, if they are struggling, help students name a specific process. For instance, if a student says he wrote the information from the math problem down and points to a chart, I will say: “Oh that’s interesting. You pulled the important information from the problem out and organized it into a chart.” In this way, I am giving him the language to match what he did, so that he now has a strategy he could use in other times of struggle.

The charts grow with us over time and are something that we refer to when students are stuck or struggling. They become a resource for students and a way for them to talk about their process when they are reflecting on and monitoring what did or did not work.

For me, as a teacher, it is important that I create a classroom environment in which students are problem solvers. This helps tie struggles to strategies so that the students will not only see value in working harder but in working smarter by trying new and different strategies and revising their process. In doing so, they will more successful the next time around.

Related Content

Esther Care, Helyn Kim, Alvin Vista

October 17, 2017

David Owen, Alvin Vista

November 15, 2017

Loren Clarke, Esther Care

December 5, 2017

Global Education K-12 Education

Global Economy and Development

Center for Universal Education

Sofoklis Goulas

June 27, 2024

June 20, 2024

Modupe (Mo) Olateju, Grace Cannon, Kelsey Rappe

June 14, 2024

Center for Teaching

Teaching problem solving.

Print Version

Tips and Techniques

Expert vs. novice problem solvers, communicate.

• Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
• If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
• In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
• When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

• Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
• Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
• Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

• Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

• Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

Teaching Guides

• Online Course Development Resources
• Principles & Frameworks
• Pedagogies & Strategies
• Reflecting & Assessing
• Challenges & Opportunities
• Populations & Contexts

Quick Links

• Services for Departments and Schools
• Examples of Online Instructional Modules

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Review Article
• Open access
• Published: 11 January 2023

The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature

• Enwei Xu   ORCID: orcid.org/0000-0001-6424-8169 1 ,
• Wei Wang 1 &
• Qingxia Wang 1  

Humanities and Social Sciences Communications volume  10 , Article number:  16 ( 2023 ) Cite this article

17k Accesses

19 Citations

3 Altmetric

Metrics details

• Science, technology and society

Collaborative problem-solving has been widely embraced in the classroom instruction of critical thinking, which is regarded as the core of curriculum reform based on key competencies in the field of education as well as a key competence for learners in the 21st century. However, the effectiveness of collaborative problem-solving in promoting students’ critical thinking remains uncertain. This current research presents the major findings of a meta-analysis of 36 pieces of the literature revealed in worldwide educational periodicals during the 21st century to identify the effectiveness of collaborative problem-solving in promoting students’ critical thinking and to determine, based on evidence, whether and to what extent collaborative problem solving can result in a rise or decrease in critical thinking. The findings show that (1) collaborative problem solving is an effective teaching approach to foster students’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]); (2) in respect to the dimensions of critical thinking, collaborative problem solving can significantly and successfully enhance students’ attitudinal tendencies (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI[0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI[0.58, 0.82]); and (3) the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have an impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. On the basis of these results, recommendations are made for further study and instruction to better support students’ critical thinking in the context of collaborative problem-solving.

Similar content being viewed by others

A meta-analysis of the effects of design thinking on student learning

Fostering twenty-first century skills among primary school students through math project-based learning

A meta-analysis to gauge the impact of pedagogies employed in mixed-ability high school biology classrooms

Introduction.

Although critical thinking has a long history in research, the concept of critical thinking, which is regarded as an essential competence for learners in the 21st century, has recently attracted more attention from researchers and teaching practitioners (National Research Council, 2012 ). Critical thinking should be the core of curriculum reform based on key competencies in the field of education (Peng and Deng, 2017 ) because students with critical thinking can not only understand the meaning of knowledge but also effectively solve practical problems in real life even after knowledge is forgotten (Kek and Huijser, 2011 ). The definition of critical thinking is not universal (Ennis, 1989 ; Castle, 2009 ; Niu et al., 2013 ). In general, the definition of critical thinking is a self-aware and self-regulated thought process (Facione, 1990 ; Niu et al., 2013 ). It refers to the cognitive skills needed to interpret, analyze, synthesize, reason, and evaluate information as well as the attitudinal tendency to apply these abilities (Halpern, 2001 ). The view that critical thinking can be taught and learned through curriculum teaching has been widely supported by many researchers (e.g., Kuncel, 2011 ; Leng and Lu, 2020 ), leading to educators’ efforts to foster it among students. In the field of teaching practice, there are three types of courses for teaching critical thinking (Ennis, 1989 ). The first is an independent curriculum in which critical thinking is taught and cultivated without involving the knowledge of specific disciplines; the second is an integrated curriculum in which critical thinking is integrated into the teaching of other disciplines as a clear teaching goal; and the third is a mixed curriculum in which critical thinking is taught in parallel to the teaching of other disciplines for mixed teaching training. Furthermore, numerous measuring tools have been developed by researchers and educators to measure critical thinking in the context of teaching practice. These include standardized measurement tools, such as WGCTA, CCTST, CCTT, and CCTDI, which have been verified by repeated experiments and are considered effective and reliable by international scholars (Facione and Facione, 1992 ). In short, descriptions of critical thinking, including its two dimensions of attitudinal tendency and cognitive skills, different types of teaching courses, and standardized measurement tools provide a complex normative framework for understanding, teaching, and evaluating critical thinking.

Cultivating critical thinking in curriculum teaching can start with a problem, and one of the most popular critical thinking instructional approaches is problem-based learning (Liu et al., 2020 ). Duch et al. ( 2001 ) noted that problem-based learning in group collaboration is progressive active learning, which can improve students’ critical thinking and problem-solving skills. Collaborative problem-solving is the organic integration of collaborative learning and problem-based learning, which takes learners as the center of the learning process and uses problems with poor structure in real-world situations as the starting point for the learning process (Liang et al., 2017 ). Students learn the knowledge needed to solve problems in a collaborative group, reach a consensus on problems in the field, and form solutions through social cooperation methods, such as dialogue, interpretation, questioning, debate, negotiation, and reflection, thus promoting the development of learners’ domain knowledge and critical thinking (Cindy, 2004 ; Liang et al., 2017 ).

Collaborative problem-solving has been widely used in the teaching practice of critical thinking, and several studies have attempted to conduct a systematic review and meta-analysis of the empirical literature on critical thinking from various perspectives. However, little attention has been paid to the impact of collaborative problem-solving on critical thinking. Therefore, the best approach for developing and enhancing critical thinking throughout collaborative problem-solving is to examine how to implement critical thinking instruction; however, this issue is still unexplored, which means that many teachers are incapable of better instructing critical thinking (Leng and Lu, 2020 ; Niu et al., 2013 ). For example, Huber ( 2016 ) provided the meta-analysis findings of 71 publications on gaining critical thinking over various time frames in college with the aim of determining whether critical thinking was truly teachable. These authors found that learners significantly improve their critical thinking while in college and that critical thinking differs with factors such as teaching strategies, intervention duration, subject area, and teaching type. The usefulness of collaborative problem-solving in fostering students’ critical thinking, however, was not determined by this study, nor did it reveal whether there existed significant variations among the different elements. A meta-analysis of 31 pieces of educational literature was conducted by Liu et al. ( 2020 ) to assess the impact of problem-solving on college students’ critical thinking. These authors found that problem-solving could promote the development of critical thinking among college students and proposed establishing a reasonable group structure for problem-solving in a follow-up study to improve students’ critical thinking. Additionally, previous empirical studies have reached inconclusive and even contradictory conclusions about whether and to what extent collaborative problem-solving increases or decreases critical thinking levels. As an illustration, Yang et al. ( 2008 ) carried out an experiment on the integrated curriculum teaching of college students based on a web bulletin board with the goal of fostering participants’ critical thinking in the context of collaborative problem-solving. These authors’ research revealed that through sharing, debating, examining, and reflecting on various experiences and ideas, collaborative problem-solving can considerably enhance students’ critical thinking in real-life problem situations. In contrast, collaborative problem-solving had a positive impact on learners’ interaction and could improve learning interest and motivation but could not significantly improve students’ critical thinking when compared to traditional classroom teaching, according to research by Naber and Wyatt ( 2014 ) and Sendag and Odabasi ( 2009 ) on undergraduate and high school students, respectively.

The above studies show that there is inconsistency regarding the effectiveness of collaborative problem-solving in promoting students’ critical thinking. Therefore, it is essential to conduct a thorough and trustworthy review to detect and decide whether and to what degree collaborative problem-solving can result in a rise or decrease in critical thinking. Meta-analysis is a quantitative analysis approach that is utilized to examine quantitative data from various separate studies that are all focused on the same research topic. This approach characterizes the effectiveness of its impact by averaging the effect sizes of numerous qualitative studies in an effort to reduce the uncertainty brought on by independent research and produce more conclusive findings (Lipsey and Wilson, 2001 ).

This paper used a meta-analytic approach and carried out a meta-analysis to examine the effectiveness of collaborative problem-solving in promoting students’ critical thinking in order to make a contribution to both research and practice. The following research questions were addressed by this meta-analysis:

What is the overall effect size of collaborative problem-solving in promoting students’ critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills)?

How are the disparities between the study conclusions impacted by various moderating variables if the impacts of various experimental designs in the included studies are heterogeneous?

This research followed the strict procedures (e.g., database searching, identification, screening, eligibility, merging, duplicate removal, and analysis of included studies) of Cooper’s ( 2010 ) proposed meta-analysis approach for examining quantitative data from various separate studies that are all focused on the same research topic. The relevant empirical research that appeared in worldwide educational periodicals within the 21st century was subjected to this meta-analysis using Rev-Man 5.4. The consistency of the data extracted separately by two researchers was tested using Cohen’s kappa coefficient, and a publication bias test and a heterogeneity test were run on the sample data to ascertain the quality of this meta-analysis.

Data sources and search strategies

There were three stages to the data collection process for this meta-analysis, as shown in Fig. 1 , which shows the number of articles included and eliminated during the selection process based on the statement and study eligibility criteria.

This flowchart shows the number of records identified, included and excluded in the article.

First, the databases used to systematically search for relevant articles were the journal papers of the Web of Science Core Collection and the Chinese Core source journal, as well as the Chinese Social Science Citation Index (CSSCI) source journal papers included in CNKI. These databases were selected because they are credible platforms that are sources of scholarly and peer-reviewed information with advanced search tools and contain literature relevant to the subject of our topic from reliable researchers and experts. The search string with the Boolean operator used in the Web of Science was “TS = (((“critical thinking” or “ct” and “pretest” or “posttest”) or (“critical thinking” or “ct” and “control group” or “quasi experiment” or “experiment”)) and (“collaboration” or “collaborative learning” or “CSCL”) and (“problem solving” or “problem-based learning” or “PBL”))”. The research area was “Education Educational Research”, and the search period was “January 1, 2000, to December 30, 2021”. A total of 412 papers were obtained. The search string with the Boolean operator used in the CNKI was “SU = (‘critical thinking’*‘collaboration’ + ‘critical thinking’*‘collaborative learning’ + ‘critical thinking’*‘CSCL’ + ‘critical thinking’*‘problem solving’ + ‘critical thinking’*‘problem-based learning’ + ‘critical thinking’*‘PBL’ + ‘critical thinking’*‘problem oriented’) AND FT = (‘experiment’ + ‘quasi experiment’ + ‘pretest’ + ‘posttest’ + ‘empirical study’)” (translated into Chinese when searching). A total of 56 studies were found throughout the search period of “January 2000 to December 2021”. From the databases, all duplicates and retractions were eliminated before exporting the references into Endnote, a program for managing bibliographic references. In all, 466 studies were found.

Second, the studies that matched the inclusion and exclusion criteria for the meta-analysis were chosen by two researchers after they had reviewed the abstracts and titles of the gathered articles, yielding a total of 126 studies.

Third, two researchers thoroughly reviewed each included article’s whole text in accordance with the inclusion and exclusion criteria. Meanwhile, a snowball search was performed using the references and citations of the included articles to ensure complete coverage of the articles. Ultimately, 36 articles were kept.

Two researchers worked together to carry out this entire process, and a consensus rate of almost 94.7% was reached after discussion and negotiation to clarify any emerging differences.

Eligibility criteria

Since not all the retrieved studies matched the criteria for this meta-analysis, eligibility criteria for both inclusion and exclusion were developed as follows:

The publication language of the included studies was limited to English and Chinese, and the full text could be obtained. Articles that did not meet the publication language and articles not published between 2000 and 2021 were excluded.

The research design of the included studies must be empirical and quantitative studies that can assess the effect of collaborative problem-solving on the development of critical thinking. Articles that could not identify the causal mechanisms by which collaborative problem-solving affects critical thinking, such as review articles and theoretical articles, were excluded.

The research method of the included studies must feature a randomized control experiment or a quasi-experiment, or a natural experiment, which have a higher degree of internal validity with strong experimental designs and can all plausibly provide evidence that critical thinking and collaborative problem-solving are causally related. Articles with non-experimental research methods, such as purely correlational or observational studies, were excluded.

The participants of the included studies were only students in school, including K-12 students and college students. Articles in which the participants were non-school students, such as social workers or adult learners, were excluded.

The research results of the included studies must mention definite signs that may be utilized to gauge critical thinking’s impact (e.g., sample size, mean value, or standard deviation). Articles that lacked specific measurement indicators for critical thinking and could not calculate the effect size were excluded.

Data coding design

In order to perform a meta-analysis, it is necessary to collect the most important information from the articles, codify that information’s properties, and convert descriptive data into quantitative data. Therefore, this study designed a data coding template (see Table 1 ). Ultimately, 16 coding fields were retained.

The designed data-coding template consisted of three pieces of information. Basic information about the papers was included in the descriptive information: the publishing year, author, serial number, and title of the paper.

The variable information for the experimental design had three variables: the independent variable (instruction method), the dependent variable (critical thinking), and the moderating variable (learning stage, teaching type, intervention duration, learning scaffold, group size, measuring tool, and subject area). Depending on the topic of this study, the intervention strategy, as the independent variable, was coded into collaborative and non-collaborative problem-solving. The dependent variable, critical thinking, was coded as a cognitive skill and an attitudinal tendency. And seven moderating variables were created by grouping and combining the experimental design variables discovered within the 36 studies (see Table 1 ), where learning stages were encoded as higher education, high school, middle school, and primary school or lower; teaching types were encoded as mixed courses, integrated courses, and independent courses; intervention durations were encoded as 0–1 weeks, 1–4 weeks, 4–12 weeks, and more than 12 weeks; group sizes were encoded as 2–3 persons, 4–6 persons, 7–10 persons, and more than 10 persons; learning scaffolds were encoded as teacher-supported learning scaffold, technique-supported learning scaffold, and resource-supported learning scaffold; measuring tools were encoded as standardized measurement tools (e.g., WGCTA, CCTT, CCTST, and CCTDI) and self-adapting measurement tools (e.g., modified or made by researchers); and subject areas were encoded according to the specific subjects used in the 36 included studies.

The data information contained three metrics for measuring critical thinking: sample size, average value, and standard deviation. It is vital to remember that studies with various experimental designs frequently adopt various formulas to determine the effect size. And this paper used Morris’ proposed standardized mean difference (SMD) calculation formula ( 2008 , p. 369; see Supplementary Table S3 ).

Procedure for extracting and coding data

According to the data coding template (see Table 1 ), the 36 papers’ information was retrieved by two researchers, who then entered them into Excel (see Supplementary Table S1 ). The results of each study were extracted separately in the data extraction procedure if an article contained numerous studies on critical thinking, or if a study assessed different critical thinking dimensions. For instance, Tiwari et al. ( 2010 ) used four time points, which were viewed as numerous different studies, to examine the outcomes of critical thinking, and Chen ( 2013 ) included the two outcome variables of attitudinal tendency and cognitive skills, which were regarded as two studies. After discussion and negotiation during data extraction, the two researchers’ consistency test coefficients were roughly 93.27%. Supplementary Table S2 details the key characteristics of the 36 included articles with 79 effect quantities, including descriptive information (e.g., the publishing year, author, serial number, and title of the paper), variable information (e.g., independent variables, dependent variables, and moderating variables), and data information (e.g., mean values, standard deviations, and sample size). Following that, testing for publication bias and heterogeneity was done on the sample data using the Rev-Man 5.4 software, and then the test results were used to conduct a meta-analysis.

Publication bias test

When the sample of studies included in a meta-analysis does not accurately reflect the general status of research on the relevant subject, publication bias is said to be exhibited in this research. The reliability and accuracy of the meta-analysis may be impacted by publication bias. Due to this, the meta-analysis needs to check the sample data for publication bias (Stewart et al., 2006 ). A popular method to check for publication bias is the funnel plot; and it is unlikely that there will be publishing bias when the data are equally dispersed on either side of the average effect size and targeted within the higher region. The data are equally dispersed within the higher portion of the efficient zone, consistent with the funnel plot connected with this analysis (see Fig. 2 ), indicating that publication bias is unlikely in this situation.

This funnel plot shows the result of publication bias of 79 effect quantities across 36 studies.

Heterogeneity test

To select the appropriate effect models for the meta-analysis, one might use the results of a heterogeneity test on the data effect sizes. In a meta-analysis, it is common practice to gauge the degree of data heterogeneity using the I 2 value, and I 2  ≥ 50% is typically understood to denote medium-high heterogeneity, which calls for the adoption of a random effect model; if not, a fixed effect model ought to be applied (Lipsey and Wilson, 2001 ). The findings of the heterogeneity test in this paper (see Table 2 ) revealed that I 2 was 86% and displayed significant heterogeneity ( P  < 0.01). To ensure accuracy and reliability, the overall effect size ought to be calculated utilizing the random effect model.

The analysis of the overall effect size

This meta-analysis utilized a random effect model to examine 79 effect quantities from 36 studies after eliminating heterogeneity. In accordance with Cohen’s criterion (Cohen, 1992 ), it is abundantly clear from the analysis results, which are shown in the forest plot of the overall effect (see Fig. 3 ), that the cumulative impact size of cooperative problem-solving is 0.82, which is statistically significant ( z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]), and can encourage learners to practice critical thinking.

This forest plot shows the analysis result of the overall effect size across 36 studies.

In addition, this study examined two distinct dimensions of critical thinking to better understand the precise contributions that collaborative problem-solving makes to the growth of critical thinking. The findings (see Table 3 ) indicate that collaborative problem-solving improves cognitive skills (ES = 0.70) and attitudinal tendency (ES = 1.17), with significant intergroup differences (chi 2  = 7.95, P  < 0.01). Although collaborative problem-solving improves both dimensions of critical thinking, it is essential to point out that the improvements in students’ attitudinal tendency are much more pronounced and have a significant comprehensive effect (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]), whereas gains in learners’ cognitive skill are slightly improved and are just above average. (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

The analysis of moderator effect size

The whole forest plot’s 79 effect quantities underwent a two-tailed test, which revealed significant heterogeneity ( I 2  = 86%, z  = 12.78, P  < 0.01), indicating differences between various effect sizes that may have been influenced by moderating factors other than sampling error. Therefore, exploring possible moderating factors that might produce considerable heterogeneity was done using subgroup analysis, such as the learning stage, learning scaffold, teaching type, group size, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, in order to further explore the key factors that influence critical thinking. The findings (see Table 4 ) indicate that various moderating factors have advantageous effects on critical thinking. In this situation, the subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), learning scaffold (chi 2  = 9.03, P  < 0.01), and teaching type (chi 2  = 7.20, P  < 0.05) are all significant moderators that can be applied to support the cultivation of critical thinking. However, since the learning stage and the measuring tools did not significantly differ among intergroup (chi 2  = 3.15, P  = 0.21 > 0.05, and chi 2  = 0.08, P  = 0.78 > 0.05), we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving. These are the precise outcomes, as follows:

Various learning stages influenced critical thinking positively, without significant intergroup differences (chi 2  = 3.15, P  = 0.21 > 0.05). High school was first on the list of effect sizes (ES = 1.36, P  < 0.01), then higher education (ES = 0.78, P  < 0.01), and middle school (ES = 0.73, P  < 0.01). These results show that, despite the learning stage’s beneficial influence on cultivating learners’ critical thinking, we are unable to explain why it is essential for cultivating critical thinking in the context of collaborative problem-solving.

Different teaching types had varying degrees of positive impact on critical thinking, with significant intergroup differences (chi 2  = 7.20, P  < 0.05). The effect size was ranked as follows: mixed courses (ES = 1.34, P  < 0.01), integrated courses (ES = 0.81, P  < 0.01), and independent courses (ES = 0.27, P  < 0.01). These results indicate that the most effective approach to cultivate critical thinking utilizing collaborative problem solving is through the teaching type of mixed courses.

Various intervention durations significantly improved critical thinking, and there were significant intergroup differences (chi 2  = 12.18, P  < 0.01). The effect sizes related to this variable showed a tendency to increase with longer intervention durations. The improvement in critical thinking reached a significant level (ES = 0.85, P  < 0.01) after more than 12 weeks of training. These findings indicate that the intervention duration and critical thinking’s impact are positively correlated, with a longer intervention duration having a greater effect.

Different learning scaffolds influenced critical thinking positively, with significant intergroup differences (chi 2  = 9.03, P  < 0.01). The resource-supported learning scaffold (ES = 0.69, P  < 0.01) acquired a medium-to-higher level of impact, the technique-supported learning scaffold (ES = 0.63, P  < 0.01) also attained a medium-to-higher level of impact, and the teacher-supported learning scaffold (ES = 0.92, P  < 0.01) displayed a high level of significant impact. These results show that the learning scaffold with teacher support has the greatest impact on cultivating critical thinking.

Various group sizes influenced critical thinking positively, and the intergroup differences were statistically significant (chi 2  = 8.77, P  < 0.05). Critical thinking showed a general declining trend with increasing group size. The overall effect size of 2–3 people in this situation was the biggest (ES = 0.99, P  < 0.01), and when the group size was greater than 7 people, the improvement in critical thinking was at the lower-middle level (ES < 0.5, P  < 0.01). These results show that the impact on critical thinking is positively connected with group size, and as group size grows, so does the overall impact.

Various measuring tools influenced critical thinking positively, with significant intergroup differences (chi 2  = 0.08, P  = 0.78 > 0.05). In this situation, the self-adapting measurement tools obtained an upper-medium level of effect (ES = 0.78), whereas the complete effect size of the standardized measurement tools was the largest, achieving a significant level of effect (ES = 0.84, P  < 0.01). These results show that, despite the beneficial influence of the measuring tool on cultivating critical thinking, we are unable to explain why it is crucial in fostering the growth of critical thinking by utilizing the approach of collaborative problem-solving.

Different subject areas had a greater impact on critical thinking, and the intergroup differences were statistically significant (chi 2  = 13.36, P  < 0.05). Mathematics had the greatest overall impact, achieving a significant level of effect (ES = 1.68, P  < 0.01), followed by science (ES = 1.25, P  < 0.01) and medical science (ES = 0.87, P  < 0.01), both of which also achieved a significant level of effect. Programming technology was the least effective (ES = 0.39, P  < 0.01), only having a medium-low degree of effect compared to education (ES = 0.72, P  < 0.01) and other fields (such as language, art, and social sciences) (ES = 0.58, P  < 0.01). These results suggest that scientific fields (e.g., mathematics, science) may be the most effective subject areas for cultivating critical thinking utilizing the approach of collaborative problem-solving.

The effectiveness of collaborative problem solving with regard to teaching critical thinking

According to this meta-analysis, using collaborative problem-solving as an intervention strategy in critical thinking teaching has a considerable amount of impact on cultivating learners’ critical thinking as a whole and has a favorable promotional effect on the two dimensions of critical thinking. According to certain studies, collaborative problem solving, the most frequently used critical thinking teaching strategy in curriculum instruction can considerably enhance students’ critical thinking (e.g., Liang et al., 2017 ; Liu et al., 2020 ; Cindy, 2004 ). This meta-analysis provides convergent data support for the above research views. Thus, the findings of this meta-analysis not only effectively address the first research query regarding the overall effect of cultivating critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills) utilizing the approach of collaborative problem-solving, but also enhance our confidence in cultivating critical thinking by using collaborative problem-solving intervention approach in the context of classroom teaching.

Furthermore, the associated improvements in attitudinal tendency are much stronger, but the corresponding improvements in cognitive skill are only marginally better. According to certain studies, cognitive skill differs from the attitudinal tendency in classroom instruction; the cultivation and development of the former as a key ability is a process of gradual accumulation, while the latter as an attitude is affected by the context of the teaching situation (e.g., a novel and exciting teaching approach, challenging and rewarding tasks) (Halpern, 2001 ; Wei and Hong, 2022 ). Collaborative problem-solving as a teaching approach is exciting and interesting, as well as rewarding and challenging; because it takes the learners as the focus and examines problems with poor structure in real situations, and it can inspire students to fully realize their potential for problem-solving, which will significantly improve their attitudinal tendency toward solving problems (Liu et al., 2020 ). Similar to how collaborative problem-solving influences attitudinal tendency, attitudinal tendency impacts cognitive skill when attempting to solve a problem (Liu et al., 2020 ; Zhang et al., 2022 ), and stronger attitudinal tendencies are associated with improved learning achievement and cognitive ability in students (Sison, 2008 ; Zhang et al., 2022 ). It can be seen that the two specific dimensions of critical thinking as well as critical thinking as a whole are affected by collaborative problem-solving, and this study illuminates the nuanced links between cognitive skills and attitudinal tendencies with regard to these two dimensions of critical thinking. To fully develop students’ capacity for critical thinking, future empirical research should pay closer attention to cognitive skills.

The moderating effects of collaborative problem solving with regard to teaching critical thinking

In order to further explore the key factors that influence critical thinking, exploring possible moderating effects that might produce considerable heterogeneity was done using subgroup analysis. The findings show that the moderating factors, such as the teaching type, learning stage, group size, learning scaffold, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, could all support the cultivation of collaborative problem-solving in critical thinking. Among them, the effect size differences between the learning stage and measuring tool are not significant, which does not explain why these two factors are crucial in supporting the cultivation of critical thinking utilizing the approach of collaborative problem-solving.

In terms of the learning stage, various learning stages influenced critical thinking positively without significant intergroup differences, indicating that we are unable to explain why it is crucial in fostering the growth of critical thinking.

Although high education accounts for 70.89% of all empirical studies performed by researchers, high school may be the appropriate learning stage to foster students’ critical thinking by utilizing the approach of collaborative problem-solving since it has the largest overall effect size. This phenomenon may be related to student’s cognitive development, which needs to be further studied in follow-up research.

With regard to teaching type, mixed course teaching may be the best teaching method to cultivate students’ critical thinking. Relevant studies have shown that in the actual teaching process if students are trained in thinking methods alone, the methods they learn are isolated and divorced from subject knowledge, which is not conducive to their transfer of thinking methods; therefore, if students’ thinking is trained only in subject teaching without systematic method training, it is challenging to apply to real-world circumstances (Ruggiero, 2012 ; Hu and Liu, 2015 ). Teaching critical thinking as mixed course teaching in parallel to other subject teachings can achieve the best effect on learners’ critical thinking, and explicit critical thinking instruction is more effective than less explicit critical thinking instruction (Bensley and Spero, 2014 ).

In terms of the intervention duration, with longer intervention times, the overall effect size shows an upward tendency. Thus, the intervention duration and critical thinking’s impact are positively correlated. Critical thinking, as a key competency for students in the 21st century, is difficult to get a meaningful improvement in a brief intervention duration. Instead, it could be developed over a lengthy period of time through consistent teaching and the progressive accumulation of knowledge (Halpern, 2001 ; Hu and Liu, 2015 ). Therefore, future empirical studies ought to take these restrictions into account throughout a longer period of critical thinking instruction.

With regard to group size, a group size of 2–3 persons has the highest effect size, and the comprehensive effect size decreases with increasing group size in general. This outcome is in line with some research findings; as an example, a group composed of two to four members is most appropriate for collaborative learning (Schellens and Valcke, 2006 ). However, the meta-analysis results also indicate that once the group size exceeds 7 people, small groups cannot produce better interaction and performance than large groups. This may be because the learning scaffolds of technique support, resource support, and teacher support improve the frequency and effectiveness of interaction among group members, and a collaborative group with more members may increase the diversity of views, which is helpful to cultivate critical thinking utilizing the approach of collaborative problem-solving.

With regard to the learning scaffold, the three different kinds of learning scaffolds can all enhance critical thinking. Among them, the teacher-supported learning scaffold has the largest overall effect size, demonstrating the interdependence of effective learning scaffolds and collaborative problem-solving. This outcome is in line with some research findings; as an example, a successful strategy is to encourage learners to collaborate, come up with solutions, and develop critical thinking skills by using learning scaffolds (Reiser, 2004 ; Xu et al., 2022 ); learning scaffolds can lower task complexity and unpleasant feelings while also enticing students to engage in learning activities (Wood et al., 2006 ); learning scaffolds are designed to assist students in using learning approaches more successfully to adapt the collaborative problem-solving process, and the teacher-supported learning scaffolds have the greatest influence on critical thinking in this process because they are more targeted, informative, and timely (Xu et al., 2022 ).

With respect to the measuring tool, despite the fact that standardized measurement tools (such as the WGCTA, CCTT, and CCTST) have been acknowledged as trustworthy and effective by worldwide experts, only 54.43% of the research included in this meta-analysis adopted them for assessment, and the results indicated no intergroup differences. These results suggest that not all teaching circumstances are appropriate for measuring critical thinking using standardized measurement tools. “The measuring tools for measuring thinking ability have limits in assessing learners in educational situations and should be adapted appropriately to accurately assess the changes in learners’ critical thinking.”, according to Simpson and Courtney ( 2002 , p. 91). As a result, in order to more fully and precisely gauge how learners’ critical thinking has evolved, we must properly modify standardized measuring tools based on collaborative problem-solving learning contexts.

With regard to the subject area, the comprehensive effect size of science departments (e.g., mathematics, science, medical science) is larger than that of language arts and social sciences. Some recent international education reforms have noted that critical thinking is a basic part of scientific literacy. Students with scientific literacy can prove the rationality of their judgment according to accurate evidence and reasonable standards when they face challenges or poorly structured problems (Kyndt et al., 2013 ), which makes critical thinking crucial for developing scientific understanding and applying this understanding to practical problem solving for problems related to science, technology, and society (Yore et al., 2007 ).

Suggestions for critical thinking teaching

Other than those stated in the discussion above, the following suggestions are offered for critical thinking instruction utilizing the approach of collaborative problem-solving.

First, teachers should put a special emphasis on the two core elements, which are collaboration and problem-solving, to design real problems based on collaborative situations. This meta-analysis provides evidence to support the view that collaborative problem-solving has a strong synergistic effect on promoting students’ critical thinking. Asking questions about real situations and allowing learners to take part in critical discussions on real problems during class instruction are key ways to teach critical thinking rather than simply reading speculative articles without practice (Mulnix, 2012 ). Furthermore, the improvement of students’ critical thinking is realized through cognitive conflict with other learners in the problem situation (Yang et al., 2008 ). Consequently, it is essential for teachers to put a special emphasis on the two core elements, which are collaboration and problem-solving, and design real problems and encourage students to discuss, negotiate, and argue based on collaborative problem-solving situations.

Second, teachers should design and implement mixed courses to cultivate learners’ critical thinking, utilizing the approach of collaborative problem-solving. Critical thinking can be taught through curriculum instruction (Kuncel, 2011 ; Leng and Lu, 2020 ), with the goal of cultivating learners’ critical thinking for flexible transfer and application in real problem-solving situations. This meta-analysis shows that mixed course teaching has a highly substantial impact on the cultivation and promotion of learners’ critical thinking. Therefore, teachers should design and implement mixed course teaching with real collaborative problem-solving situations in combination with the knowledge content of specific disciplines in conventional teaching, teach methods and strategies of critical thinking based on poorly structured problems to help students master critical thinking, and provide practical activities in which students can interact with each other to develop knowledge construction and critical thinking utilizing the approach of collaborative problem-solving.

Third, teachers should be more trained in critical thinking, particularly preservice teachers, and they also should be conscious of the ways in which teachers’ support for learning scaffolds can promote critical thinking. The learning scaffold supported by teachers had the greatest impact on learners’ critical thinking, in addition to being more directive, targeted, and timely (Wood et al., 2006 ). Critical thinking can only be effectively taught when teachers recognize the significance of critical thinking for students’ growth and use the proper approaches while designing instructional activities (Forawi, 2016 ). Therefore, with the intention of enabling teachers to create learning scaffolds to cultivate learners’ critical thinking utilizing the approach of collaborative problem solving, it is essential to concentrate on the teacher-supported learning scaffolds and enhance the instruction for teaching critical thinking to teachers, especially preservice teachers.

Implications and limitations

There are certain limitations in this meta-analysis, but future research can correct them. First, the search languages were restricted to English and Chinese, so it is possible that pertinent studies that were written in other languages were overlooked, resulting in an inadequate number of articles for review. Second, these data provided by the included studies are partially missing, such as whether teachers were trained in the theory and practice of critical thinking, the average age and gender of learners, and the differences in critical thinking among learners of various ages and genders. Third, as is typical for review articles, more studies were released while this meta-analysis was being done; therefore, it had a time limit. With the development of relevant research, future studies focusing on these issues are highly relevant and needed.

Conclusions

The subject of the magnitude of collaborative problem-solving’s impact on fostering students’ critical thinking, which received scant attention from other studies, was successfully addressed by this study. The question of the effectiveness of collaborative problem-solving in promoting students’ critical thinking was addressed in this study, which addressed a topic that had gotten little attention in earlier research. The following conclusions can be made:

Regarding the results obtained, collaborative problem solving is an effective teaching approach to foster learners’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]). With respect to the dimensions of critical thinking, collaborative problem-solving can significantly and effectively improve students’ attitudinal tendency, and the comprehensive effect is significant (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

As demonstrated by both the results and the discussion, there are varying degrees of beneficial effects on students’ critical thinking from all seven moderating factors, which were found across 36 studies. In this context, the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have a positive impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. Since the learning stage (chi 2  = 3.15, P  = 0.21 > 0.05) and measuring tools (chi 2  = 0.08, P  = 0.78 > 0.05) did not demonstrate any significant intergroup differences, we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving.

Data availability

All data generated or analyzed during this study are included within the article and its supplementary information files, and the supplementary information files are available in the Dataverse repository: https://doi.org/10.7910/DVN/IPFJO6 .

Bensley DA, Spero RA (2014) Improving critical thinking skills and meta-cognitive monitoring through direct infusion. Think Skills Creat 12:55–68. https://doi.org/10.1016/j.tsc.2014.02.001

Article   Google Scholar  

Castle A (2009) Defining and assessing critical thinking skills for student radiographers. Radiography 15(1):70–76. https://doi.org/10.1016/j.radi.2007.10.007

Chen XD (2013) An empirical study on the influence of PBL teaching model on critical thinking ability of non-English majors. J PLA Foreign Lang College 36 (04):68–72

Google Scholar  

Cohen A (1992) Antecedents of organizational commitment across occupational groups: a meta-analysis. J Organ Behav. https://doi.org/10.1002/job.4030130602

Cooper H (2010) Research synthesis and meta-analysis: a step-by-step approach, 4th edn. Sage, London, England

Cindy HS (2004) Problem-based learning: what and how do students learn? Educ Psychol Rev 51(1):31–39

Duch BJ, Gron SD, Allen DE (2001) The power of problem-based learning: a practical “how to” for teaching undergraduate courses in any discipline. Stylus Educ Sci 2:190–198

Ennis RH (1989) Critical thinking and subject specificity: clarification and needed research. Educ Res 18(3):4–10. https://doi.org/10.3102/0013189x018003004

Facione PA (1990) Critical thinking: a statement of expert consensus for purposes of educational assessment and instruction. Research findings and recommendations. Eric document reproduction service. https://eric.ed.gov/?id=ed315423

Facione PA, Facione NC (1992) The California Critical Thinking Dispositions Inventory (CCTDI) and the CCTDI test manual. California Academic Press, Millbrae, CA

Forawi SA (2016) Standard-based science education and critical thinking. Think Skills Creat 20:52–62. https://doi.org/10.1016/j.tsc.2016.02.005

Halpern DF (2001) Assessing the effectiveness of critical thinking instruction. J Gen Educ 50(4):270–286. https://doi.org/10.2307/27797889

Hu WP, Liu J (2015) Cultivation of pupils’ thinking ability: a five-year follow-up study. Psychol Behav Res 13(05):648–654. https://doi.org/10.3969/j.issn.1672-0628.2015.05.010

Huber K (2016) Does college teach critical thinking? A meta-analysis. Rev Educ Res 86(2):431–468. https://doi.org/10.3102/0034654315605917

Kek MYCA, Huijser H (2011) The power of problem-based learning in developing critical thinking skills: preparing students for tomorrow’s digital futures in today’s classrooms. High Educ Res Dev 30(3):329–341. https://doi.org/10.1080/07294360.2010.501074

Kuncel NR (2011) Measurement and meaning of critical thinking (Research report for the NRC 21st Century Skills Workshop). National Research Council, Washington, DC

Kyndt E, Raes E, Lismont B, Timmers F, Cascallar E, Dochy F (2013) A meta-analysis of the effects of face-to-face cooperative learning. Do recent studies falsify or verify earlier findings? Educ Res Rev 10(2):133–149. https://doi.org/10.1016/j.edurev.2013.02.002

Leng J, Lu XX (2020) Is critical thinking really teachable?—A meta-analysis based on 79 experimental or quasi experimental studies. Open Educ Res 26(06):110–118. https://doi.org/10.13966/j.cnki.kfjyyj.2020.06.011

Liang YZ, Zhu K, Zhao CL (2017) An empirical study on the depth of interaction promoted by collaborative problem solving learning activities. J E-educ Res 38(10):87–92. https://doi.org/10.13811/j.cnki.eer.2017.10.014

Lipsey M, Wilson D (2001) Practical meta-analysis. International Educational and Professional, London, pp. 92–160

Liu Z, Wu W, Jiang Q (2020) A study on the influence of problem based learning on college students’ critical thinking-based on a meta-analysis of 31 studies. Explor High Educ 03:43–49

Morris SB (2008) Estimating effect sizes from pretest-posttest-control group designs. Organ Res Methods 11(2):364–386. https://doi.org/10.1177/1094428106291059

Article   ADS   Google Scholar  

Mulnix JW (2012) Thinking critically about critical thinking. Educ Philos Theory 44(5):464–479. https://doi.org/10.1111/j.1469-5812.2010.00673.x

Naber J, Wyatt TH (2014) The effect of reflective writing interventions on the critical thinking skills and dispositions of baccalaureate nursing students. Nurse Educ Today 34(1):67–72. https://doi.org/10.1016/j.nedt.2013.04.002

National Research Council (2012) Education for life and work: developing transferable knowledge and skills in the 21st century. The National Academies Press, Washington, DC

Niu L, Behar HLS, Garvan CW (2013) Do instructional interventions influence college students’ critical thinking skills? A meta-analysis. Educ Res Rev 9(12):114–128. https://doi.org/10.1016/j.edurev.2012.12.002

Peng ZM, Deng L (2017) Towards the core of education reform: cultivating critical thinking skills as the core of skills in the 21st century. Res Educ Dev 24:57–63. https://doi.org/10.14121/j.cnki.1008-3855.2017.24.011

Reiser BJ (2004) Scaffolding complex learning: the mechanisms of structuring and problematizing student work. J Learn Sci 13(3):273–304. https://doi.org/10.1207/s15327809jls1303_2

Ruggiero VR (2012) The art of thinking: a guide to critical and creative thought, 4th edn. Harper Collins College Publishers, New York

Schellens T, Valcke M (2006) Fostering knowledge construction in university students through asynchronous discussion groups. Comput Educ 46(4):349–370. https://doi.org/10.1016/j.compedu.2004.07.010

Sendag S, Odabasi HF (2009) Effects of an online problem based learning course on content knowledge acquisition and critical thinking skills. Comput Educ 53(1):132–141. https://doi.org/10.1016/j.compedu.2009.01.008

Sison R (2008) Investigating Pair Programming in a Software Engineering Course in an Asian Setting. 2008 15th Asia-Pacific Software Engineering Conference, pp. 325–331. https://doi.org/10.1109/APSEC.2008.61

Simpson E, Courtney M (2002) Critical thinking in nursing education: literature review. Mary Courtney 8(2):89–98

Stewart L, Tierney J, Burdett S (2006) Do systematic reviews based on individual patient data offer a means of circumventing biases associated with trial publications? Publication bias in meta-analysis. John Wiley and Sons Inc, New York, pp. 261–286

Tiwari A, Lai P, So M, Yuen K (2010) A comparison of the effects of problem-based learning and lecturing on the development of students’ critical thinking. Med Educ 40(6):547–554. https://doi.org/10.1111/j.1365-2929.2006.02481.x

Wood D, Bruner JS, Ross G (2006) The role of tutoring in problem solving. J Child Psychol Psychiatry 17(2):89–100. https://doi.org/10.1111/j.1469-7610.1976.tb00381.x

Wei T, Hong S (2022) The meaning and realization of teachable critical thinking. Educ Theory Practice 10:51–57

Xu EW, Wang W, Wang QX (2022) A meta-analysis of the effectiveness of programming teaching in promoting K-12 students’ computational thinking. Educ Inf Technol. https://doi.org/10.1007/s10639-022-11445-2

Yang YC, Newby T, Bill R (2008) Facilitating interactions through structured web-based bulletin boards: a quasi-experimental study on promoting learners’ critical thinking skills. Comput Educ 50(4):1572–1585. https://doi.org/10.1016/j.compedu.2007.04.006

Yore LD, Pimm D, Tuan HL (2007) The literacy component of mathematical and scientific literacy. Int J Sci Math Educ 5(4):559–589. https://doi.org/10.1007/s10763-007-9089-4

Zhang T, Zhang S, Gao QQ, Wang JH (2022) Research on the development of learners’ critical thinking in online peer review. Audio Visual Educ Res 6:53–60. https://doi.org/10.13811/j.cnki.eer.2022.06.08

Download references

Acknowledgements

This research was supported by the graduate scientific research and innovation project of Xinjiang Uygur Autonomous Region named “Research on in-depth learning of high school information technology courses for the cultivation of computing thinking” (No. XJ2022G190) and the independent innovation fund project for doctoral students of the College of Educational Science of Xinjiang Normal University named “Research on project-based teaching of high school information technology courses from the perspective of discipline core literacy” (No. XJNUJKYA2003).

Author information

Authors and affiliations.

College of Educational Science, Xinjiang Normal University, 830017, Urumqi, Xinjiang, China

Enwei Xu, Wei Wang & Qingxia Wang

You can also search for this author in PubMed   Google Scholar

Corresponding authors

Correspondence to Enwei Xu or Wei Wang .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Informed consent

Additional information.

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

Supplementary information

Supplementary tables, rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and permissions

About this article

Cite this article.

Xu, E., Wang, W. & Wang, Q. The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature. Humanit Soc Sci Commun 10 , 16 (2023). https://doi.org/10.1057/s41599-023-01508-1

Download citation

Received : 07 August 2022

Accepted : 04 January 2023

Published : 11 January 2023

DOI : https://doi.org/10.1057/s41599-023-01508-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

Impacts of online collaborative learning on students’ intercultural communication apprehension and intercultural communicative competence.

• Hoa Thi Hoang Chau
• Hung Phu Bui
• Quynh Thi Huong Dinh

Education and Information Technologies (2024)

Exploring the effects of digital technology on deep learning: a meta-analysis

Sustainable electricity generation and farm-grid utilization from photovoltaic aquaculture: a bibliometric analysis.

• A. A. Amusa
• M. Alhassan

International Journal of Environmental Science and Technology (2024)

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Information

• Author Services

Initiatives

You are accessing a machine-readable page. In order to be human-readable, please install an RSS reader.

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to https://www.mdpi.com/openaccess .

Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications.

Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Original Submission Date Received: .

• Active Journals
• Find a Journal
• Proceedings Series
• For Authors
• For Reviewers
• For Editors
• For Librarians
• For Publishers
• For Societies
• For Conference Organizers
• Open Access Policy
• Institutional Open Access Program
• Special Issues Guidelines
• Editorial Process
• Research and Publication Ethics
• Article Processing Charges
• Testimonials
• Preprints.org
• SciProfiles
• Encyclopedia

Article Menu

• Subscribe SciFeed
• Recommended Articles
• Google Scholar
• on Google Scholar
• Table of Contents

Find support for a specific problem in the support section of our website.

Please let us know what you think of our products and services.

Visit our dedicated information section to learn more about MDPI.

JSmol Viewer

Problem posing and problem solving in primary school: opportunities for the development of different literacies.

1. Introduction

2. theoretical framework, 2.1. mathematical literacy.

“An individual’s capacity to formulate, employ and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts, and tools to describe, explain and predict phenomena. It assists individuals to recognize the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged, and reflective citizens” [ 9 ]. (pp. 4–5)

2.2. Problem Posing and Problem Solving

2.2.1. problem posing, 2.2.2. problem solving, 2.3. mathematical connections, 2.3.1. financial education, 2.3.2. consumer education, 3. purpose and research question, 4. method and materials, 4.1. participants, 4.2. intervention phases, 4.3. data collection, 5.1. analysis of problem 1.

• Gabriel’s parents have €68.37, if they buy one of each type cake, how many euros will they end up with? (Explain how you thought.)
• With the money left, will Gabriel’s parents be able to buy three packages of popcorn? (Explain how you thought.)
• With €30.47, Gabriel’s parents still wanted to buy two more products, and had €21.27 left. How many products did they buy? (Explain how you thought.)
• Analysis of the resolution of Question 1
• Analysis of the resolution of Question 2
• Analysis of the resolution of Question 3

5.2. Analysis of Problem 2

• If we bought 1 cake costing €20 plus 2 packets of chips costing €0.60, how much money would we spend? 1.1. Gabriel and his parents invited 28 Gabriel’s friends, from his class 13 classmates liked gummies and 5 liked gelatins, how many people liked both? 1.2. If Gabriel’s parents had €30, with how much money would they stay?

5.3. Analysis of Problem 3

5.4. analysis of problem 4.

Click here to enlarge figure

5.5. Analysis of Problem 5

6. conclusions, 6.1. summary of key findings, 6.2. limitations of research, author contributions, institutional review board statement, informed consent statement, data availability statement, acknowledgments, conflicts of interest.

• Azevedo, F. Literacias: Contextos e práticas. In Modelos e Práticas em Literacia ; Azevedo, F., Sardinha, M., Eds.; Lidel: Lisboa, Portugal, 2009; pp. 1–16. [ Google Scholar ]
• Dias, A.; Oliveira, A.; Pereira, C.; Abreu, M.; Alves, P.; Bastos, R.; Silva, R.; Narciso, S. Referencial de Educação Financeira para a Educação Pré-Escolar, o Ensino Básico, o Ensino Secundário e a Educação e Formação de Adultos ; Ministério de Educação e Ciência: Lisboa, Portugal, 2013.
• Dias, A.; Santos, F.; Figueiredo, I.; Carreto, N.; Silva, R.; Passos, S. Referencial de Educação do Consumidor ; Ministério de Educação: Lisboa, Portugal, 2019.
• Piedade, B.; Reis, S. O que é um problema matemático?–Conceções de alunos do 4º ano de escolaridade. Interações 2019 , 50 , 180–196. [ Google Scholar ]
• Lester, F.K. Research on mathematical problem solving. In Research in Mathematics Education ; National Council of Teachers of Mathematics: Reston, VA, USA, 1980; pp. 286–323. [ Google Scholar ]
• Passarella, S. Real Contexts in Problem-Posing: An Exploratory Study of Students’ Creativity. Int. J. Innov. Sci. Math. Educ. 2022 , 30 , 15–29. [ Google Scholar ] [ CrossRef ]
• Akyüz, G. Non-routine problem-solving performances of mathematics teacher candidates. Educ. Res. Rev. 2020 , 15 , 214–224. [ Google Scholar ]
• Skovsmose, O. Cenários para a Investigação. Bolema 2000 , 14 , 66–91. [ Google Scholar ]
• OECD. PISA 2021 Mathematics: A Broadened Perspective ; OECD Publishing: Paris, France, 2017.
• Canavarro, A.P.; Mestre, C.; Gomes, D.; Santos, E.; Santos, L.; Brunheira, L.; Vicente, M.; Gouveia, M.J.; Correia, P.; Marques, P.; et al. Aprendizagens Essenciais de Matemática no Ensino Básico ; Ministério de Educação e Ciência: Lisboa, Portugal, 2021.
• Liljedahl, P.; Santos-Trigo, M.; Malaspina, U.; Bruder, R. Problem Solving in Mathematics Education ; ICME-13 Topical Surveys; Springer: Cham, Switzerland, 2016. [ Google Scholar ]
• Ellerton, N. Engaging pre-service middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educ. Stud. Math 2013 , 83 , 87–101. [ Google Scholar ] [ CrossRef ]
• Singer, F.; Ellerton, N.; Cai, J. Problem posing research in mathematics education: New questions and directions. Educ. Stud. Math. 2013 , 83 , 9–26. [ Google Scholar ] [ CrossRef ]
• Kilpatrick, J. Problem formulating: Where do good problem come from? In Cognitive Science and Mathematics Education ; Schoenfeld, A.H., Ed.; Erlbaum: New York, USA, 1987; pp. 123–147. [ Google Scholar ]
• Cai, J.; Hwang, S. Making Mathematics Challenging through Problem Posing in the Classroom. In Mathematical Challenges for All ; Leikin, R., Ed.; Research in Mathematics Education; Springer: Berlin/Heidelberg, Germany, 2023; pp. 115–145. [ Google Scholar ]
• Wang, M.; Walkington, C.; Rouse, A. A Meta-Analysis on the Effects of Problem-Posing in Mathematics Education on Performance and Dispositions. Investig. Math. Learn. 2022 , 14 , 265–287. [ Google Scholar ] [ CrossRef ]
• Christou, C.; Mousoulides, N.; Pittalis, M.; Pitta-Pantazi, D.; Sriraman, B. An Empirical Taxonomy of Problem Posing Processes. ZDM Int. J. Math. Educ. 2005 , 37 , 149–158. [ Google Scholar ] [ CrossRef ]
• Stoyanova, E.; Ellerton, N.F. A framework for research into students’ problem posing in school mathematics. In Technology in Mathematics Education ; Clarkson, P.C., Ed.; Mathematics Education Research Group of Australasia: Melbourne, Australia, 1996; pp. 518–525. [ Google Scholar ]
• Van den Heuvel-Panhuizen, M. The role of contexts in assessment problems in mathematics. Learn. Math. 2005 , 25 , 2–23. [ Google Scholar ]
• Papadopoulos, I.; Patsiala, N.; Baumanns, L.; Rott, B. Multiple approaches to problem posing: Theoretical considerations regarding its definition, conceptualisation, and implementation. CEPS J. 2022 , 12 , 13–34. [ Google Scholar ] [ CrossRef ]
• Polya, G. How to Solve It: A New Aspect of Mathematical Method ; Princeton University Press: Princeton, NJ, USA, 1945. [ Google Scholar ]
• Barabé, G.; Proulx, J. Problem posing: A review of sorts. In Proceedings of the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, MI, USA, 5–8 November 2015; pp. 1277–1284. [ Google Scholar ]
• Silver, E. On mathematical problem posing. Learn. Math. 1994 , 14 , 19–28. [ Google Scholar ]
• Emre-Akdoğan, E.; Argün, Z. Instructional design-based research on problem solving strategies. Acta Didact. Napoc. 2016 , 9 , 15–24. [ Google Scholar ]
• Schoenfeld, A. Pólya, Problem Solving, and Education. Math. Mag. 1987 , 60 , 283–291. [ Google Scholar ] [ CrossRef ]
• Prayekti, N.; Nusantara, T.; Sudirman, S.; Susanto, H.; Rofiki, I. Students’ mental models in mathematics problem-solving. J. Crit. Rev. 2020 , 7 , 468–470. [ Google Scholar ]
• Rott, B.; Specht, B.; Knipping, C. A descriptive phase model of problem solving processes. ZDM–Math. Educ. 2021 , 53 , 737–752. [ Google Scholar ] [ CrossRef ]
• Ponte, P. Gestão Curricular em Matemática. In O Professor e o Desenvolvimento Curricular ; GTI, Ed.; APM: Lisboa, Portugal, 2005; pp. 11–34. [ Google Scholar ]
• Charles, R.; Lester, F. Mathematical Problem Solving ; Springhouse, Learning Institute, 1986. [ Google Scholar ]
• Palhares, P.; Cardoso, M.; Fernandes, J.; Fonseca, L.; Gomes, M.; Hirst, K.; Portela, J.; Ralha, M.; Vale, M. Elementos de Matemática para Professores do Ensino Básico ; LIDEL: Lisboa, Portugal, 2004. [ Google Scholar ]
• National Council of Teachers of Mathematics (NCTM). Princípios e Normas para a Matemática Escolar , 1st ed.; APM: Lisboa, Portugal, 2007. [ Google Scholar ]
• Canavarro, A.P. O que a investigação nos diz acerca da aprendizagem da matemática com conexões-ideias da teoria ilustradas com exemplos. Educ. Matemática 2017 , 144–145 , 38–42. [ Google Scholar ]
• Jacinto, H.; Pires, M.V. Tarefas e recursos para a promoção de conexões matemáticas. In Encontro de Investigação em Educação Matemática do EIEM 2019: Livro de atas ; Amado, N., Canavarro, A.P., Carreira, S., Ferreira, R.T., Vale, I., Eds.; Sociedade Portuguesa de Investigação em Educação Matemática: Coimbra, Portugal, 2019; pp. 189–195. [ Google Scholar ]
• Bivar, A.; Grosso, C.; Oliveira, F.; Timóteo, M.C. Programa e Metas Curriculares de Matemática do Ensino Básico ; Ministério da Educação e da Ciência: Lisboa, Portugal, 2013.
• OECD. Financial Education in Schools ; OCDE INFE: Paris, France, 2012.
• Martins, G.; Gomes, C.; Brocardo, J.; Pedroso, J.; Carrilho, J.; Silva, L.; Encarnação, M.; Horta, M.; Calçada, M.; Nery; et al. Perfil dos Alunos à Saída da Escolaridade Obrigatória ; Ministério da Educação e Direção-Geral da Educação: Lisboa, Portugal, 2017.
• Nascimento, F. Educação Financeira no Ensino da Matemática: Um estudo de caso do Ensino Básico. Master’s Dissertation, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Caparica, Portugal, 2015. Repositórios Científicos de Acesso Aberto de Portugal. [ Google Scholar ]
• Ferreira, C. Cidadania no 1° CEB: Contexto para a Promoção da Matemática e da Educação Financeira. Master’s Dissertation, Escola Superior de Educação de Coimbra, Caparica, Portugal, 2023. Repositórios Científicos de Acesso Aberto de Portugal. [ Google Scholar ]
• Kuzma, I.; Chaikovska, H.; Levchyk, I.; Yankovych, O. Formation of Financial Literacy in Primary School Students. J. Effic. Responsib. Educ. Sci. 2022 , 15 , 142–155. [ Google Scholar ] [ CrossRef ]
• Fonseca, L.; Santiago, A. Matemática e Educação financeira: Possíveis conexões. Educ. Matemática 2019 , 154 , 77–80. [ Google Scholar ]
• Gall, M.; Gall, J.P.; Borg, R. Educational research: An introduction ; Allyn & Bacon: Boston, MA, USA, 2007. [ Google Scholar ]
• Merriam, S.B. Qualitative Research and Case Study Applications in Education ; Jossey-Bass Publishers: San Francisco, CA, USA, 2002. [ Google Scholar ]
• Cheng, E.; Ling, L. The Approach of Learning Study: Its Origin and Implications. OECD Educ. Work. Pap. 2013 , 94 , 1–28. [ Google Scholar ]
• Lopes, J.; Pinto, A.; Viegas, C. Melhorar Práticas de Ensino de Ciências e Tecnologia: Registar e Investigar com Narrações Multimodais ; Edições Sílabo: Lisboa, Portugal, 2018. [ Google Scholar ]
• Bogdan, R.; Biklen, S. Investigação Qualitativa em Educação: Uma Introdução à Teoria e aos Métodos ; Porto Editora: Porto, Portugal, 1994. [ Google Scholar ]
• Almeida, P. Quando os problemas não caem do céu. Educ. Matemática 2014 , 130 , 64–68. [ Google Scholar ]

Share and Cite

Santos, R.; Santiago, A.; Cruz, C. Problem Posing and Problem Solving in Primary School: Opportunities for the Development of Different Literacies. Educ. Sci. 2024 , 14 , 97. https://doi.org/10.3390/educsci14010097

Santos R, Santiago A, Cruz C. Problem Posing and Problem Solving in Primary School: Opportunities for the Development of Different Literacies. Education Sciences . 2024; 14(1):97. https://doi.org/10.3390/educsci14010097

Santos, Rita, Ana Santiago, and Catarina Cruz. 2024. "Problem Posing and Problem Solving in Primary School: Opportunities for the Development of Different Literacies" Education Sciences 14, no. 1: 97. https://doi.org/10.3390/educsci14010097

Article Metrics

Article access statistics, further information, mdpi initiatives, follow mdpi.

Subscribe to receive issue release notifications and newsletters from MDPI journals

Problem-Solving

Jabberwocky

Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically.

Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.

Problem-solving involves three basic functions:

Seeking information

Generating new knowledge

Making decisions

Problem-solving is, and should be, a very real part of the curriculum. It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum. It provides students with opportunities to use their newly acquired knowledge in meaningful, real-life activities and assists them in working at higher levels of thinking (see Levels of Questions ).

Here is a five-stage model that most students can easily memorize and put into action and which has direct applications to many areas of the curriculum as well as everyday life:

Expert Opinion

Here are some techniques that will help students understand the nature of a problem and the conditions that surround it:

• List all related relevant facts.
• Make a list of all the given information.
• Restate the problem in their own words.
• List the conditions that surround a problem.
• Describe related known problems.

It's Elementary

For younger students, illustrations are helpful in organizing data, manipulating information, and outlining the limits of a problem and its possible solution(s). Students can use drawings to help them look at a problem from many different perspectives.

Understand the problem. It's important that students understand the nature of a problem and its related goals. Encourage students to frame a problem in their own words.

Describe any barriers. Students need to be aware of any barriers or constraints that may be preventing them from achieving their goal. In short, what is creating the problem? Encouraging students to verbalize these impediments is always an important step.

Identify various solutions. After the nature and parameters of a problem are understood, students will need to select one or more appropriate strategies to help resolve the problem. Students need to understand that they have many strategies available to them and that no single strategy will work for all problems. Here are some problem-solving possibilities:

Create visual images. Many problem-solvers find it useful to create “mind pictures” of a problem and its potential solutions prior to working on the problem. Mental imaging allows the problem-solvers to map out many dimensions of a problem and “see” it clearly.

Guesstimate. Give students opportunities to engage in some trial-and-error approaches to problem-solving. It should be understood, however, that this is not a singular approach to problem-solving but rather an attempt to gather some preliminary data.

Create a table. A table is an orderly arrangement of data. When students have opportunities to design and create tables of information, they begin to understand that they can group and organize most data relative to a problem.

Use manipulatives. By moving objects around on a table or desk, students can develop patterns and organize elements of a problem into recognizable and visually satisfying components.

Work backward. It's frequently helpful for students to take the data presented at the end of a problem and use a series of computations to arrive at the data presented at the beginning of the problem.

Look for a pattern. Looking for patterns is an important problem-solving strategy because many problems are similar and fall into predictable patterns. A pattern, by definition, is a regular, systematic repetition and may be numerical, visual, or behavioral.

Create a systematic list. Recording information in list form is a process used quite frequently to map out a plan of attack for defining and solving problems. Encourage students to record their ideas in lists to determine regularities, patterns, or similarities between problem elements.

Try out a solution. When working through a strategy or combination of strategies, it will be important for students to …

Keep accurate and up-to-date records of their thoughts, proceedings, and procedures. Recording the data collected, the predictions made, and the strategies used is an important part of the problem solving process.

Try to work through a selected strategy or combination of strategies until it becomes evident that it's not working, it needs to be modified, or it is yielding inappropriate data. As students become more proficient problem-solvers, they should feel comfortable rejecting potential strategies at any time during their quest for solutions.

Monitor with great care the steps undertaken as part of a solution. Although it might be a natural tendency for students to “rush” through a strategy to arrive at a quick answer, encourage them to carefully assess and monitor their progress.

Feel comfortable putting a problem aside for a period of time and tackling it at a later time. For example, scientists rarely come up with a solution the first time they approach a problem. Students should also feel comfortable letting a problem rest for a while and returning to it later.

Evaluate the results. It's vitally important that students have multiple opportunities to assess their own problem-solving skills and the solutions they generate from using those skills. Frequently, students are overly dependent upon teachers to evaluate their performance in the classroom. The process of self-assessment is not easy, however. It involves risk-taking, self-assurance, and a certain level of independence. But it can be effectively promoted by asking students questions such as “How do you feel about your progress so far?” “Are you satisfied with the results you obtained?” and “Why do you believe this is an appropriate response to the problem?”

Featured High School Resources

Related Resources

About the author

TeacherVision Editorial Staff

The TeacherVision editorial team is comprised of teachers, experts, and content professionals dedicated to bringing you the most accurate and relevant information in the teaching space.

• Skip to content
• Skip to search
• Staff portal (Inside the department)
• Student portal
• Key links for students

Other users

• Forgot password

Notifications

{{item.title}}, my essentials, ask for help, contact edconnect, directory a to z, how to guides, inclusive practice hub, problem solving guide.

Some students may need support to learn effective problem-solving skills. This resource can assist students to think of and evaluate options to a problem or situation. 

You can encourage and support students to use this tool to:

- come up with two options

- write the pros and cons of each option, and

- implement the option they think is best. 

In high school settings, some students may respond better to a short conversation. For these students, you can use the first page of the guide as a prompt sheet to facilitate talking through a problem. Short notes in a workbook of a student’s choosing as a reminder of decisions made may also be helpful.

School Excellence Framework alignment

Australian professional standards for teachers alignment.

Standard 1: Know students and how they learn

Primary teachers, SLSOs

This resource can be used to support students to think of and evaluate options to a problem or situation. It includes a template for students to consider and compare two potential solutions.

November 2021.  Share your feedback here

Padding removal

Explore other topics.

Not logged in

• Request account

Problem Solving in Primary Education

Page actions.

About. This document encourages teachers to think about problem-solving in the geography, history, science and maths curriculum, and provides some examples of subject-based problem-solving to explore.

Pedagogical content. Problem-solving and reasoning (ta) are important skills to learn, and engage with in teaching. This document provides some guidance and practical examples on how to use problem-solving skills in the primary curriculum. (edit)

• ResourceInfo
• Problem Solving
• Teacher Education
• Cross-curricular
• OER4Schools
• OER Guidance for Schools
• Raspberry Pi
• Qualitative Research Skills
• Login / Create account

OER4Schools Resource

• Introduction to OER4Schools
• 0.1 - Overview
• 0.2 - Detailed outline
• 0.3 - How to use this resource
• 0.4 - An introduction to facilitating the OER4Schools programme
• 0.5 - Further links and pointers
• 0.6 - Table of contents
• Unit 1 - Introduction to interactive teaching and the use of ICT
• 1.1 - What is interactive teaching? An introduction to the interactive Zambian classroom
• 1.2 - Introduction to interactive teaching with ICT
• 1.3 - Activity planning and reflection
• 1.4 - ICTs in interactive teaching
• 1.5 - Effective use of ICT
• 1.6 - Leadership for Learning
• Unit 2 - Whole class dialogue and effective questioning
• 2.1 - Introduction to whole class dialogue and effective questioning
• 2.2 - Questioning
• 2.3 - More on questioning
• 2.4 - Concept mapping
• 2.5 - Engaging the community
• Unit 3 - Group work
• 3.1 - Group work: Same task and different tasks group work
• 3.2 - When to use group work and how to manage it
• 3.3 - Mixed pace group work with and without ICT
• 3.4 - Talking points and effective group work
• 3.5 - Review of group work
• 3.6 - Designing interactive lesson plans
• Unit 4 - Assessment for learning and lesson pacing
• 4.1 - Introduction to Assessment for Learning
• 4.2 - Learning objectives and success criteria
• 4.3 - Formative feedback
• 4.4 - Peer and self-assessment
• 4.5 - Review of AfL and lesson pacing
• Unit 5 - Enquiry-based learning and project work
• 5.1 - Introduction to enquiry-based learning
• 5.2 - Starting the enquiry-based learning process
• 5.3 - Collecting and interpreting information: Part one
• 5.4 - Collecting and interpreting information: Part two
• 5.5 - Presenting findings of enquiries
• Unit 6 - Into the future
• 6.1 - Programme review and action research
• 7 - Appendices
• 7.1 - List of concepts, methods and techniques for reference.
• 7.2 - A session template for making your own sessions
• 7.3 - Video for OER4Schools
• 8 - Induction sessions
• 8.1 - A workshop for school leaders
• 8.2 - A workshop for OER4Schools programme facilitators
• 8.3 - OER4Schools Taster Session - eLA 2013
• 8.4 - Mobile Learning Week 2014
• 8.5 - eLearning Africa 2014
• 8.6 - Faculty of Education Workshop May 2014
• 8.7 - AVU workshop November 2014

ORBIT Lesson Ideas

• All Lesson Ideas and Resources
• Primary Maths
• Primary Science
• Secondary Maths
• Secondary Science
• Teaching Approaches
• Teaching Tools
• Recent changes
• Gallery of new files
• Special pages

User page tools

• Browse properties
• What links here
• Related changes
• Permanent link
• Page information

Print/export

• Create a book
• Download as PDF
• Download as Plain text
• Printable version

• This page was last edited on 5 December 2012, at 13:50.
• Content is available under Creative Commons Attribution-ShareAlike or Attribution-NonCommercial unless otherwise noted.
• Privacy policy
• About OER in Education
• Disclaimers
• Mobile view

Or search by topic

Number and algebra

• The Number System and Place Value
• Calculations and Numerical Methods
• Fractions, Decimals, Percentages, Ratio and Proportion
• Properties of Numbers
• Patterns, Sequences and Structure
• Algebraic expressions, equations and formulae
• Coordinates, Functions and Graphs

Geometry and measure

• Angles, Polygons, and Geometrical Proof
• 3D Geometry, Shape and Space
• Measuring and calculating with units
• Transformations and constructions
• Pythagoras and Trigonometry
• Vectors and Matrices

Probability and statistics

• Handling, Processing and Representing Data
• Probability

Working mathematically

• Thinking mathematically
• Mathematical mindsets
• Cross-curricular contexts
• Physical and digital manipulatives

For younger learners

• Early Years Foundation Stage

Advanced mathematics

• Decision Mathematics and Combinatorics
• Advanced Probability and Statistics

Problem Solving

Problem Solving and the New Curriculum   Age 5 to 11

Developing a Classroom Culture That Supports a Problem-solving Approach to Mathematics   Age 5 to 11

Developing Excellence in Problem Solving with Young Learners   Age 5 to 11

Using NRICH Tasks to Develop Key Problem-solving Skills   Age 5 to 11

Trial and Improvement at KS1   Age 5 to 7

Trial and Improvement at KS2   Age 7 to 11

Working Systematically - Primary Teachers   Age 5 to 11

Number Patterns   Age 5 to 11

Working Backwards at KS1   Age 5 to 7

Working Backwards at KS2   Age 7 to 11

Reasoning   Age 5 to 11

Visualising at KS1 - Primary Teachers   Age 5 to 7

Visualising at KS2 - Primary Teachers   Age 7 to 11

Conjecturing and Generalising at KS1 - Primary Teachers   Age 5 to 7

Conjecturing and Generalising at KS2 - Primary Teachers   Age 7 to 11

• Mathematical Problem Solving in the Early Years
• Low Threshold High Ceiling - an Introduction
• What's All the Talking About?
• Group-worthy Tasks and Their Potential to Support Children to Develop Independent Problem-solving Skills
• Developing the Classroom Culture: Using the Dotty Six Activity as a Springboard for Investigation

Problem solving skills are multi-faceted – a multitude of cogs are required to get the entire working machine of problem solving going. With that in mind, how can educators cultivate an environment that improves problem solving skills in the classroom?

In this article, we’ll discuss how you can teach problem solving skills in the classroom and provide a quick overview of its importance to child development.

The importance of problem solving for child development

Our entire lives are filled with problems. The problems themselves are inevitable, but it’s how we approach overcoming them that defines and shapes our futures. Problem solving skills can help to boost:

• Academic performance
• Career and life readiness
• Social skills

There is ample evidence to support this. In 2016, the Advisory Committee on Mathematics Education (ACME) stated that “In the modern world, young people need to be able to engage with and interpret data and information. They need to become flexible thinkers capable of dealing with novel problems and situations and analysing their own and others’ solutions to these.”

A 2016 meta-analysis v of existing research on the relationship between problem solving and academic achievement concluded that “…as from the senior grade of primary school and from earlier periods, development of problem solving abilities is important.”

The logic of having strong problem solving skills is sound. Equipped with what they need to solve problems, pupils grow in confidence. They’ll be more likely to hit a problem head on, and less likely to be negatively affected if they fail. These skills can applied to many aspects of life, stretching well beyond your job. Problem solving skills are also at play during many human interactions and social situations.

Strategies for teaching problem solving in school

Be a model problem solver, provide real-life contexts, never be afraid to go back to manipulatives, don’t just give them the answer.

If you encounter a problem when going about your day in school, why not get pupils involved in solving it? It’ll enforce the fact that problems are a natural occurrence for us all and give them valuable exposure and practice at solving them.

Get them involved as much as you can. Ask them questions about the problem that seeks their advice. Confidence is a huge part of problem solving. Without it, pupils will be too afraid to speak up to offer solutions they aren’t sure are right. But by seeking it out, you show them that you value their opinion, helping to build that confidence.

Engage pupils in problem solving by providing them with real-life contexts – problems that are found, or have been found, in the real world. You can also take the opportunity to link problem solving questions to the topic you are focusing on, or the class reader you are using.

For World War 2 topics, you might discuss the transportation of evacuees or for nature, you might look at climate change and the problem-solving issues real scientists face today. Not only are real-life contexts engaging, they ask pupils to explore the world around them and prepare them for futures in the workforce.

If you take a mastery approach to the teaching of maths, some pupils may struggle to go beyond the use of manipulatives. However, manipulatives and pictorial representations can be helpful at any learning stage – we draw out diagrams to explain ourselves for a reason. Give all pupils problem solving questions but differentiate by giving manipulatives to those who may struggle.

It’s good to expose all pupils to problem solving questions as a way of raising expectations and providing opportunity to all.

It’s a tenant of teaching across a vast array of areas, and problem solving skills is no different. Life isn’t about the failures that well inevitably hit, it’s about how you problem solve your way through them. Learning this life lesson early is so important for child development, and teachers are at the very heart of it.

Allow your class to sometimes get it wrong and in the long-term they’ll benefit from knowing that is all part of the process. Don’t just get them the answer, provide them with the tools to approach the problem in the right way and come to the correct solution in their own time.

Look for cross-curricular opportunities

Problem solving should appear in all subjects. Computational thinking is one of the main skills gained from coding and programming lessons. If you don’t already teach coding to your pupils, there are resources specifically designed to hone problem solving skills without the need for specialist computing knowledge. E.a.R.L coding robot is one of those resources. Pupils have to use logical thinking to program E.a.R.L to move around the classroom. Problem solving can be incorporated by providing obstacles for the floor robot to move around and a challenge of under so many steps can be given to pupils.

Problem solving can (and should) also appear regularly in P.E. lessons. Group work is especially effective in this setting. Problem solving is made a lot easier with more than one head involved. Give pupils problems that require cooperation, negotiation and creative thinking – all skills needed for great problem solving ability!

Never underestimate the power of language

Commonly, when it comes to problem solving in maths, it is not the maths that is the issue but the words that surround the calculation. It is a great idea to set aside time for constructive discussion about maths and problem solving.

Ask pupils about what they already know and what connections they can make when introducing a new topic. Write their answers on the board and add words and phrases yourself, creating a bank of vocabulary. Rich discussions about vocabulary used in problem solving questions and the use of precise mathematical language will help deepen pupils’ conceptual understanding.

There is no right or wrong answer

Problem solving can be a trial and error endeavour, but it’s all about correcting the process and thought behind a solution. Reinforcing the idea that making mistakes is ok is a crucial part of develop problem solving skills. For more advanced pupils who are used to getting everything right, this can an especially difficult step to make.

This might be where you can come in with an earlier suggestion. Take a problem on yourself and intentionally get it wrong at first. Show how that can help you to refine your method and get it right next time. Normalising this type of hiccup in the process will give your pupils the confidence to try things when they aren’t sure they will work.

Break it down

As pupils grow older and the problems they face become more complex, it might be helpful for you to help them break it down into more manageable chunks.

Get at the root of the problem, making it a less intimating prospect that’s easier to solve. To gently push them in right direction, ask open questions that aid them to think critically about what they need to do or what they have just done.

Here are a few examples:

• What do you think will happen if…?
• What would you do next time if you were to try this again?
• Why did you decide to do what you just did?

Pin It on Pinterest

How to Teach Effective Problem-Solving Skills in Mathematics | Primary

This webinar will provide headteachers, mathematics leads, teachers and teaching assistants with practical guidance and creative methods they can use to nurture and develop pupils’ problem-solving skills in mathematics.

• Description
• Learning Outcomes
• Institution

Webinar Duration: 1 hour 9 minutes (approx.)

Problem-solving has long been at the heart of the mathematics curriculum. Teaching children how to problem solve in mathematics can support children’s ability to critically evaluate, encourage independence and develop their skills in reasoning and creativity. It is also an essential part of developing mastery of the subject.

In this webinar, the Association of Teachers of Mathematics (ATM), who aim to support the teaching and learning of mathematics in the UK, will explore strategies that schools can use to teach problem-solving which are creative, engaging, fun and reflect a better understanding of the needs of the learner.

• Understanding how to plan and implement effective teaching practice in mathematics which supports children’s ability to problem solve and improve critical thinking skills.
• Recognising successful techniques that can be used in the classroom which improve fluency and reasoning in mathematics.
• Appreciating the importance of making problem-solving learning tailored towards the needs of children and ensuring continuous sharing and evaluation of different methods used.
• Understanding how to implement different approaches to teaching about problem-solving and equipping children with different tools they can use for the rest of their life.
• Recognising the advantages of promoting a culture which encourages discussion between peers and supports trust and confidence in the classroom.

Tony is the lead author for Oxford International Primary Mathematics . Other publications include Understanding and Teaching Primary Mathematics and How to develop confident mathematicians in the early years for Routledge; Approaches to learning and teaching Primary: A toolkit for international teachers for CUP; Explore Mathematics for the new standards curriculum in Jamaica ; and BZ Math for primary schools in Belize. His books, Being a Teacher and Transforming Teaching , both draw on Tony’s international experience and share the experiences of educators around the world. Tony is also editor of Mathematics Teaching , the journal of The Association of Teachers of Mathematics. 

Tony has worked with Ministries of Education in Macedonia and Oman to develop and implement new primary and secondary mathematics curricula. He teaches the international PGEI delivered by the University of Nottingham in SE Asia, leading the course in Thailand. 

He became a lecturer in secondary mathematics education at the University of Nottingham, gaining his PhD in 1999. Since then, he taught secondary and primary teacher education in Nottingham and Leeds, becoming Head of the School of Education and Childhood at Leeds Metropolitan University. In 2012, he left the university sector to work full time as a writer and freelance education consultant. 

Tony started his career teaching mathematics in secondary schools in Sheffield, England. He then worked as an advisory teacher for anti-racist and multicultural education, completing a Master’s degree in multicultural education, before spending time with 3 commercial publishers.

The Hechinger Report

Covering Innovation & Inequality in Education

Why schools are teaching math word problems all wrong

Share this:

• Click to share on LinkedIn (Opens in new window)
• Click to share on Pinterest (Opens in new window)
• Click to share on Reddit (Opens in new window)
• Click to share on WhatsApp (Opens in new window)
• Click to email a link to a friend (Opens in new window)

The Hechinger Report is a national nonprofit newsroom that reports on one topic: education. Sign up for our  weekly newsletters  to get stories like this delivered directly to your inbox. Consider supporting our stories and becoming  a member  today.

Get important education news and analysis delivered straight to your inbox

• Weekly Update
• Future of Learning
• Higher Education
• Early Childhood
• Proof Points

CENTRAL FALLS, R.I. — When Natalia Molina began teaching her second grade students word problems earlier this school year, every lesson felt difficult. Most students were stymied by problems such as: “Sally went shopping. She spent $86 on groceries and $39 on clothing. How much more did Sally spend on groceries than on clothing?”

Both Molina, a first-year teacher, and her students had been trained to tackle word problems by zeroing in on key words like “and,” “more” and “total”  — a simplistic approach that Molina said too often led her students astray. After recognizing the word “and,” for instance, they might mistakenly assume that they needed to add two nearby numbers together to arrive at an answer.

Some weaker readers, lost in a sea of text, couldn’t recognize any words at all.

“I saw how overwhelmed they would get,” said Molina, who teaches at Segue Institute for Learning, a predominantly Hispanic charter school in this small city just north of Providence.

So, with the help of a trainer doing work in Rhode Island through a state grant, Molina and some of her colleagues revamped their approach to teaching word problems this winter — an effort that they said is already paying off in terms of increased student confidence and ability. “It has been a game changer for them,” Molina said.

Perhaps no single educational task encompasses as many different skills as the word problem. Between reading, executive functioning, problem solving, computation and vocabulary, there are a lot of ways for students to go wrong. And for that reason, students perform significantly worse overall on word problems compared to questions more narrowly focused on computation or shapes (for example: “Solve 7 + _ = 22” or “What is 64 x 3?”).

If a student excels at word problems, it’s a good sign that they’re generally excelling at school. “Word-problem solving in lower grades is one of the better indicators of overall school success in K-12,” said Lynn Fuchs, a research professor at Vanderbilt University. In a large national survey , for instance, algebra teachers rated word-problem solving as the most important among 15 skills required to excel in the subject.

Teacher takeaways

• Don’t instruct students to focus mainly on “key words” in word problems such as “and” or “more” 
• Mix question types in any lesson so that students don’t assume they just apply the same operation (addition, subtraction) again and again
• Teach students the underlying structure — or schema — of the word problem

Yet most experts and many educators agree that too many schools are doing it wrong, particularly in the elementary grades. And in a small but growing number of classrooms, teachers like Molina are working to change that. “With word problems, there are more struggling learners than non-struggling learners” because they are taught so poorly, said Nicole Bucka, who works with teachers throughout Rhode Island to provide strategies for struggling learners.

Too many teachers, particularly in the early grades, rely on key words to introduce math problems. Posters displaying the terms — sum, minus, fewer, etc. — tied to operations including addition and subtraction are a staple in elementary school classrooms across the country.

Key words can be a convenient crutch for both students and teachers, but they become virtually meaningless as the problems become harder, according to researchers. Key words can help first graders figure out whether to add or subtract more than half of the time, but the strategy rarely works for the multi-step problems students encounter starting in second and third grade. “With multi-step problems, key words don’t work 90 percent of the time,” said Sarah Powell, a professor at the University of Texas in Austin who studies word problems and whose research has highlighted the inefficacy of key words . “But the average kindergarten teacher is not thinking about that; they are teaching 5-year-olds, not 9-year-olds.”

Many teachers in the youngest grades hand out worksheets featuring the same type of word problem repeated over and over again. That’s what Molina’s colleague, Cassandra Santiago, did sometimes last year when leading a classroom on her own for the first time. “It was a mistake,” the first grade teacher said. “It’s really important to mix them up. It makes them think more critically about the parts they have to solve.”

Another flaw with word problem instruction is that the overwhelming majority of questions are divorced from the actual problem-solving a child might have to do outside the classroom in their daily life — or ever, really. “I’ve seen questions about two trains going on the same track,” said William Schmidt, a University Distinguished Professor at Michigan State University. “First, why would they be going on the same track and, second, who cares?”

Schmidt worked on an analysis of about 8,000 word problems used in 23 textbooks in 19 countries. He found that less than one percent had “real world applications” and involved “higher order math applications .”

“That is one of the reasons why children have problems with mathematics,” he said. “They don’t see the connection to the real world … We’re at this point in math right now where we are just teaching students how to manipulate numbers.”

He said a question, aimed at middle schoolers, that does have real world connections and involves more than manipulating numbers, might be: “Shopping at the new store in town includes a 43% discount on all items which are priced the same at $2. The state you live in has a 7% sales tax. You want to buy many things but only have a total of $52 to spend. Describe in words how many things you could buy.”

Schmidt added that relevancy of word problems is one area where few, if any, countries excel. “No one was a shining star leading the way,” he said. 

In her brightly decorated classroom one Tuesday afternoon, Santiago, the first grade teacher, gave each student a set of animal-shaped objects and a sheet of blue paper (the water) and green (the grass). “We’re going to work on a number story,” she told them. “I want you to use your animals to tell me the story.”

“ Once upon a time,” the story began. In this tale, three animals played in the water, and two animals played in the grass. Santiago allowed some time for the ducks, pigs and bears to frolic in the wilds of each student’s desk before she asked the children to write a number sentence that would tell them how many animals they have altogether.

Some of the students relied more on pictorial representations (three dots on one side of a line and two dots on the other) and others on the number sentence (3+2 = 5) but all of them eventually got to five. And Santiago made sure that her next question mixed up the order of operations (so students didn’t incorrectly assume that all they ever have to do is add): “Some more animals came and now there are seven. So how many more came?”

One approach to early elementary word problems that is taking off in some schools, including Segue Institute, has its origins in a special education intervention for struggling math students. Teachers avoid emphasizing key words and ask students instead to identify first the conceptual type of word problem (or schema, as many practitioners and researchers refer to it) they are dealing with: “Total problems,” for instance, involve combining two parts to find a new amount; “change problems” involve increasing or decreasing the amount of something. Total problems do not necessarily involve adding, however.

“The schemas that students learn in kindergarten will continue with them throughout their whole career,” said Powell, the word-problem researcher, who regularly works with districts across the country to help implement the approach. 

In Olathe, Kansas — a district inspired by Powell’s work — teachers had struggled for years with word problems, said Kelly Ulmer, a math support specialist whose goal is to assist in closing academic gaps that resulted from lost instruction time during the pandemic. “We’ve all tried these traditional approaches that weren’t working,” she said. “Sometimes you get pushback on new initiatives from veteran teachers and one of the things that showed us how badly this was needed is that the veteran teachers were the most excited and engaged — they have tried so many things” that haven’t worked.

In Rhode Island, many elementary schools initially used the strategy with students who required extra help, including those in special education, but expanded this use to make it part of the core instruction for all, said Bucka. In some respects, it’s similar to the recent, well publicized evolution of reading instruction in which some special education interventions for struggling readers  — most notably, a greater reliance on phonics in the early grades — have gone mainstream.

There is an extensive research bas e showing that focusing on the different conceptual types of word problems is an effective way of teaching math, although much of the research focuses specifically on students experiencing difficulties in the subject. 

Molina has found asking students to identify word problems by type to be a useful tool with nearly all of her second graders; next school year she hopes to introduce the strategy much earlier.

One recent afternoon, a lesson on word problems started with everyone standing up and chanting in unison: “Part plus part equals total” (they brought two hands together). “Total minus part equals part ” (they took one hand away) .

It’s a way to help students remember different conceptual frameworks for word problems. And it’s especially effective for the students who learn well through listening and repeating. For visual learners, the different types of word problems were mapped out on individual dry erase mats.

The real work began when Molina passed out questions, and the students— organized into the Penguin, Flower Bloom, Red Panda and Marshmallow teams — had to figure out which framework they were dealing with on their own and then work toward an answer. A few months ago, many of them would have automatically shut down when they saw the text on the page, Molina said.

For the Red Pandas, the question under scrutiny was: “The clothing store had 47 shirts. They sold 21, how many do they have now?”

“It’s a total problem,” one student said.

“No, it’s not total,” responded another.

“I think it’s about change,” said a third.

None of the students seemed worried about their lack of consensus, however. And neither was Molina. A correct answer is always nice but those come more often now that most of the students have made a crucial leap. “I notice them thinking more and more,” she said, “about what the question is actually asking.”

This story about word problems was produced by The Hechinger Report , a nonprofit, independent news organization focused on inequality and innovation in education. Sign up for the Hechinger newsletter .

Related articles

The Hechinger Report provides in-depth, fact-based, unbiased reporting on education that is free to all readers. But that doesn't mean it's free to produce. Our work keeps educators and the public informed about pressing issues at schools and on campuses throughout the country. We tell the whole story, even when the details are inconvenient. Help us keep doing that.

Join us today.

Sarah Carr CONTRIBUTING EDITOR

Email:... More by Sarah Carr

Letters to the Editor

At The Hechinger Report, we publish thoughtful letters from readers that contribute to the ongoing discussion about the education topics we cover. Please read our guidelines for more information. We will not consider letters that do not contain a full name and valid email address. You may submit news tips or ideas here without a full name, but not letters.

By submitting your name, you grant us permission to publish it with your letter. We will never publish your email address. You must fill out all fields to submit a letter.

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Sign me up for the newsletter!

More From Forbes

Stumped five ways to hone your problem-solving skills.

• Share to Facebook
• Share to Twitter
• Share to Linkedin

Respect the worth of other people's insights

Problems continuously arise in organizational life, making problem-solving an essential skill for leaders. Leaders who are good at tackling conundrums are likely to be more effective at overcoming obstacles and guiding their teams to achieve their goals. So, what’s the secret to better problem-solving skills?

1. Understand the root cause of the problem

“Too often, people fail because they haven’t correctly defined what the problem is,” says David Ross, an international strategist, founder of consultancy Phoenix Strategic Management and author of Confronting the Storm: Regenerating Leadership and Hope in the Age of Uncertainty .

Ross explains that as teams grapple with “wicked” problems – those where there can be several root causes for why a problem exists – there can often be disagreement on the initial assumptions made. As a result, their chances of successfully solving the problem are low.

“Before commencing the process of solving the problem, it is worthwhile identifying who your key stakeholders are and talking to them about the issue,” Ross recommends. “Who could be affected by the issue? What is the problem – and why? How are people affected?”

He argues that if leaders treat people with dignity, respecting the worth of their insights, they are more likely to successfully solve problems.

Best High-Yield Savings Accounts Of 2024

Best 5% interest savings accounts of 2024, 2. unfocus the mind.

“To solve problems, we need to commit to making time to face a problem in its full complexity, which also requires that we take back control of our thinking,” says Chris Griffiths, an expert on creativity and innovative thinking skills, founder and CEO of software provider OpenGenius, and co-author of The Focus Fix: Finding Clarity, Creativity and Resilience in an Overwhelming World .

To do this, it’s necessary to harness the power of the unfocused mind, according to Griffiths. “It might sound oxymoronic, but just like our devices, our brain needs time to recharge,” he says. “ A plethora of research has shown that daydreaming allows us to make creative connections and see abstract solutions that are not obvious when we’re engaged in direct work.”

To make use of the unfocused mind in problem solving, you must begin by getting to know the problem from all angles. “At this stage, don’t worry about actually solving the problem,” says Griffiths. “You’re simply giving your subconscious mind the information it needs to get creative with when you zone out. From here, pick a monotonous or rhythmic activity that will help you to activate the daydreaming state – that might be a walk, some doodling, or even some chores.”

Do this regularly, argues Griffiths, and you’ll soon find that flashes of inspiration and novel solutions naturally present themselves while you’re ostensibly thinking of other things. He says: “By allowing you to access the fullest creative potential of your own brain, daydreaming acts as a skeleton key for a wide range of problems.”

3. Be comfortable making judgment calls

“Admitting to not knowing the future takes courage,” says Professor Stephen Wyatt, founder and lead consultant at consultancy Corporate Rebirth and author of Antidote to the Crisis of Leadership: Opportunity in Complexity . “Leaders are worried our teams won’t respect us and our boards will lose faith in us, but what doesn’t work is drawing up plans and forecasts and holding yourself or others rigidly to them.”

Wyatt advises leaders to heighten their situational awareness – to look broadly, integrate more perspectives and be able to connect the dots. “We need to be comfortable in making judgment calls as the future is unknown,” he says. “There is no data on it. But equally, very few initiatives cannot be adjusted, refined or reviewed while in motion.”

Leaders need to stay vigilant, according to Wyatt, create the capacity of the enterprise to adapt and maintain the support of stakeholders. “The concept of the infallible leader needs to be updated,” he concludes.

4. Be prepared to fail and learn

“Organisations, and arguably society more widely, are obsessed with problems and the notion of problems,” says Steve Hearsum, founder of organizational change consultancy Edge + Stretch and author of No Silver Bullet: Bursting the Bubble of the Organisational Quick Fix .

Hearsum argues that this tendency is complicated by the myth of fixability, namely the idea that all problems, however complex, have a solution. “Our need for certainty, to minimize and dampen the anxiety of ‘not knowing,’ leads us to oversimplify and ignore or filter out anything that challenges the idea that there is a solution,” he says.

Leaders need to shift their mindset to cultivate their comfort with not knowing and couple that with being OK with being wrong, sometimes, notes Hearsum. He adds: “That means developing reflexivity to understand your own beliefs and judgments, and what influences these, asking questions and experimenting.”

5. Unleash the power of empathy

Leaders must be able to communicate problems in order to find solutions to them. But they should avoid bombarding their teams with complex, technical details since these can overwhelm their people’s cognitive load, says Dr Jessica Barker MBE , author of Hacked: The Secrets Behind Cyber Attacks .

Instead, she recommends that leaders frame their messages in ways that cut through jargon and ensure that their advice is relevant, accessible and actionable. “An essential leadership skill for this is empathy,” Barker explains. “When you’re trying to build a positive culture, it is crucial to understand why people are not practicing the behaviors you want rather than trying to force that behavioral change with fear, uncertainty and doubt.”

• Editorial Standards
• Reprints & Permissions

Join The Conversation

One Community. Many Voices. Create a free account to share your thoughts. 

Forbes Community Guidelines

Our community is about connecting people through open and thoughtful conversations. We want our readers to share their views and exchange ideas and facts in a safe space.

In order to do so, please follow the posting rules in our site's  Terms of Service.   We've summarized some of those key rules below. Simply put, keep it civil.

Your post will be rejected if we notice that it seems to contain:

• False or intentionally out-of-context or misleading information
• Insults, profanity, incoherent, obscene or inflammatory language or threats of any kind
• Attacks on the identity of other commenters or the article's author
• Content that otherwise violates our site's  terms.

User accounts will be blocked if we notice or believe that users are engaged in:

• Continuous attempts to re-post comments that have been previously moderated/rejected
• Racist, sexist, homophobic or other discriminatory comments
• Attempts or tactics that put the site security at risk
• Actions that otherwise violate our site's  terms.

So, how can you be a power user?

• Stay on topic and share your insights
• Feel free to be clear and thoughtful to get your point across
• ‘Like’ or ‘Dislike’ to show your point of view.
• Protect your community.
• Use the report tool to alert us when someone breaks the rules.

Thanks for reading our community guidelines. Please read the full list of posting rules found in our site's  Terms of Service.

BrainFlex+: Tricky Puzzles 17+

Play, learn, improve, brainflex, co., designed for iphone.

• 5.0 • 1 Rating

iPhone Screenshots

Description.

Get Smarter with Brain-Boosting Puzzle Games! Train your cognitive skills like memory, logic, and problem-solving through our fun and challenging brain games. Based on cognitive research, these tricky puzzles will give your mind a workout while keeping you entertained. Unique Puzzles: • Block Escape - control small blocks to find a best route from chaotic obstacles, improving your thinking ability; • Pointer Rotation - aim the pointer at the disc quickly and accurately, which is an excellent and interesting reaction training; • Logic Connection - use your imagination and logical ability to connect 1000+ different but closely related pictures; • Double Ring Rotation - control two rings to make timely and correct reactions, exercising your left and right brains concurrently. Super Assistance: • 30+ unique brain teasers for all ages and levels • Personalized daily training and progress tracking • Increasing difficulty to continually challenge you Excited? Try This App to Start Brain Training! Elevate your brainpower and unlock your full potential. User Agreement: https://plusbrainflex.com/userEn.html Privacy Policy: https://plusbrainflex.com/Privacy.html If you have any questions or suggestions, contact us([email protected]).

Version 1.1

Our update contents: 1. Modify layout of homepage to make it easier to use. 2. Optimized operation logic of game pages. 3. Added functions of sound and vibration setting. 4. Multi-language available.

Ratings and Reviews

App privacy.

The developer, BrainFlex, Co. , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

Data Used to Track You

The following data may be used to track you across apps and websites owned by other companies:

• Identifiers

Data Not Linked to You

The following data may be collected but it is not linked to your identity:

• Diagnostics

Privacy practices may vary, for example, based on the features you use or your age. Learn More

Information

English, Simplified Chinese

• Developer Website
• App Support
• Privacy Policy