The role of working memory in mental arithmetic
Why this work is in the frame
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Bibliographic record
Abstract
We reviewed the literature on the role of working memory in the solution of arithmetic problems such as 3 + 4 or 345 + 29. The literature was neither comprehensive nor systematic, but a few conclusions are tenable. First, all three components of the working memory system proposed by Baddeley (i.e., central executive, phonological loop, and visual‐spatial sketchpad) play a role in mental arithmetic, albeit under different conditions. Second, mental arithmetic requires central executive resources, even for single‐digit problems. Third, further progress in understanding the role of working memory in arithmetic requires that researchers systematically manipulate factors such as presentation conditions (e.g., operand duration, format), problem complexity, task requirements (e.g., verification vs production), and response requirements (e.g., spoken vs written); and that they consider individual differences in solution procedures. Fourth, the encoding‐complex model (Campbell, 1994) seems more likely to account for the variability observed in arithmetic solutions than other models of numerical processing. Finally, working memory researchers are urged to use mental arithmetic as a primary task because the results of the present review suggest that solution of problems that involve multiple digits are likely to involve an interaction of all the components of the working memory system.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 it