Shifts in meta-level learning agreement during mathematics peer learning: integrating positioning theory and commognitive framework
Bibliographic record
Abstract
Abstract Symmetric positional structures are often seen as conducive to peer learning, yet some argue that asymmetric expert–novice dynamics are essential in contexts such as meta-level learning, in which students shift to more advanced mathematics discourses. In this study, we investigate positioning dynamics within the context of meta-level peer learning through a case study of two 9th graders, Orna and Tamara, who participated in interviews and a peer activity aimed at shifting from visually based Configural discourse to Deductive discourse in geometry. We integrate Positioning Theory with the Commognitive framework to define the Meta-level Learning Agreement (MLA) as consisting of three components: (1) agreement on the leading discourse, (2) agreement on positions, and (3) agreement on the course of action. In their stories about peer learning during interviews, the students echoed divergent storylines: Tamara maintained a fixed expert–novice storyline, consistently positioning herself as expert, while Orna embraced a more flexible collaboration storyline. These differences played out dynamically during two meta-level shifts occurring within their peer interaction. When Configural discourse led, Tamara’s fixed expert positioning steered the solution. But once Orna began prioritizing Deductive discourse, she resisted Tamara’s position as expert. Full MLA agreement was reached only after instructor interventions, when both students prioritized Deductive discourse, agreed on a deductive course of action and assumed symmetrical co-constructor positions. These findings illuminate how symmetric and asymmetric structures function in meta-level peer learning and how mathematics discourse and positioning reciprocally shape one another. We discuss the study’s contribution to peer learning research.
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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 | 0.008 | 0.025 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.005 | 0.004 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.001 | 0.002 |
| 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".