Surprises in Elementary Mathematics Reform: Toward a Model of Situated Professional Development
Bibliographic record
Abstract
We engaged three elementary teachers in a reform-oriented professional development intervention in mathematics. The teachers work in an inner-city school with a student population exhibiting similar characteristics to students in border communities in the United States. Individual problem-solving sessions with four students in each of the teacher’s classrooms were videotaped, and over the course of eight weeks, we viewed the videoclips with the teachers in collaborative discussion sessions to observe and interpret their students’ solution strategies. Preliminary analyses of interview and classroom observation data indicate that our situated approach to professional development enhanced the teachers’ interest in learning about children’s thinking and helped them to recognize that mathematical understanding is constructed and not “received.†Moreover, our data indicated that our intervention gave them tools to discriminate among the various problem-solving strategies used by their students. Our journey toward a more relevant and personally meaningful approach to professional development for teachers of at-risk students is also reported.
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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 | 0.006 | 0.016 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.014 |
| Scholarly communication | 0.006 | 0.006 |
| Open science | 0.002 | 0.008 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".