Teaching undergraduate mathematics fully online: a review from the perspective of communities of practice
Bibliographic record
Abstract
Abstract The use of fully online (FO) mathematics teaching has been increasing worldwide. Despite claims and findings that mathematics is more challenging to teach FO than face-to-face (F2F), we know little about FO mathematics teaching. In this paper, we address this gap by working to elucidate the differences between teaching in the FO and F2F modalities. We do this by examining FO and F2F teaching from the perspective of Communities of Practice (Wenger, Social learning systems and communities of practice, 2010) by comparing and contrasting current FO practices (or “ways of doing”) in thegeneralundergraduate education communitywithcurrent F2F practices in the undergraduatemathematicscommunity. We identify six key differences between the two paradigms, which we recast to spotlight areas for technological and pedagogical development.
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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 | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.006 | 0.006 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".