Bidirectional associations in multiplication memory: Conditions of negative and positive transfer.
Bibliographic record
Abstract
A variety of experimental evidence indicates that the memory representation for multiplication facts (e.g., 6 x 9 = 54) incorporates bidirectional links with a forward association from factors to product and a reverse association from product to factors. Surprisingly, the authors did not find evidence in Experiment 1 of facilitative transfer-of-practice from multiplication (6 x 9 = ?) to factoring (54 = ? x ?); in fact, multiplication practice produced item-specific interference with factoring. Similarly, the authors found no evidence in Experiment 2 that repetition of specific factoring problems (54 = ? x ?) facilitated performance of corresponding multiplication problems (6 x 9 = ?). In Experiment 3, participants practiced both multiplication and factoring and presented facilitative transfer in both directions. Thus, bidirectional facilitation occurred if both operations were practiced, but interference occurred when only one operation was practiced. We propose that this seemingly paradoxical behavior occurs because it is adaptive for the bidirectional retrieval structure to retain operational flexibility in the context of practicing both operations, whereas it is adaptive to specialize the memory representation for the practiced operation (i.e., factoring or multiplication) when only one operation is practiced.
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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 | 0.004 | 0.027 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.011 | 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".