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A Meta-Analysis of the Impact of Problem Posing Strategies on Students’ Learning of Mathematics
Open accessAbstract
This is a review of experimental research in which students have been taught to pose mathematical problems as a means of developing their learning. Hence, the aim of the research is to combine the empirical evidence regarding the functionality of problem posing strategies and to explore the aspects which could influence the integration of problem posing in mathematical education. In this direction, a meta-analysis approach was utilized in this study. 20 experimental research published between years of 2000 and 2020 are contained in this research and 31 effect sizes were computed. According to random effects model, it was found that problem posing strategy has significant impact on learners’ problem-solving skills, mathematics achievement, level of problems posed, and attitudes towards mathematics (ES = 1.328; 1.142; 1.152; 0.643; p=0.05). These effects also were analyzed according to methodological and instructional variables. The findings obtained in the research was discussed in the light of the literature and suggestions were made for the future studies.
Overview
CoChat Summary
TL;DR
This meta-analysis of 20 experimental studies (31 effect sizes) found that problem posing-based mathematics teaching had positive effects on students’ mathematical learning outcomes. Effects were high for problem-solving skills, problem-posing ability, and mathematics achievement, and moderate for attitudes/beliefs.
Key findings
- Across 20 studies with 2,349 students (1,091 experimental, 1,258 control), random-effects mean effect sizes were 1.328 for skill-based outcomes, 1.152 for ability-based outcomes, 1.142 for knowledge-based outcomes, and 0.643 for attitude-belief outcomes (all p<0.05).
- Using Cohen’s classification, attitude effects were moderate, while ability-based, knowledge-based, and skill-based effects were high.
- Moderator analyses found study type moderated ability-based outcomes (Qb=50.028, p<0.05) and attitude outcomes (Qb=4.534, p<0.05); study method and sample group moderated skill-based outcomes (Qb=27.509, p<0.05 for both); duration moderated knowledge (Qb=12.450, p<0.05) and skill-based outcomes (Qb=29.998, p<0.05); learning area moderated skill-based outcomes (Qb=26.043, p<0.05).
- Publication bias checks—funnel plot, Duval Tweedie Trim and Fill, and classic fail-safe N—indicated no publication bias; the fail-safe N required 68 ability-based, 87 attitude, 557 knowledge, and 185 skill-based contrary studies to invalidate the results.
Methods
- Meta-analysis of experimental research published between 2000 and 2020; databases searched were Web of Science, National Thesis Center, ProQuest Dissertations & Theses Global, ERIC, and Google Scholar; 339 studies were found and 20 met inclusion criteria, producing 31 effect sizes.
- Outcomes were coded as ability-based, attitude-belief, knowledge-based, and skill-based; effect sizes used Cohen’s d, and a random-effects model was applied because heterogeneity was high; analyses used CMA software.
- Moderator variables were methodological (study type, study method, sample group, measurement tool) and instructional (learning area, problem type, preparation for problem posing, duration); Qb values tested moderator differences; publication bias was assessed with funnel plot, Duval Tweedie Trim and Fill, and classic fail-safe N.
Limitations
- The paper states that it only brings together experimental studies related to problem posing; it recommends future experimental studies with larger sampling groups and relational meta-analyses examining correlations between problem posing and mathematical learning outcomes.
- Evident from the text: heterogeneity was high (e.g., knowledge Q=123.665, p<0.05), and the number of effect sizes per outcome was small (ability k=5, attitude k=7, knowledge k=12, skill k=7), with some moderator categories containing only 1–2 studies, so moderator findings should be interpreted cautiously.
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0 Valid · 0 Not valid · 18 Not checked · 43 Own results and interpretations
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As a result, it appears study type, method, sample group and scale tool did not have moderator roles for knowledge outcomes [Qb = 0.926, p > 0.05; Qb = 3.575, p > 0.05; Qb = 3.815, p > 0.05; Qb = 0.113, p > 0.05].”
§ A Meta-Analysis of the Impact of Problem Posing Strategies on Students' Learning of Mathematics > 3.2. Effect Sizes related to Moderator Variables
hedged- Asserted: passes — The authors put it forward as true.
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Another result of this research is that methodological moderator analysis showed some methodological characteristics had significant differences for mathematics achievement.”
§ A Meta-Analysis of the Impact of Problem Posing Strategies on Students' Learning of Mathematics > 4. Discussion
plainstates an association- Asserted: passes — The authors put it forward as true.
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In the paper
“Similarly, the duration spent on problem-generation activities changes the effect size for skill-based outcomes [Qb = 29.998,p <”
§ A Meta-Analysis of the Impact of Problem Posing Strategies on Students' Learning of Mathematics > 3.2. Effect Sizes related to Moderator Variables
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Additionally, in this study, some characteristics were found to display significant differences for attitudes to mathematics, ability to generate problems and ability to solve problems as a result of methodological moderator analysis.”
§ A Meta-Analysis of the Impact of Problem Posing Strategies on Students' Learning of Mathematics > 4. Discussion
plainstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“According to random effects model, it was found that problem posing strategy has significant impact on learners' problem-solving skills, mathematics achievement, level of problems posed, and attitudes towards mathematics (ES = 1.328; 1.142; 1.152; 0.643; p=0.05).”
- Also stated in: § 3.1. Weighted Effect Size Indices · plain
“According to the random effects model given in Table 5, the metaanalysis results for mean effect size were calculated as 1.152 for ability-based; 0.643 for attitude-belief; 1.142 for knowledge-based; and 1.328 for skillbased (p<0.05).”
- Also stated in: § 4. Discussion · plain
“Accordingly, mean effect size on the mathematical learning outcomes was 1.152 for level of problems posed, 1.142 for mathematics achievement, 1.328 for problem-solving skills and 0.643 for attitudes towards mathematics (p<0.05).”
§ A Meta-Analysis of the Impact of Problem Posing Strategies on Students' Learning of Mathematics > Abstract
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Also stated in: § 3.1. Weighted Effect Size Indices · plain
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Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“While these reviews occasionally ventured into a few studies examining the effect of engaging in problem posing activities on the development of problem posing, their primary focus remained on demonstrating the merit of problem posing as a tool on a broad-based impact for learning mathematics as opposed to examining problem posing as a goal.”
From Enhancing mathematical problem posing competence: a meta-analysis of intervention studies (2024) · cites this paper as Kul & Çelik, 2020
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Percentages, sums and reported differences re-computed from the paper’s own numbers.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
“| | Numbers | | 6 1.364 0.515 0.857 | 1.403 | 7.623 0.10 | | | |”
§ A Meta-Analysis of the Impact of Problem Posing Strategies on Students' Learning of Mathematics > 4. Discussion
Reported 1.364 · recomputed 1.13
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
“| | Not Stated | | 1 1.694 0.515 0.354 | 0.273 | | | | |”
§ A Meta-Analysis of the Impact of Problem Posing Strategies on Students' Learning of Mathematics > 4. Discussion
Reported 1.694 · recomputed 0.3135
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
“| 16-20 hours | 4 0.863 0.141 0.795 | 1.838 | | | | |”
§ A Meta-Analysis of the Impact of Problem Posing Strategies on Students' Learning of Mathematics > 4. Discussion
Reported 0.863 · recomputed 1.3165
Citations
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Statistical Power Analysis for the Behavioral Sciences
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The Handbook of Research Synthesis and Meta-Analysis
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How to Solve It. A New Aspect of Mathematical Method.
Bell, E. T., & Polya, G. (1945) · The American Mathematical Monthly · doi:10.2307/2306109 · Cited by 1,806
Research Synthesis and Meta-Analysis: A Step-by-Step Approach
Cooper, H. (2017) · doi:10.4135/9781071878644 · Cited by 1,716
Teaching Students to Generate Questions: A Review of the Intervention Studies
Rosenshine, B., Meister, C., & Chapman, S. (1996) · Review of Educational Research · doi:10.2307/1170607 · Cited by 888
Student-generated questions: A meaningful aspect of learning in science
Chin, C., & Brown, D. E. (2002) · International Journal of Science Education · doi:10.1080/09500690110095249 · Cited by 384
Problem-Posing Research in Mathematics Education: Some Answered and Unanswered Questions
Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015) · Springer eBooks · doi:10.1007/978-1-4614-6258-3_1 · Cited by 257
The Development of Fifth-Grade Children's Problem-Posing Abilities
English, L. D. (1997) · Educational Studies in Mathematics · doi:10.1023/a:1002963618035 · Cited by 178
Experiments and Relational Studies in Problem Solving: A Meta-Analysis
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Developing pre-service teachers understanding of fractions through problem posing
Toluk-Uçar, Z. (2009) · Teaching and Teacher Education · doi:10.1016/j.tate.2008.08.003 · Cited by 168
Research works printed but not linked: 7
- 2098 · DOI
- Çoğaltay, N., Karadağ, E., & Öztekin, Ö. (2014). The effect of school principals' transformational leadership behaviors on teachers' organizational commitment: a meta analysis study. educational administration: Theory and Practice, 20(4), 483-500. https://doi.org/10.14527/kuey.2014.019 · doi:10.14527/kuey.2014.019
- El Sayed, R. A. E. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers' problem solving performance. Journal of Science and Mathematics Education in Southeast Asia, 25(1), 56-69. https://inst.eecs.berkeley.edu/~cs375/fa18/resources /Oman- problemssolving.pdf
- Kaya, D. R. (2016). Problem solving based learning in math educatiȯn: Meta -analysis study [Unpublished master's thesis]. Recep Tayyip Erdoğan University, Rize.
- Lavy, I., & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, 3, 129-136. PME.
- Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28. https://doi.org/10.2307/749366 · doi:10.2307/749366
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Cited by
Meaningful Learning in Mathematics: A Research Synthesis of Teaching Approaches
Koskinen, R., & Pitkäniemi, H. (2022) · International Electronic Journal of Mathematics Education · doi:10.29333/iejme/11715 · Cited by 139
Bognar, B., Horvat, S. M., & Matić, L. J. (2025) · Education Sciences · doi:10.3390/educsci15010076 · Cited by 61
Wang, M., Walkington, C., & Rouse, A. (2022) · Investigations in Mathematics Learning · doi:10.1080/19477503.2022.2105104 · Cited by 55
Enhancing mathematical problem posing competence: a meta-analysis of intervention studies
Zhang, L., Stylianides, G. J., & Stylianides, A. J. (2024) · International Journal of STEM Education · doi:10.1186/s40594-024-00507-1 · Cited by 51
Zhang, C., Zhou, Y., Wijaya, T. T., Chen, J., & Ning, Y. (2024) · Thinking Skills and Creativity · doi:10.1016/j.tsc.2024.101587 · Cited by 32
Metadata
- Authors
- KUL, Ü., & ÇELİK, S.
- Affiliations
- Artvin Coruh University (TR)
- ORCID
- KUL, Ümit
- Venue
- Revista Romaneasca pentru Educatie Multidimensionala
- Publisher
- Asociatia LUMEN
- Published
- 2020-09-21
- Volume
- 12
- Issue
- 3
- Pages
- 341-368
- ISSN
- 2066-7329 (ISSN-L)
- 2067-9270
- OpenAlex
- W3092570935
- Cited by
- 31
- References
- 38
- Citations by year
- 2026: 7 · 2025: 7 · 2024: 7 · 2023: 4 · 2022: 6
- FWCI
- 0.58
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- cc-by-nc-nd
- Locations
- Revista Romaneasca pentru Educatie Multidimensionala (publishedVersion, cc-by-nc-nd)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Social Sciences › Education › Mathematics Education and Pedagogy
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Social Sciences › Education › Problem and Project Based Learning
- Keywords
- problem posing, mathematical problem posing, mathematics learning, mathematical problem solving ability, mathematics achievement, attitudes towards mathematics, mathematics education
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