A Culturally Responsive Framework for Critically Examining Priorities in Approximations of Practice
Bibliographic record
Abstract
A recent focus in research is for mathematics teacher educators (MTEs) to examine the approximations of practice they use to build prospective teachers' (PTs) knowledge and pedagogies for mathematics teaching. This chapter focuses on conducting an audit, or analysis, of the approximations of practice that the first author used to structure learning opportunities during secondary mathematics education coursework in a university-based classroom. Through a critical examination of her approximations, she identifies the strengths and shortcomings in PTs' opportunities to develop culturally responsive pedagogies (CRP). By drawing on a recently developed CRP self-study framework, along with the second author's critical friend contributions, the authors conclude that MTEs should examine opportunities for expanding teacher modeling of CRP practices, as well as collaborate with PTs to collectively brainstorm and problem solve together to enact practices in ways that move beyond what all parties have experienced previously, or are capable of creating individually.
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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 | 0.043 | 0.045 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.007 | 0.005 |
| Science and technology studies | 0.010 | 0.093 |
| Scholarly communication | 0.021 | 0.020 |
| Open science | 0.005 | 0.011 |
| Research integrity | 0.004 | 0.010 |
| Insufficient payload (model declined to judge) | 0.004 | 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".