Problem Posing in Consumer Mathematics Classes: Not Just for Future Mathematicians
Why this work is in the frame
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Bibliographic record
Abstract
Problem posing is recognized as a key component of mathematics (Ellerton, 2013). However, in many curricula, problem solving often dominates over problem posing (Stoyanova, 2003). This focus on problem solving exists despite research that shows that problem posing improves students' problem-solving skills, attitudes, confidence, understanding of concepts, and mathematical thinking (Singer, Ellerton, & Cai, 2013); reinforces basic mathematical skills, increases motivation, responsibility, and thinking flexibility (Ponte & Henriques, 2013); and is useful for teachers to assess students' cognitive processes, identify misconceptions, and modify instruction (Ponte & Henriques, 2013). Further, problem posing can play a large part in student motivation (McLeod, 1992). The potential for problem posing as a motivational tool in nonuniversity track mathematics classes has not received much attention. This case study examines a program based on problem posing, in six grade 11 consumer mathematics classes, over a 3-year period. The program was very successful across a number of dimensions, including engagement, motivation, self-efficacy, and achievement. This paper also examines models of problem posing, and suggests modifications to enhance their efficacy.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it