Operand–operator compatibility in cognitive arithmetic.
Bibliographic record
Abstract
Adults' simple addition performance (e.g., 3 + 4 = ?) is faster, more accurate, and more often based on direct memory retrieval (rather than a procedural method, such as counting) when problems are presented in digit format (3 + 4) than written-word format (three + four). A possible explanation is that the mathematical symbol + is more compatible to memory retrieval with Arabic numerals than word numerals. To investigate this, two groups of 42 participants received eight blocks of 72 simple addition problems. For one group, operand format (digits or words) switched across trials within each block and operator (the symbol + or the word plus) alternated between blocks. For the other group, operator switched across trials, whereas operand format alternated between blocks. In the switch-format condition, compatible formats (e.g., 3 + 4, three plus four) were solved by direct memory retrieval more often than were incompatible formats (3 plus 4, three + four). There was no compatibility effect on use of direct memory retrieval when operand format was fixed within blocks and operator format switched across trials. There was also a reaction time (RT) advantage only for digit operands with + relative to plus when format switched, but + facilitated only word problems when operand format was blocked. The results indicate that operand-operator compatibility and format switching had previously unsuspected effects that qualify previous research examining format effects in arithmetic.
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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 | 0.016 |
| Meta-epidemiology (narrow) | 0.000 | 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 | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.007 | 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".