The Presence of Diagrams and Problems Requiring Diagram Construction: Comparing Mathematical Word Problems in Japanese and Canadian Textbooks
Bibliographic record
Abstract
Abstract It is generally considered beneficial for learners to construct and use appropriate diagrams when solving mathematical word problems. However, previous research has indicated that learners tend not to use diagrams spontaneously. In the present study, we analyzed textbooks in Japan and Canada, focusing on the possibility that such inadequacy in diagram use may be affected by the presence (or absence) of diagrams in textbooks, the kinds of diagrams that are included, and whether problems requiring the construction of diagrams are provided in those textbooks. One set each of Japanese and Canadian elementary school textbooks were analyzed, focusing on the chapters dealing with division. Results revealed that the Japanese textbooks contain worked examples and exercise problems accompanied by diagrams more than the Canadian textbooks. Furthermore, the Japanese textbooks often use line diagrams and tables that abstractly represent quantitative relationships and they include more problems that require students to use diagrams. However, to encourage students to use diagrams spontaneously, it may be necessary to include problems that scaffold the use of diagrams in a step-by-step manner in both the Canadian and the Japanese textbooks.
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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 | 0.002 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.006 | 0.011 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".