Improvisational coactions and the growth of collective mathematical understanding
Bibliographic record
Abstract
In this paper we consider the phenomenon of the growth of collective mathematical understanding and explore its dependence on the particular way that a group of learners work together collaboratively. We label this group process as improvisational coaction. In an earlier paper (Martin, Towers and Pirie, 2006) we drew on the theoretical work of Becker (2000 Becker, H. 2000. The etiquette of improvisation. Mind, Culture, and Activity, 7(3): 171–6. [Taylor & Francis Online] , [Google Scholar]), Sawyer (2001 Sawyer, R. K. 2001. Creating conversations: Improvisation in everyday discourse, Cresskill, NJ: Hampton Press. [Google Scholar], 2003 Sawyer, R. K. 2003. Group creativity: Music, theatre, collaboration, Mahwah, NJ: Lawrence Erlbaum Associates. [Crossref] , [Google Scholar], 2004 Sawyer, R. K. 2004. Creative teaching: Collaborative discussion as disciplined improvisation. Educational Researcher, 23(2): 12–20. [Google Scholar]), and Berliner (1994 Berliner, P. 1994. Thinking in jazz: The infinite art of improvisation, Chicago: University of Chicago Press. [Crossref] , [Google Scholar]) in improvisational jazz and theatre, to characterise the growth of collective mathematical understanding as a creative and emergent improvisational process. Here, we extend that conceptual analysis to a yet-finer grain to explore one element of that framework, improvisational coaction, and its relationship to the growth of mathematical understanding at the level of the group. In particular we identify improvisational coaction as a particular form of interaction, and through using data extracts we derive four characteristics of the phenomenon and consider how these occasion the growth of collective mathematical understanding.
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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 | 0.008 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.005 | 0.018 |
| Scholarly communication | 0.010 | 0.016 |
| Open science | 0.002 | 0.015 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".