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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".