From Arithmetic to Algebra: Triangular Numbers, technology and ACODESA
Why this work is in the frame
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Bibliographic record
Abstract
The aim of this document is to address the articulation between arithmetic and algebra. The literature reports a discussion of arithmetic or algebraic thinking, not mentioning at all the importance of a pre-algebraic thinking related to an arithmeticalgebraic thinking. Through activities designed for this purpose, we propose a visual approach, with the intention of promoting mathematical visualization processes, which in turn constitute cognitive structures on the control exercised by students in solving a mathematical task. Our design is linked to a theoretical framework for action, collaborative learning (ACODESA) and use of technology in the mathematics classroom. In this study, we present our research project between Quebec and Mexico, but restrict ourselves to the results obtained with the Mexican population in relation to polygonal numbers in secondary school.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 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