Does Practice and Knowledge Equal Knowledge and Practice
Bibliographic record
Abstract
Debate surrounds the value of procedural practice in learning conceptual material in mathematical domains (Schoenfeld, 2004).We investigated whether purely procedural practice could lead to conceptual gains and explored cognitive load theory as a mechanism for those gains (Sweller, 1988).In a laboratory experiment, 93 undergraduates practiced a procedure by solving 30 problems of an algebra analog and were given conceptual tests before, during and after practice.The conceptual tests tapped students' understanding of the underlying structure of the domain.Participants' conceptual knowledge increased with procedural practice, particularly between no practice and some practice.Consistent with cognitive load theory performance on the conceptual test after practice was significantly related to procedural performance at the end of practice.However, this relationship between procedural learning and conceptual learning only held if participants had been alerted earlier in practice to the conceptual nature of the task.These results are consistent with the proposal by Rittle-Johnson, Siegler, & Alibali, ( 2001) that there is an iterative relationship between conceptual understanding and procedural skill.
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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 | 0.012 | 0.084 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.017 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.004 | 0.002 |
| Insufficient payload (model declined to judge) | 0.014 | 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".