Researching Mathematics Pedagogy
Bibliographic record
Abstract
The Observing Teachers project involved working with groups of middle school mathematics teachers in different regions of Canada to construct videos representing their practice. Groups then worked together to select videos that were typical of their region to be sent to teachers in other regions. The same groups then discussed the videos received from other regions. This research design drew on enactivist principles. In this chapter, we draw on these principles to reflect on some of the challenges that arose in implementing the project. In particular, we refer to three aspects of enactivist research highlighted by Simmt and Kieren (2015): the role of observers, the relationship between ontology and epistemology, and the role of ethics. Thinking about these ideas led us to notice four emergent themes relating to the process of enacting the project: researcher-teacher-learner relationships; unexpected events; learning to be a researcher; and insiders-outsiders. Underlying these themes is the importance of relationships in the conduct of research with mathematics teachers.
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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 | 0.004 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.005 | 0.015 |
| Scholarly communication | 0.008 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| 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".