Linear algebra learning focused on plausible reasoning in engineering programs
Bibliographic record
Abstract
A methodological strategy is proposed for the teaching of Linear Algebra in engineering programs focused on plausible reasoning. These concepts were developed by [1] and [2], through the formulation and adaptation of interesting problems, whose design admitted a didactic model and a methodological procedure for the generation of conjectures through the mediation of technology and geometric visualization as key factors in the construction of the main concepts of the discipline by the students. The difficulties in the teaching and learning of Linear Algebra have been studied since last century, in particular since the nineties. The LACSG (Linear Algebra Curriculum Study Group) in the USA is a reference point. On the other hand, Anna Sierpinska and Jean-Luc Dorier lead another group in Canada and Europe. Both groups coincide that one of the greatest problems in the teaching and learning of Linear Algebra is the formal approach of the classes that are traditionally taught. The starting point of this study is the great difficulties students experience when assimilating definitions, theorems and demonstrations, which are elusive for the future engineers.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 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".