Relation Between Mathematical Proof Problem Solving, Math Anxiety, Self-Efficacy, Learning Engagement, and Backward Reasoning
Bibliographic record
Abstract
Providing adequate proof is one essential mathematical method, but it is a difficult task for many school-age students. While previous studies have revealed the cognitive factors of proving the proof, the function of affective factors and learning engagement has been largely unexplored. This study examined the effects and processes associated with math anxiety, self-efficacy, engagement, and backward reasoning on the provision of proof when solving math problems about geometric similarity. A survey was conducted on 160 junior high school students, from which it was found that: (a) self-efficacy was indirectly and directly positively associated with the provision of proof when solving math problems and was mediated by math anxiety and backward reasoning; (b) math anxiety was indirectly and negatively associated with the provision of proof when solving difficult proof problems and was mediated by backward reasoning; (c) the use of backward reasoning was positively associated with the provision of proof when solving proof problems; (d) cognitive engagement was indirectly and positively associated with the provision of proof when solving proof problems and was mediated by self-efficacy and backward reasoning. The results suggest that improving cognitive engagement, self-efficacy, and backward reasoning may be effective in the provision of proof when solving proof problems.
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How this classification was reachedexpand
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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".