Teachers' Perspectives and Pedagogical Documentation in Early Years Mathematics: Tensions and Possibilities
Bibliographic record
Abstract
In this dissertation, I endeavour to explore the transformative potential of pedagogical documentation in early years mathematics education with a focus on the implementation challenges and divergent perspectives within the context of the Ontario Kindergarten Program (2016). Pedagogical documentation offers teachers an opportunity to explore the possibilities of children’s theories, while challenging discourses that underscore neoliberalist practices. Pedagogical documentation includes collecting materials (e.g., photos, videos, written transcriptions, etc.) to be revisited and considered by students and educators together, to create pedagogical trajectories that are emergent and responsive. This study examines the perspectives of 12 Ontario Kindergarten teachers regarding pedagogical documentation in their kindergarten math classrooms, revealing tensions and inconsistencies with the literature and practices as outlined in the Ontario Kindergarten Program (2016) document. The teachers convened for ten weeks where video and audio recordings of every meeting were kept. Teachers examined two specific examples of pedagogical documentation of learning events. ‘The Price of Apples’ documentation portrayed three children engaged in a learning event about selling apples (Appendix A). ‘The Columns of the Municipal Theatre’ documentation portrayed a class visiting the columns outside a municipal building in their town (Appendix C). Through phenomenography-inspired analysis, the data demonstrated how the participants thought about pedagogical documentation as a way to collect evidence of student ideas. Interestingly, an analysis of high-frequency words uncovered key terms such as ‘centres’, ‘grades’, and ‘values’ that stand out in contrast to existing literature on pedagogical documentation. The results of this study indicate that participants used pedagogical documentation to capture evidence of student ideas, however, they did not speak of pedagogical documentation as a “way of being” with children, as a practice that nourishes emergent curriculum making, or as a method to build upon students’ mathematical ideas. This research not only exposes the tensions and inconsistencies in the use of pedagogical documentation within the Ontario Kindergarten program, but also contributes to the discourse by highlighting nuanced perspectives of the participants. In turn this paves the way for a more comprehensive understanding of the transformative potential of pedagogical documentation in early years mathematics education.
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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 | 0.026 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.027 | 0.046 |
| Scholarly communication | 0.019 | 0.012 |
| Open science | 0.002 | 0.012 |
| Research integrity | 0.004 | 0.007 |
| 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".