The right answer for the wrong reason: how prospective teachers leverage pedagogical opportunities
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Responding to the pedagogical opportunities afforded by student thinking allows teachers to develop mathematical understanding that is directly related to students’ intellectual needs. Knowing which instances of student thinking provide such opportunities, however, is not always clear – and neither is the most effective way to leverage this thinking. Using a novel type of scripting task, our study explores how prospective teachers (n=35) would respond to a student’s strategy that produces a correct answer via incorrect reasoning. We first categorise participants’ responses according to whether they recognise this opportunity as a Mathematically Significant Pedagogical Opportunities to Build on Student Thinking (Leatham et al., Citation2015); for those that did, we next examine the means by which they seek to engender a sense of disequilibrium in the student-characters of their scripts.
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.
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 | 0.006 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 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 it