Extraneous Details on LEGO Bricks Can Prompt Children’s Inappropriate Counting Strategies in Fraction Division Problem Solving
Bibliographic record
Abstract
Extraneous details in visual representations can prompt children to use well-rehearsed, yet inappropriate, strategies that can hinder mathematics learning. Prior domain knowledge can reduce the negative effects of extraneous details in instructional materials. The present study tested whether prior knowledge of fractions and instruction on measurement division (MD) could overcome children’s inappropriate counting strategies when solving fraction division problems with images of LEGO® bricks. Fourth and fifth graders (N = 39) were randomly assigned to two instructional conditions: one that demonstrated how to solve fraction division problems using LEGO bricks that included explanations on MD concepts, and the other with the same demonstrations but without explanations. All participants then completed a task that measured whether the studs on the bricks prompted inappropriate counting when solving the problems. Almost one-third of the sample counted the studs to some degree. Greater prior knowledge of fractions concepts and knowledge of how to represent fractions with LEGO bricks were related to fewer inappropriate counting strategies, but contrary to expectations, fraction magnitude was not related. The two conditions did not differ on participants’ counting strategies. Extraneous details on LEGO bricks are related to the application of well-practiced counting strategies for children with lower domain knowledge.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| 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".