Mimicry of proofs with computers: the case of Linear Algebra
Bibliographic record
Abstract
This article examines the idea of 'following the flow of a proof with an example' in order to assist the learner in the challenging task of understanding mathematical proofs. This strategy is termed 'mimicry of a proof'. However, such mimicry can be impractical or unreasonably demanding when the mathematical objects in the proof are difficult to manipulate without technological enhancement. This is the case with many proofs in Linear Algebra, in which the manipulated objects are vectors or matrices. Therefore, the article focuses on the idea of proof mimicry with a computer algebra system (CAS). As examples, this strategy is applied to the proofs of two theorems: the basis theorem and the orthogonalization theorem. In addition, pedagogical guidelines to be followed in constructing a set of computer activities for students are presented and examined.
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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 | 0.005 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.011 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".