Secondary-Level Student Teachers' Conceptions of Mathematical Proof.
Bibliographic record
Abstract
Recent reforms in mathematics education have led to an increased emphasis on proof and reasoning in mathematics curricula. The National Council of Teachers of Mathematics highlights the important role that teachers ’ knowledge and beliefs play in shaping students ’ understanding of mathematics, their confidence in and outlook on mathematics education, and their ability to use math to solve fundamental problems. It is crucial that teachers, especially the uninitiated, understand on a deep level the mathematical concepts that they are expected to teach to adolescents. Thus, it becomes critical for teacher educators to assess the understanding and abilities of student teachers in constructing mathematical proof. The analysis in this study is based on three factors: 1) meaning of proof, 2) ideas about teaching methods on proof, and 3) ideas about the use-fullness of proof in a mathematics classroom. An analysis of the data collected from this study indicates that current student teachers ’ conceptions of mathematical proof are limited. The uneasiness expressed by student teachers about mathematical proof may suggest an examination of students ’ experiences with the mathematical proof in both secondary and post secondary classrooms.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".