Unifying dialogic learning and mathematics learning: A discursive lens for the study of dialogic mathematics peer learning
Why this work is in the frame
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Bibliographic record
Abstract
Background Although it has been suggested that peer interactions that are meaningful both mathematically and dialogically are rare, not much is known about them. We draw on commognition to suggest a unified definition of dialogic mathematics peer learning as a peer interaction including two features: (a) a shift from familiar ways and rules of doing mathematics to newer, more developed ones; (b) openness to and critical engagement with each other’s suggestions that involves reliance on the more developed rules.Method We empirically demonstrate the affordances of the suggested lens by micro-analyzing five dyadic interactions of middle-school students working on a geometric task designed to encourage a shift from familiar visual/configural ways of doing geometry to more developed deductive ones.Findings Only one out of the five interactions included both features of dialogic mathematics peer learning; three interactions lacked both features; and one interaction included the openness and critical engagement feature but still not the mathematical shift feature.Contribution The paper provides discursive conceptual and methodological tools for examining the intersection between two important strands of the learning sciences—mathematics learning and dialogic learning—as well as empirical and practical conclusions that foreground the complexity and fragility of this intersection.
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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 | 0.022 | 0.014 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.004 |
| 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