Using “Tapestries” to Document the Collective Mathematical Thinking of Small Groups
Bibliographic record
Abstract
A challenge in mathematics education research has been to document the complex nature of collective mathematical learning. This paper describes a method of data analysis that offers a visual representation of collective discourse during mathematical tasks. Using data extracts from a study of small groups in a middle years classroom, I color code collective utterances to create a “tapestry,” a type of transcript that offers researchers the ability to move between individual and collective planes of focus during analysis. The nature of collective thinking is revealed by tapestries, including how utterances bump against each other, the role of utterances evolves as the context of discussion changes, and the potential for self-structuring within collective discourse.
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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 | 0.009 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.004 | 0.008 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.006 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".