One is Not Born a Mathematician: In Conversation with Vasily Davydov
Bibliographic record
Abstract
That mathematics education has been one of the central concerns of educational systems worldwide is no secret. It is also an established consensus that as far back as eighty years ago, Russian psychologists such as Vygotsky, Luria, Meshcheryakov, and Davydov have pioneered work that contributed to the understanding of teaching and learning and shifted the trajectory of schooling in the Western World. Looking back, we feel that there is more to this legacy that awaits to be further explained and extended to potentially address some of the pressing issues in mathematics education. To bring forth this legacy, the authors engage in an imaginary conversation with Vasily Davydov to tease out notions that include, inter alia, language and interaction, learning and teaching, and empirical and theoretical thinking. The utilisation of a conversation as a method of inquiry for the purpose of this paper was intentional as it not only encompasses the very method of teaching advocated by Davydov, thus conveying that the means is the message, but it is also conducive to the exploration of simultaneously surfacing ideas and phenomena. The questions asked, clarifications provided, and contradictions that still remain chart a map that displays theoretical vistas and empirical landscapes drawn and inspired by Davydov's legacy. Specifically, Fellus and Biton bring forth citations from Davydov's works that are used as signposts in the conversation that unfolds.
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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 | 0.012 | 0.042 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.016 | 0.020 |
| Scholarly communication | 0.012 | 0.013 |
| Open science | 0.002 | 0.007 |
| Research integrity | 0.007 | 0.022 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".