The Effects of Proof Features and Question Probing on Understanding Geometry Proof
Bibliographic record
Abstract
This study aims to investigate how the written formats, complexity of proofs and the types of understanding questions affect students' understanding of geometry proof. Theoretically, Duval's three levels of organizing statements - micro, local and global, are applied to assess 153 ninth graders' understanding of geometry proof. The results show (a) there was no interaction among written formats, complexity of proofs, and types of understanding questions in terms of students' understanding of geometry proof; (b) local understanding is the easiest for students; (c) the effects of the complexity of proofs on local and global understanding were statistically significant. It is noted that the generalizability of the results is limited by the task of proof texts without their corresponding propositions. The factor mixing proof steps and familiarity of propositions should be taken into account while arranging learning sequence of reading proofs. Afterward, further research is proposed in this paper.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".