Teacher candidates' online math journals: a search for pedagogical surprise
Bibliographic record
Abstract
Surprise and insight are an integral part of doing mathematics. However, surprise does not appear to be on the radar of most mathematics curriculum documents. In this paper, we present an analysis of TCs' online journals and their associated online discussions from a K-6 mathematics teacher education blended course. This online component of an otherwise face-to-face course also included readings and viewings of documentaries from classroombased research, along with mathematician interviews, animations, and other support material (available at researchideas.ca/wmt), which connected to, and extended face-to-face course activities. We address the question: How did this limited online experience affect TCs’ thinking about mathematics teaching and learning? Participants were 168 K-6 TCs, distributed among six sections of a mandatory mathematics methods course. We employed a case study approach and qualitative content analysis of TC discussions of journals and related online resources, and we identified six themes: (1) low floor, high ceiling approach; (2) contrast with personal math learning experience; (3) visual and concrete representations; (4) real world contexts; (5) aesthetic math experience; and (6) sharing math experiences.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".