INTERPRETAÇÕES DO INFINITO MATEMÁTICO A PARTIR DA EPISTEMOLOGIA GENÉTICA
Bibliographic record
Abstract
In this report, we present a study about the mathematical infinity with regard to the Genetic Epistemology. Through the Piagetian clinical method, an explorato-ry study was carried out to understand the different conceptions about the mathematical infinity. The subjects were between 13 and 73 years old and they have been addressed to manipulate concrete experiments and then have been asked to respond to a semi-structured interview. Using mathematical tests in which the results tend to infinity or to very large numbers, we notice how the subject faces a feasibility issue without having a concrete material to handle. Regarding the results, we find out three levels of understanding on the theme: Inconceivable Existence, Existence little conceivable and Infinite as a representa-tion of something that has no end. We found that the notion of the mathemati-cal infinity did not depend on age, degree of education or professional area of the participants and we conclude that this notion is constructed by different levels of the thought. The presented study could be useful for teachers of basic and higher education, since it exposes how the interviewees organize its thoughts when facing the addressed issues.
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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 | 0.009 | 0.026 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.002 | 0.019 |
| Scholarly communication | 0.007 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".