Mathematical Thinking: Teachers Perceptions and Students Performance
Bibliographic record
Abstract
This paper was investigated the teachers rating of the six different aspects of mathematical thinking developed by the researcher: Searching for patterns , Induction, Deduction, symbolism, Logical thinking and Mathematical proof in relation to level of importance, level of difficulty, and time spent in teaching each aspect. This paper was also aimed to examine any possible consistencies and inconsistencies between teacher opinions about the level of importance of mathematical thinking aspects to mathematics achievement, level of difficulty and test data collected. Also, it was examined if the students were familiar with solving specific problems (such as rice problem) logical ways like searching for patterns rather than more traditional approaches and if they also applying the fourth step in problem solving according to Polya, (1990) (i.e., looking back (a checking the answer)). Key words: Mathematical thinking; Teacher perceptions; Students performance Resume Ce document a etudie la notation des six aspects differents de la pensee mathematique des enseignants developpe par le chercheur: la recherche de modeles, a induction, deduction, le symbolisme, la pensee logique et mathematique la preuve par rapport au niveau d'importance, le niveau de difficulte et le temps passe dans l'enseignement de chaque aspect. Ce document visait egalement a examiner toute consistances et des incoherences eventuelles entre les opinions des enseignants sur le niveau d'importance des aspects la pensee mathematique a la reussite en mathematiques, niveau de difficulte et les donnees recueillies lors des essais. En outre, il a ete examine si les eleves ont ete familiarises avec la resolution de problemes specifiques (tels que les problemes du riz) facons logiques, tels que la recherche de modeles plutot que des approches plus traditionnelles, et si ils ont egalement l'application de la quatrieme etape dans la resolution de problemes en fonction de Polya, (1990) (a savoir, en regardant en arriere (une verification de la reponse)). Mots cles: Pensee mathematique; Les perceptions des enseignants et le rendement des etudiants
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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 | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".