Cognitive Models of Task Performance for Mathematical Reasoning
Bibliographic record
Abstract
It is an understatement to say that mathematical knowledge and skill are valuable for the jobs and careers of the twenty-first century. In fact, they are essential for individuals who want to have the widest array of career options available and a high quality of life. Learners who shun mathematics shut themselves off from many lucrative career paths. According to a recently published article in the Wall Street Journal (Needleman, January 26, 2009), “Doing the Math to Find Good Jobs,” the best occupations in America all required advanced mathematics. According to data compiled by the U.S. Bureau of Labor Statistics and Census, the top five jobs in a list of two hundred included mathematician, actuary, statistician, biologist, and software engineer. These jobs were rated highest because they combined large salaries with desirable working conditions, namely, indoor office environments, unadulterated air, absence of heavy lifting and physical hardship, and conveniences such as controlling one's work schedule. The worst jobs were lumberjack, dairy farmer, taxi driver, seaman, and emergency medical technician. Most of the jobs at the lower end of the list did not require advanced mathematics. The importance of mathematics for maximizing the likelihood of obtaining a desirable job in the future would make one think that students, desirous of having an edge for a future career, would be clamoring to learn and perform as well as possible in mathematics. Yet this is not the case.
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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 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.022 | 0.003 |
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".