Conceptual knowledge of arithmetic for Chinese- and Canadian-educated adults.
Bibliographic record
Abstract
This study investigated whether Canadian- and Chinese-educated adults differ in their understanding of simple arithmetic concepts. Participants (n = 21 per group) solved 3-term addition and subtraction (e.g., 5 + 22 - 22 and 3 + 24 - 26) and multiplication and division (e.g., 2 × 28 ÷ 28 and 4 × 39 ÷ 13) problems. All problems could be solved more easily if conceptual knowledge of the relationship between the 2 operations in each problem was understood and applied. Accuracy, solution time, and immediately retrospective self-reports of problem-solving strategy data were collected. Participants also completed a timed arithmetic fluency task. Chinese-educated participants demonstrated stronger conceptual understanding of arithmetic on all problems and outperformed Canadian-educated participants on the fluency task. A cluster analysis revealed 4 groups of individuals: weak concept users, who rarely used conceptual knowledge to aid their problem solving; strong concept users, who almost exclusively used their conceptual knowledge to facilitate problem solving; addition and subtraction concept users, who frequently used conceptual knowledge except on difficult multiplication and division problems; and multiplication and division concept users, who frequently used conceptual knowledge except on difficult addition and subtraction problems. Chinese-educated participants were more likely to be in the strong concept clusters, and none were in the weak concept cluster, providing further evidence of stronger conceptual knowledge of arithmetic. These results demonstrate for the 1st time that there are strong cross-cultural differences in conceptual knowledge of simple arithmetic, even in adulthood. (PsycINFO Database Record
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 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".