Using Pictorial Maps to Scaffold Problem Solving in Primary-Grade Arithmetic
Bibliographic record
Abstract
In this study, primary-grade students learned to solve and create arithmetic word problems using a three-phase process of visual representation. The study compared an experimental group (n=32) of third graders in Thailand using pictorial maps with a control group (n=31) using text-based problems. The visual representations called pictorial maps are unique in that they focus on place (location) in order to situate math problems in authentic contexts. In phase 1, students were given a pictorial map with imprinted objects representing keywords to help them solve a word problem. In phase 2, they used a blank pictorial map on which they could place plastic chips with imprinted images representing the problem’s keywords. In phase 3, they used a blank sheet with cut-outs of images representing keywords that they could use to represent their own word problems. Results revealed significantly higher post-test scores for the experimental group. Implications point to the value of mathematics’ teachers working with art teachers in their school to identify ways to use drawing to support representations of keywords and of other elements in word problems.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".