Proportionality: problem-solving strategies used by Elementary School students in Quebec Proporcionalidade: estratégias utilizadas na Proporcionalidade: estratégias utilizadas na Fundamental no Quebec
Bibliographic record
Abstract
This study sought to determine the problem-solving strategies most used by 13- and 14- year-old 8th graders with regard to the concept of direct and inverse proportion. We also examined whether these students were able to recognize non-prortional contexts and specific challenges with regard to problem solving prior to learning the concept. Students from a Montréal, Québec Elementary School participated in this study. Our analysis revealed the used of several problem-solving strategies. The results show the potential and the diversity of the strategies employed prior to learning the concept of proportions and some of the challenges related to this concept. Keywords: Proportionality. Problem Solving. Mathematics Instruction. Nosso estudo tem como objetivo explicitar as estratégias usadas por alunos do ensino fundamental (6a série, 13-14 anos) no Quebec antes do ensino do conceito de proporção na escola. Mais especificamente, procuramos identificar as estratégias utilizadas pelos alunos para resolver problemas de proporção direta e inversa. Observaremos também se os alunos são capazes de identificar quais problemas são proporcionais e quais não são proporcionais. Por último, observaremos quais dificuldades aparecem quando os alunos resolvem problemas de proporção direta e inversa. Para isso, um estudo de caso foi feito com um grupo de alunos (33 alunos) de 6a série de uma escola de Montreal no Quebec. A análise realizada mostra que os alunos utilizam diferentes estratégias para resolver problemas. Os resultados obtidos mostram também o potencial e a diversidade das estratégias utilizadas antes do ensino formal da proporcionalidade na escola e as dificuldades presentes. Palavras-chave: Proporção. Resolução de Problemas. Ensino de Matemática.
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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 | 0.000 | 0.002 |
| 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 | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".