An Enactivist Perspective on Teaching Mathematics: Reconceptualising and Expanding Teaching Actions.
Bibliographic record
Abstract
We reject a trajectory approach to teaching that classifies good and bad teaching actions and seeks to move teachers' practices from one of these poles to the other. In this article we offer instead a conceptualisation of mathematics teaching actions as a landscape of possibilities. We draw together terms commonly used in the literature to describe teaching strategies, and add our own, to offer an expanded view of teaching actions. We illustrate each with data extracts drawn from our various studies of mathematics teachers and classrooms, and explain how a range of teaching actions can be woven into a coherent teaching practice. Note that we are not talking about growth in teaching in this paper, nor about change in teachers' practice over time. We aim to simply talk about and conceptualise teaching in ways that can broaden our understanding of it.
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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 | 0.013 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.007 | 0.066 |
| Scholarly communication | 0.015 | 0.017 |
| Open science | 0.003 | 0.013 |
| Research integrity | 0.004 | 0.007 |
| 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".