Documenting Knowing-in-Action: A Mathematics Teacher’s Curricular Decision-Making Images
Bibliographic record
Abstract
Research on mathematics teacher curricular decision-making has focused more on what decisions teachers make and less on how teachers make curricular decisions. Teaching images are a well-known concept in teacher education as a form of teachers’ practical knowledge (PK) and threads that connect teachers’ past experiences to action in the present moment. In this study, I built on a three-year relationship with a veteran secondary mathematics teacher to construct her curricular decision-making images. I used a narrative inquiry methodology to interact and construct data alongside the teacher while she planned and taught a mathematics lesson. Data consisted of transcripts of conversations between the teacher and me, and my weekly journals. A narrative analysis revealed two teaching images: bringing the outside inside and reading students and moments. The teacher made decisions informed by past and in-the-moment teaching experiences, as well as personal commitments such as portraying students as professionals. Teacher images allow mathematics teacher educators and researchers to communicate how teachers make curricular decisions by working alongside teachers. This study contributes to curricular decision-making research by offering images as a form of PK that communicates practicing mathematics teachers’ knowledge-in-action. Keywords: mathematics teachers, curriculum decision-making, practical knowledge, teacher images, narrative inquiry
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 teacher head, 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".