Teachers' reported understanding and implementation of a new grade 8 mathematics curriculum
Bibliographic record
Abstract
This dissertation is a two-stage qualitative examination of the interpretation and implementation of mathematical reform in Grade 8 classrooms in four regions of Ontario. It is also an examination and amplification of M. Simon's (1995b; 1997) theoretical model of reform-based mathematical instruction. Eighteen teachers were selected from a wider group who had voluntarily participated in the Impact Math workshops that had been designed by the Ontario Institute for Studies in Education to support mathematical reform in Grades 7 and 8. The teachers selected were those most likely to be using the Impact Math curriculum units and the new Ontario curriculum as intended, that is, in a reform-based instructional manner. The theoretical underpinnings and classroom interpretation of reform-based instruction vary widely in the research literature. In this study Simon's theoretical model was linked to codes of expected classroom practice drawn from the literature on reform instruction. This model and attendant codes were used to analyze the first stage data. The analysis revealed that the teachers could be loosely grouped into three patterns of mathematical reform interpretation and implementation: surface reform, mixed practice and substantive reform. In all three patterns, teachers espoused the basic tenets of reform but implemented it to varying degrees, from superficial to substantive. The coded model was used to develop a detailed description of each of these three patterns. Three teachers were chosen from the mixed practice pattern for a second stage of in-depth case study. The analysis of the second stage data (extended in-class observation and interviews) reaffirmed the finding that although all of the teachers espoused mathematical reform instructional methods—their interpretation varied in distinctive ways. The model worked well to identify the factors (e.g. teachers' own mathematical knowledge, teachers' concept of worthwhile mathematical discussion or, lack of time) that were particularly important in influencing the teachers' interpretation and implementation of reform practice. The interplay of these identified factors and teachers' instruction have implications for mathematical reform beyond this study. Modifications were made to the Simon model to make it a more effective research tool in further studies of reform instruction. Recommendations for further research are discussed.
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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 | 0.003 | 0.015 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".