Instilling creativity in pre-service teachers through investigation of mathematical puzzles: Case of magic squares
Bibliographic record
Abstract
This article explores puzzle-based learning (PBL) to develop creative thinking in preservice mathematics teachers (PTs).Through a case study involving a magic square puzzle, PTs engaged in trial-and-error, pattern recognition, and collaborative reflection, moving from surface-level problem-solving to deeper mathematical inquiry.Guided by Polya's framework of "looking back," PTs revisited and refined their initial strategies, leading to a "feeding forward" process where each solution attempt informed further questioning, exploration, and refinement.The study highlights how PBL fosters essential 21st-century skills, such as adaptive reasoning and reflective practice, preparing future educators to guide their students through similarly complex, open-ended problems.We conclude that integrating puzzles into teacher education programs can enhance PTs' problem-solving abilities and equip them with strategies to foster a culture of inquiry and creative thinking in their future classrooms.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.008 | 0.013 |
| Scholarly communication | 0.005 | 0.004 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".