Encountering ideas about teaching and learning mathematics in undergraduate mathematics courses
Bibliographic record
Abstract
Abstract We study the ideas about teaching and learning mathematics that undergraduate students generate when they encounter tasks designed to embed approximations of teaching practice in mathematics courses taken by a general population of students. These tasks attend to the dual goals of developing an understanding of mathematics content and an understanding of how teachers provide classroom experiences that foster mathematics learning. The study employs a qualitative, multiple-case study methodology, with four cases bounded by the content areas of abstract algebra, single variable calculus, discrete mathematics, and introductory statistics. The data for the study come from undergraduate students’ written work on mathematical tasks, interviews with a subset of students from each course, and interviews with each instructor throughout the term during which they implemented the tasks. Our findings indicate that students identified the broad applicability of teaching skills (discussed by 32 of the 61 interviewed students), recognized the value of examining hypothetical learners’ mathematical work (discussed by 59 of the 61 interviewed students), and reported empathy for hypothetical learners (discussed by 38 of the 61 interviewed students). These findings persisted across the course content and course levels we studied, leading us to conclude that our findings can transfer to additional mathematics courses in secondary mathematics teacher preparation.
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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 | 0.009 | 0.026 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.007 | 0.003 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| 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".