Bibliographic record
Abstract
Abstract Learning is here considered to have taken place when someone has developed the habit, propensity, and disposition to attend productively to things not previously noticed, and in ways not previously experienced, to do with some specific and particular content. ‘Active learning’ sounds like a tautology, but was introduced as a contrast to the more passive activity of students sitting in lectures listening and transcribing mathematics written on a board or screen onto their own paper. The stance taken here is that effective and efficient learning involves active engagement in activity, but includes enculturation through being in the presence of a relative expert1 who themselves is manifesting mathematical thinking, not simply passing on the records of the results of previous mathematical thought. Such ‘passivity’ does not necessarily require intention. Following Bennett2 actions are here taken to involve three agents or impulses: initiating, responding, and reconciling or mediating. All three agents are thus active, but in different ways. Interactions intended to contribute to learning are considered to be actions, and so involve three agents: learner, teacher (in some manifestation), and mathematical content, all within a culture or ethos. Since there are six different ways in which the triple of agents can be assigned to the triple of impulses, six different modes are possible. Analysing these modes sheds light on different ways in which learning could be said to be ‘active’. Activity takes place within a mode of interaction. Again following Bennett, effective activity is here taken to require appropriate relationships among the gap between current state and intended goal, the resources available, and the tasks set. 1Vygotsky (1978) pointed out that ‘higher psychological processes’ are first encountered in others. 2Bennett (1993); see also Shantock Systematics Group (1975)
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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 | 0.017 | 0.042 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.006 | 0.067 |
| Scholarly communication | 0.020 | 0.037 |
| Open science | 0.002 | 0.009 |
| Research integrity | 0.011 | 0.010 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
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".