Different Procedures for Solving Mathematical Word Problems in High School
Bibliographic record
Abstract
The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. This kind of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school problems are solved by using basic arithmetic rules and in secondary school, the purpose is to generalize the resolution procedures through putting in practice algebraic procedures which turn to be more effective in terms of resolving word problem. This study attempts to analyse the procedures employed to solve mathematical problems by a sample of students in 9th and 10th grades of High School (N=406) from the Basque Country (Spain). For this purpose, the procedure used by the students when resolving three mathematical problems was examined and classified in three categories. These categories are related to the utilization of arithmetic rules or, as the case may be, algebraic procedures. The results indicate a significant relationship between the procedure used to solve the problems and educational level of the students. Educational implications of the findings are discussed.
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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 | 0.004 | 0.019 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".