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The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis
Open accessAbstract
The purpose of the study was to meta-synthesize research findings on the effectiveness of problem posing and to investigate the factors that might affect the incorporation of problem posing in the teaching and learning of mathematics. The eligibility criteria for inclusion of literature in the meta-analysis was: published between 1989 and 2011, reported problem posing as an intervention, employed experimental research design, and provided data necessary to compute effect sizes. The large positive effect sizes (Hedges’ g) showed that problem posing activities provide considerable benefits for: mathematics achievement, problem solving skills, levels of problems posed, and attitudes toward mathematics. Several noteworthy limitations of this study were discussed.
Overview
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TL;DR
This meta-analysis synthesizes 14 datasets from 13 experimental/quasi-experimental studies (1989–2011) on problem posing in mathematics and finds positive effects across knowledge, skill, ability, and attitude-belief outcomes. The largest weighted mean effect was for knowledge-based outcomes (Hedges’ g = 1.31), with effects ranging from .76 to 1.31 across outcomes.
Key findings
- Problem posing had positive, statistically significant effects on all four coded learning outcomes: knowledge-based (mean Hedges’ g = 1.31, 95% CI 1.04–1.59), skill-based (g = .83, 95% CI .58–1.08), ability-based (g = .77, 95% CI .57–.98), and attitude-beliefs (g = .76, 95% CI .59–.93).
- The meta-analysis included 14 unique datasets from 13 studies, with approximately 1,316 participants, mostly school students in grades 3–12 (1,038 participants) and preservice teachers (n = 278).
- Moderator analyses found educational setting, publication source, and presentation type were statistically significant for several outcomes; for ability-based outcomes all hypothesized moderators were significant (p < .001), and for attitude-beliefs educational setting, research design, publication source, and presentation type were significant (p < .001).
- Homogeneity tests showed heterogeneity for knowledge-based (Q = 68.12, df = 3, p < .001), ability-based (Q = 24.65, df = 6, p < .001), and attitude-beliefs (Q = 71.78, df = 5, p < .001), while skill-based effects were homogeneous (Q = 7.06, df = 4, p = .13).
Methods
- Design: meta-analysis of studies published 1989–2011 that reported problem posing as an intervention without a computer system/program, used experimental research designs (treatment-control or pretest-posttest), were in English, and reported statistical data for effect-size calculation.
- Data/sample: searches of ERIC, ProQuest Dissertations and Theses, PsycINFO, manual journal searches, and Google Scholar yielded 3,730 initial works; after screening, 14 individual studies/datasets met criteria.
- Analysis: studies were coded with a 35-item coding sheet (inter-rater coding 80%, resolved to 100%); effect sizes used Glass’ Δ, Hedges’ g, and odds ratios converted to Hedges’ g, with Q homogeneity tests, funnel plots for publication bias, and fixed-effect moderator analyses via ANOVA.
Limitations
- The paper states that few quantitative studies published on problem posing included relevant data for effect-size calculation; many studies lacked detailed intervention descriptions, making replication difficult and aggregation more complex, and some did not clearly present results systematically.
- The paper states that only a small number of selected studies included randomization; many used quasi-experimental two-group or single-group pre-post designs, and one-group designs tend to inflate effect sizes.
- The paper states that sample size is perhaps the most limiting aspect, partly because most studies were qualitative and did not report means and standard deviations; too few quantitative studies provided both adequate descriptions to code learning outcomes and the means/SDs for instruments used.
- Evident from the text: the synthesis rests on only 14 datasets, and some moderator cells were based on one study (e.g., teacher preparation knowledge-based, non-specific problem posing skill-based), limiting robustness.
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0 Valid · 0 Not valid · 27 Not checked · 51 Own results and interpretations
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In the paper
“In addition, the Q within (Q = 4.95, p = .08)showed the effects of studies within grade 3-12 and teacher preparation groups could have come from the same distribution of effects.”
§ The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis > 5.4.1 Knowledge-Based
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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In the paper
“With Q statistic (chi-square) as a variance indicator, four studies under knowledge-based were heterogeneous wherein Q = 68.12(df = 3, p < .001)indicating significant variability of one or more effects from the mean.”
§ The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis > 5.3 Homogeneity of Effect Sizes and Publication Bias
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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In the paper
“Preservice teachers, that are students in a teacher preparation program, were strongly influenced by problem-posing interventions across all learning outcomes.”
§ The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis > 6. Discussion
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In the paper
“large positive effect sizes ranging from .76 to 1.31”
§ The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis > 6. Discussion
plain- 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
“All the hypothesized moderators had statistically (p < .001)significant effects on student ability-based as shown in Table 6.”
§ The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis > 5.4.3 Ability-Based
plainstates an association- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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Claims other papers make about this one
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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 Rosli et al., 2014
Experimental — accuracy not yet measuredIn the citing paper
“For example, for sample level, Rosli et al. (2014) found that prospective teachers were strongly influenced by engaging in problem posing activities across all mathematical learning outcomes compared to grade 4-12 students.”
From Enhancing mathematical problem posing competence: a meta-analysis of intervention studies (2024) · cites this paper as Rosli et al., 2014
In the citing paper
“However, Rosli, Capraro and Capraro (2014) identified significant differences for educational stage and publication type for mathematical success as a result of methodological moderator variables.”
From A Meta-Analysis of the Impact of Problem Posing Strategies on Students’ Learning of Mathematics (2020) · cites this paper as Rosli, Capraro and Capraro (2014)
In the citing paper
“For example, Rosli, Capraro and Capraro in a meta-analysis study in 2014 calculated 22 effect sizes for 14 studies and found the effect of problem posing-based teaching on level of problems posed was 0.77, attitudes and beliefs related to mathematics was 0.76, mathematics achievement was 1.31 and problem-solving skills was 0.83.”
From A Meta-Analysis of the Impact of Problem Posing Strategies on Students’ Learning of Mathematics (2020) · cites this paper as Rosli, Capraro and Capraro (2014)
In the citing paper
“In this regard, only two meta-analysis studies found in the literature directly address and measure the effectiveness of problem-posing.”
From A Meta-Analysis of the Impact of Problem Posing Strategies on Students’ Learning of Mathematics (2020) · cites this paper as Rosli, Capraro and Capraro (2014)
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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
§ The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis > 4.2 Inclusion Criteria and Literature Search
“only 14 individual studies were selected because they satisfied the requirements for this meta-analysis.”
§ The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis > 5.1 Description of Selected Studies
“A total of 14 unique datasets (from 13 studies) were included in the current meta-analysis.”
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
§ The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis > 6. Discussion
“| English | | Educational Studies | 27 | Gr. | 4 | AB (levels of problem), SB | Recognition of problem |”
§ The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis > References
“English, L. D. (1997). The development of fifth-grade children's problem posing abilities.”
Citations
Cites
Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009) · doi:10.1002/9780470743386 · Cited by 14,225
(2002) · Cited by 13,211
Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2021) · doi:10.1002/9781119558378 · Cited by 9,799
(2000) · Cited by 9,198
National Council of Teachers of Mathematics
(1979) · The Mathematics Teacher · doi:10.5951/mt.72.8.0637 · Cited by 8,499
Cognitive Science and Mathematics Education
Schoenfeld, A. H. (2013) · Routledge eBooks · doi:10.4324/9780203062685 · Cited by 983
Meta-analysis of screening and diagnostic tests.
Hasselblad, V., & Hedges, L. V. (1995) · Psychological Bulletin · doi:10.1037/0033-2909.117.1.167 · Cited by 579
Brown, S. I., & Walter, M. I. (2005) · Psychology Press eBooks · doi:10.4324/9781410611833 · Cited by 511
Misleading funnel plot for detection of bias in meta-analysis
Tang, J.-L., & Liu, J. L. (2000) · Journal of Clinical Epidemiology · doi:10.1016/s0895-4356(99)00204-8 · Cited by 420
Cai, J., & Hwang, S. (2002) · The Journal of Mathematical Behavior · doi:10.1016/s0732-3123(02)00142-6 · Cited by 320
Research works printed but not linked: 5
- Akay, H., & Boz, N. (2010). The effect of problem posing oriented analysis-II course on the attitudes toward mathematics and mathematics self-efficacy. Australian Journal of Teacher Education, 35, 59-75.
- Demir, B. B. (2005). The effect of instruction with problem posing on tenth grade students' probability achievement and attitudes toward probability (Unpublished master's thesis). Middle East Technical University, Turkey.
- Dickerson, V. M. (1999). The impact of problem posing intervention on the mathematical problem solving achievement of seventh graders (Unpublished doctoral dissertation). Emory University, Atlanta, GA.
- Schloemer, C. G. (1994). Integrating problem posing into instruction in advanced algebra: Feasibility and outcomes (Unpublished doctoral dissertation). University of Pittsburg, PA.
- Stoyanova, E., & Ellerton, (1996). A framework for research into students' problem posing in school mathematics. In P. C. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Mathematics Education Research Group of Australasia. The University of Melbourne.
Cited by
Rahmah, S., & Lubis, A. H. (2024) · Journal of Indonesian Primary School. · doi:10.62945/jips.v1i4.409 · Cited by 302
Prof., U. P. I., Darhim, D., Prabawanto, S., Dr., U. P. I., Susilo, B. E., & Universitas Negeri Semarang, S. (2020) · International Journal of Instruction · doi:10.29333/iji.2020.1347a · Cited by 100
Paloloang, M. F. B., Juandi, D., Tamur, M., Paloloang, B., & Adem, A. M. G. (2020) · AKSIOMA Jurnal Program Studi Pendidikan Matematika · doi:10.24127/ajpm.v9i4.3049 · Cited by 95
The effects of problem-posing intervention types on elementary students’ problem-solving
Kopparla, M., Bicer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., Caldwell, C., Capraro, M. M., & Capraro, R. M. (2019) · Educational Studies · doi:10.1080/03055698.2018.1509785 · Cited by 57
Self-citationThe Effect of Online Problem Posing on Students' Problem-Solving Abilitiy in Mathematics
Suarsana, I. M., Lestari, I. A. P. D., Ganesha Universitiy of Education, I., & Mertasari, N. M. S. (2018) · International Journal of Instruction · doi:10.29333/iji.2019.12152a · Cited by 88
Metadata
- Authors
- Rosli, R., Capraro, M. M., & Capraro, R. M.
- Affiliations
- National University of Malaysia (MY)
- Texas A&M University (US)
- Venue
- International Education Studies
- Published
- 2014-12-22
- Volume
- 7
- Issue
- 13
- ISSN
- 1913-9020 (ISSN-L)
- 1913-9039
- OpenAlex
- W2126401369
- Cited by
- 106
- References
- 42
- Citations by year
- 2026: 12 · 2025: 8 · 2024: 14 · 2023: 9 · 2022: 7 · 2021: 10 · 2020: 14 · 2019: 9 · 2018: 13 · 2017: 7 · 2016: 3
- FWCI
- 1.19
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by
- Locations
- International Education Studies (publishedVersion, cc-by)
- Greater South Information System
- 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, mathematics learning, mathematics achievement, problem-solving skills, attitudes toward mathematics, mathematics education, effect size
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