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The Impacts of Problem‐Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics
Open accessAbstract
This study investigates the impact of problem‐posing on the mathematical proficiency and engagement of 56 Developmental Mathematics (DM) students enrolled in a noncredit college mathematics course. Using a quasi‐experimental design, one of two existing classes was selected as the experimental group and received a 5‐week intervention focused on problem‐posing with word problems. The other class served as the control group, receiving the same instruction but without engaging in problem‐posing. Both the experimental group of 25 participants and the control group showed significant improvement on the posttest compared to the pretest in mathematical proficiency, with the experimental group demonstrating more pronounced growth. Further analysis, which divided students into three subgroups based on pretest scores, revealed that students in the lower two subgroups of the experimental group significantly outperformed all other groups on the posttest. A qualitative analysis identified potential reasons for the growth in these subgroups. Students in the experimental group built confidence by first mimicking previous problems and verifying their calculations. They also personalized their problem‐posing experiences, which contributed to increased engagement, persistence, and deeper understanding of the material, ultimately enhancing their mathematical proficiency. The study demonstrates that DM students are both capable of and willing to engage in problem‐posing.
Overview
CoChat Summary
TL;DR
A 5-week problem-posing intervention in a developmental mathematics course was associated with greater percentage growth in mathematical proficiency than control, but overall posttest differences were not significant. Qualitative themes of mimicking, making numbers work, and personalization help explain engagement and growth, especially in lower- and middle-performing experimental subgroups.
Key findings
- The experimental group showed more growth (35.29 points; 63.01%) than the control group (21.98 points; 53.53%), though the control group outperformed the experimental group on both pretest and posttest.
- Pretest scores differed significantly between experimental (M = 44, SD = 12.44) and control (M = 58.78, SD = 16.56) groups, t(54) = 3.698, p = 0.000; posttest scores did not differ significantly, t(54) = 0.385, p = 0.702.
- Within-group gains were significant for the experimental group (44 to 79.29; t = 6.836, df = 48, p = 2.36E-13) and control group (58.78 to 80.76; t = 5.286, df = 60, p = 1.84E-6).
- Subgroup analysis showed the largest changes for middle experimental (44.10 to 82.14; change 38.05), low experimental (33.33 to 75.71; change 42.38), and low control (43.18 to 79.55; change 36.36); the high control subgroup did not improve significantly (82.29 to 88.84; t = 1.049, df = 11, p = 0.3168094).
- Qualitative analysis identified three themes: mimicking, making the numbers work, and personalization; 17 of 18 lower/middle experimental students initially mimicked problems, 15 of 18 used the same or slightly changed numbers, and 14 preferred flexibility in semi-structured and free problem-posing.
Methods
- Quasi-experimental, two-group pretest-posttest design with 56 developmental mathematics students at a public university in the Southeastern United States; 25 experimental and 31 control participants completed both pretest and posttest.
- The experimental group received a 5-week problem-posing intervention with word problems, scaffolded through structured, semi-structured, free, and free-plus levels; the control group received the same instruction without problem-posing.
- Quantitative analysis used means, standard deviations, percent growth, independent-samples t-tests, and low/middle/high pretest subgroups; qualitative analysis used six volunteer interviews (30–60 min), student written work, observation journals, and a coding matrix for personalized, mimicked, and non-mimicked problems.
Limitations
- The paper states that small sample sizes limit generalizability and that validity and reliability for the pretest/posttest instrument were not formally established; future iterations require stronger validity and reliability measures for tests and coding.
- The paper acknowledges the quasi-experimental design and cross-referencing of qualitative and quantitative data could prematurely assert impact; the first author taught both groups, devoted more time to the intervention course, and may have introduced bias or contextual factors.
- The paper notes the intervention occurred in the last 5 weeks and word problems served as review for both groups, which may explain overall growth and reduce clarity about intervention effects; some students found personalization distracting or unnecessary. Evident from the text: individual students were not randomized, only intact classes were assigned, and subgroup analyses relied on very small numbers.
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Claims the paper makes
0 Valid · 0 Not valid · 23 Not checked · 85 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
“After performing a two-sample t-test on the pretest and posttest for the groups, we note that except for the high group in the control course, all the groups did significantly better on the posttest than the pretest (Table 7).”
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > 4.1.1 | Comparisons Within the Courses
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
“Both the experimental group of 25 participants and the control group showed significant improvement on the posttest compared to the pretest in mathematical proficiency, with the experimental group demonstrating more pronounced growth.”
- Also stated in: § 4.1 | Impact on Mathematical Proficiency · plain
“Students of the experimental course showed more growth (35.29)than those in the control course (21.98), even though the control course outperformed the experimental course on both pretest and posttest.”
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > Abstract
plainstates a causen = 25- 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: § 4.1 | Impact on Mathematical Proficiency · plain
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
“Almost all students used specific wording provided in the word bank and later adapted it to their own phrases and words and their own contextual problems.”
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > 4.2 | Mimicking
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.
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
“Students in the experimental group relied on the mimicking as additional scaffolding.”
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > 4.2 | Mimicking
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.
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
“While the overall posttest results showed no significant difference between the experimental and control classes,”
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > 5 | Discussion, Limitations, and Future Directions
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.
41 more claims
Create a free account to see all 108 claims and to verify the 25 references still open.
- Probably not a substantial claim. 38
- It may state two separate claims as one. 42
- The quote only partly states this claim. 1
Statistics recomputed
Every reported test result, recomputed from its test statistic and degrees of freedom. A result shows as not adding up only once an independent check has confirmed it.
- Not confirmedt(54) = 3.698reported p = 0 · recomputed p < .001
“t(54) = 3.698, p = .000”
- Consistentt(54) = 0.385reported p = .702 · recomputed p = .702
“t(54) = 0.385, p = .702”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated major: it would touch a result — a value a result rests on, reported and recomputed p-values on opposite sides of the significance level, two passages that conflict with no sign which is right, or a cited work retracted before this paper was published.
In the paper
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > Abstract
“students in the lower two subgroups of the experimental group significantly outperformed all other groups on the posttest.”
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > 5.1 | Study Design and Data Collection
“| Middle (experimental) | 44.10 | 82.14 | 38.05 | | Low (experimental) | 33.33 | 75.71 | 42.38 | | Low (control) | 43.18 | 79.55 | 36.36 | | High (experimental) | 59.13 | 81.12 | 22.00 | | Middle (control) | 57.41 | 76.49 | 19.08 | | High (control) | 82.29 | 88.84 | 6.55 |”
Rated major: it would touch a result — a value a result rests on, reported and recomputed p-values on opposite sides of the significance level, two passages that conflict with no sign which is right, or a cited work retracted before this paper was published.
In the paper
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > 4.1.1 | Comparisons Within the Courses
“Groups were created based on score benchmarks in the course curriculum with students' scores less than or equal to 50% in the low, students greater than 50% and less than or equal to 75% in the middle, and greater than 75% in the high group.”
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > 5.1 | Study Design and Data Collection
“| Middle (experimental) | 44.10 | 82.14 | 38.05 | | Low (experimental) | 33.33 | 75.71 | 42.38 | | Low (control) | 43.18 | 79.55 | 36.36 | | High (experimental) | 59.13 | 81.12 | 22.00 |”
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 Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > 4.1 | Impact on Mathematical Proficiency
“The 25 participants in the experimental course (M = 44, SD = 12.44) compared to the 31 participants in the control course (M = 58.78,SD = 16.56)demonstrated significantly higher scores, t(54) = 3.698, p = 0.000.”
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > 4.1 | Impact on Mathematical Proficiency
“even though the control course outperformed the experimental course on both pretest and posttest.”
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
“| Personalized | 7 | 111 | 68 | 17 | 211 |”
§ The Impacts of Problem-Posing Intervention on the Mathematical Proficiency of Undergraduate Developmental Mathematics Students' Developmental Mathematics > 5.1 | Study Design and Data Collection
Reported 211 · recomputed 203
Citations
Cites
Designing and Conducting Mixed Methods Research
Robinson, P. (2007) · Australian and New Zealand Journal of Public Health · doi:10.1111/j.1753-6405.2007.00096.x · Cited by 23,258
Qualitative Data Analysis: A Methods Sourcebook
Miles, M. B., Huberman, A. M., & Saldaña, J. (1988) · Cited by 20,701
Mertens, D. M. (1997) · Cited by 3,679
Handbook of International Research in Mathematics Education
(2015) · Routledge eBooks · doi:10.4324/9780203448946 · Cited by 1,006
Word problems in mathematics education: a survey
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020) · ZDM · doi:10.1007/s11858-020-01130-4 · Cited by 422
Cognitive Load Theory: Recent Theoretical Advances
Sweller, J. (2010) · Cognitive Load Theory · doi:10.1017/cbo9780511844744.004 · Cited by 412
Children's Problem Posing within Formal and Informal Contexts
English, L. D. (1998) · Journal for Research in Mathematics Education · doi:10.2307/749719 · Cited by 304
Cai, J., & Hwang, S. (2020) · International Journal of Educational Research · doi:10.1016/j.ijer.2019.01.001 · Cited by 215
Empirical research on problem solving and problem posing: a look at the state of the art
Liljedahl, P., & Cai, J. (2021) · ZDM – Mathematics Education · doi:10.1007/s11858-021-01291-w · Cited by 171
How to Solve It: A New Aspect of Mathematical Method
POLYA, G. (2014) · doi:10.2307/j.ctvc773pk · Cited by 140
Research works printed but not linked: 2
- Coltharp J., 2020, Instruction Type, Student Major, and Success in Developmental Mathematics, Journal of Developmental Education, 1, 18
- Stoyanova E., 1996, A Framework for Research into Students’ Problem Posing in School Mathematics, Technology in Mathematics Education, 4, 518
Cited by
How to Pose It: Developing a Problem‐Posing Framework
Contreras, J. N. (2020) · School Science and Mathematics · doi:10.1111/ssm.70046
Ersoy, M., & Dağyar, M. (2026) · Eurasia Journal of Mathematics Science and Technology Education · doi:10.29333/ejmste/18740
Examining AI interaction profiles in generative AI supported fraction division problem posing
İncikabı, S. (2026) · Frontiers in Psychology · doi:10.3389/fpsyg.2026.1946583
Metadata
- Authors
- Sevier, J., Fernandes, A., & Cifarelli, V.
- Affiliations
- Appalachian State University (US)
- University of North Carolina at Charlotte (US)
- Corresponding author
- Sevier, John
- Venue
- School Science and Mathematics
- Publisher
- Wiley
- Published
- 2025-05-19
- Volume
- 126
- Issue
- 5
- Pages
- 441-453
- ISSN
- 0036-6803 (ISSN-L)
- 1949-8594
- OpenAlex
- W4410510427
- Cited by
- 3
- References
- 30
- Citations by year
- 2026: 2
- FWCI
- 1.61
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by-nc-nd
- creativecommons.org/licenses/by-nc-nd/4.0/ (vor)
- doi.wiley.com/10.1002/tdm_license_1.1 (tdm)
- Locations
- School Science and Mathematics (publishedVersion, cc-by-nc-nd)
- Topics
- Social Sciences › Education › Mathematics Education and Pedagogy
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Social Sciences › Education › Mathematics Education and Programs
- Keywords
- problem posing, mathematics proficiency, developmental mathematics, undergraduate students, word problems, student engagement, student persistence, intervention, student self-confidence, personalized learning
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