Developing a tutorial to address student difficulties in learning curl: a link between qualitative and mathematical reasoning
Bibliographic record
Abstract
Many university students have difficulty understanding the concept of curl in our upper-level mechanics courses. This difficulty poses considerable problems when students learn upper-level physics, as the concept of curl is closely related to a wide variety of topics in physics, such as Maxwell’s equations, Faraday’s law, and conservative fields. However, few studies have considered the reasons that students experience difficulty or ways to help students overcome their difficulty grasping the notion of curl. Therefore, in this study, we try to address student difficulty in learning curl. First, we developed a questionnaire to investigate student difficulties in understanding curl and to obtain comments on a tutorial. The questionnaire involved an explanation and a Likert scale form (degrees 0 to 4). We administered a diagnostic test in which we posed two kinds of curl problems. As a result, students who showed qualitative reasoning to solve two types of curl problems were better at solving a curved-line problem than they were at solving a straight-line problem. In contrast, students who showed mathematical reasoning were better at solving the straight-line problem. Based on these results, we developed a tutorial to aid students in using both qualitative and mathematical reasoning. Use of the tutorial enhanced students’ explanations about the curl concept and increased a percentage of correct answers.
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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 | 0.005 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".