Aspects that Affect Whole Number Learning: Cultural Artefacts and Mathematical Tasks
Bibliographic record
Abstract
Abstract The core of this chapter is the notion of artefact, starting from the discussion of the meaning of the word in the literature and offering a gallery of cultural artefacts from the participants’ reports and the literature. The idea of artefacts is considered in a broad sense, to include also language and texts. The use of cultural artefacts as teaching aids is addressed. A special section is devoted to the artefacts (teaching aids) from technologies (including virtual manipulatives). The issue of tasks is simply skimmed, but it is not possible to discuss about artefacts without considering the way of using artefacts with suitable tasks. Some examples of tasks are reported to elaborate about aspects that may foster learning whole number arithmetic (WNA). Artefacts and tasks appear as an inseparable pair, to be considered within a cultural and institutional context. Some future challenges are outlined concerning the issue of teacher education, in order to cope with this complex map.
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.003 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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".