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Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education
Open accessAbstract
Mathematical problem posing, a form of authentic mathematical inquiry and creation, has been acknowledged as important by educators and curriculum frameworks internationally and has been the focus of several intervention studies with students and teachers. However, the intervention components and measured outcomes of these prior studies varied, highlighting the diverse approaches researchers have taken to support and measure mathematical problem-posing competence. In this systematic review, we examined 39 intervention studies published over the past three decades, all aimed at developing mathematical problem-posing competence, and we identified nine common intervention components suggested or utilized within these studies. Also, we derived clusters of measured outcomes related to mathematical problem-posing competence used in the interventions. Our findings deepen understanding of approaches to supporting and measuring mathematical problem-posing competence, thus casting light on what works, including methods for measuring progress, in problem-posing interventions. We discuss implications of our findings for future research and practice.
Overview
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TL;DR
This systematic review synthesizes 39 intervention studies aimed at developing mathematical problem-posing competence and identifies nine common intervention components plus clusters of measured outcomes. It finds varied approaches to supporting and measuring problem posing, with engagement in problem-posing activities and interactive learning environments most frequent, and calls for more standardized and broader affective measurement.
Key findings
- Across 39 studies, nine intervention components were identified: overview of what problem posing is (7; 17.9%), discussion of what “good” problems are (4; 10.3%), engagement with problem posing activities (19; 48.7%), evaluation of posed problems (5; 12.8%), comprehension of the problem posing situation (4; 10.3%), use of strategies involved in problem posing (11; 28.2%), use of problem-posing examples (4; 10.3%), use of technology in problem posing (9; 23.1%), and creation of an interactive learning environment (15; 38.5%).
- Measured outcomes clustered into quantity of posed problems, quality of posed problems, and affective-motivational disposition. Quality criteria included difficulty/complexity (11 studies), type (12), strategy variability (9), creativity (9), solvability (3), cognitive demand (3), openness (3), clarity (2), and other (11); quantity included number of posed problems (10) and lesson episodes involving problem posing (2).
- Affective-motivational outcomes were examined in only 10 of 39 studies, with a substantial focus (9 of the 10 studies) placed singularly on beliefs about mathematical problem posing; 7 of these 10 were published after 2015, and methods were dominated by self-designed questionnaires containing only one or two questions.
- Of 39 included studies, 5 suggested intervention components without empirical results; 34 reported experimental design/statistical data, but one lacked enough experimental detail; 33 were summarized in Figure 2. Participants included school students (15 studies, mostly ages 5–18), prospective teachers (14, mostly ages 18–22), and in-service teachers (4, mostly over 23); durations ranged from less than one day (13) to more than one month (12).
Methods
- PRISMA-guided systematic review. Searched Web of Science, ERIC, PsycINFO, and Springer in July 2021, plus the first 15 pages of Google Scholar, using Boolean search terms combining math/algebra/etc. with “problem posing” or problem-posing.
- Inclusion criteria: peer-reviewed journal articles or book chapters, English, published January 1990–June 2021, term in title and/or abstract/keywords, and report of at least one intervention component related to mathematical problem posing with case analysis or statistical evidence. From 1,412 publications, 509 were full-text reviewed and 39 met criteria.
- Data extraction/coding by two trained research assistants; interrater agreement was 100% for 30 randomly selected publications, and Cohen’s kappa was 0.9 across coding points for the 39 studies. Intervention components were coded using Bicer’s (2021) instructional practices and Boller et al.’s (2014) typology, with the constant comparative method.
Limitations
- The paper states that the review period does not extend to the present day, due to COVID-related logistical and financial constraints and delays in preparing the findings for publication.
- Evident from the text: only 39 studies were included, 5 provided no empirical results and one experimental study lacked sufficient detail; the field lacks a standardized test for mathematical problem-posing competence and consensus on what constitutes good problems and competent problem posers.
- Evident from the text: affective outcomes were measured in a minority of studies (10/39), mostly beliefs, often with narrow self-designed questionnaires, raising validity concerns.
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“we derived clusters of measured outcomes related to mathematical problem-posing competence used in the interventions”
§ Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education > Abstract
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In the paper
“we identified nine common intervention components suggested or utilized within these studies”
§ Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education > Abstract
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“Finally, a total of 39 publications met the inclusion criteria and were retained for systematic review.”
§ Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education > Inclusion and exclusion criteria.
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“Evaluation of posed problems (EPP) 5 (12.8%)”
§ Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education > Intervention components for enhancing mathematical problem-posing competence
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“Comprehension of the problem posing situation (CPPS) 4 (10.3%)”
§ Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education > Intervention components for enhancing mathematical problem-posing competence
plainn = 39- Asserted: passes — The authors put it forward as true.
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§ Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education > FIGURE 3 A possible overview organizational structure of the identified intervention components
“During all the interventions, participants were required to engage in particular activity-based practice including WPP, WGP, PPA, and EPP.”
§ Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education > Intervention components for enhancing mathematical problem-posing competence
“TABLE 1 Frequency and proportion of publications from those included in the systematic review (N=39) that incorporated a particular category of intervention component Categories of Intervention Components No. Activity-based Practice Overview of what problem posing is (WPP) 7 (17.9%)Discussion of what 'good' problems are (WGP) 4 (10.3%)Engagement with problem posing activities (PPA) 19 (48.7%)Evaluation of posed problems (EPP) 5 (12.8%)”
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
§ Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education > ) Affectivemotivational disposition
“Beliefs about problem posing (11 studies)”
§ Approaches to Supporting and Measuring Mathematical Problem Posing: A Systematic Review of Interventions in Mathematics Education > FIGURE 4 An overview of measured criterion-behavior changes from interventions on enhancing mathematical problem-posing competence
“a relatively small number of the intervention studies we reviewed (10 out of 39) ventured into evaluating or considering the affective changes of mathematical problem-posing competence, with a substantial focus (9 of the 10 studies) placed singularly on beliefs about mathematical problem posing.”
Citations
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Cited by
Ulusoy, F. (2025) · Journal of Mathematics Teacher Education · doi:10.1007/s10857-025-09697-z · Cited by 7
Krawitz, J., Meyer-Jenßen, L., Krausmüller, K., & Rakoczy, K. (2026) · ZDM · doi:10.1007/s11858-025-01762-4 · Cited by 5
Bokhove, C. (2025) · Asian Journal for Mathematics Education · doi:10.1177/27527263251346212 · Cited by 5
Investigating Authentic Nature of PISA Mathematics Items
İncikabı, S. (2025) · School Science and Mathematics · doi:10.1111/ssm.18402 · Cited by 4
Torregrosa, A., Albarracín, L., & Gorgorió, N. (2026) · The Journal of Mathematical Behavior · doi:10.1016/j.jmathb.2026.101348 · Cited by 3
Metadata
- Authors
- Zhang, L., Stylianides, A. J., & Stylianides, G. J.
- Affiliations
- Chengdu University (CN)
- University of Cambridge (GB)
- University of Oxford (GB)
- Corresponding author
- Zhang, Ling
- Venue
- International Journal of Science and Mathematics Education
- Published
- 2025-01-25
- Volume
- 23
- Issue
- 7
- Pages
- 2225-2254
- ISSN
- 1571-0068 (ISSN-L)
- 1573-1774
- OpenAlex
- W4406786598
- Semantic Scholar
- da49c7626aaadf6e9a1c1e9938fcb85f4355b6ce
- Cited by
- 17
- References
- 101
- Citations by year
- 2026: 13 · 2025: 4
- FWCI
- 1.74
- Type
- journal article
- Language
- en
- Open access
- green
- ora.ox.ac.uk
- Licence
- cc-by
- www.springernature.com/gp/researchers/text-and-data-mining (tdm)
- www.springernature.com/gp/researchers/text-and-data-mining (vor)
- Locations
- International Journal of Science and Mathematics Education (publishedVersion)
- Oxford University Research Archive (ORA) (University of Oxford) (submittedVersion, cc-by)
- Apollo (University of Cambridge) (submittedVersion, cc-by)
- Apollo (cc-by)
- 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
- mathematical problem posing, intervention components, mathematics education intervention
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