The Structure of Students’ Mathematical Errors in Solving Calculus Problems Based on Cognitive Style
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Bibliographic record
Abstract
The understanding mathematical concept is an error that often occurs in classroom learning among students when solving mathematical problems. The most difficult part for students is solving problems, because it requires numeracy skills, high concept mastery, as well as the ability to use good language, and so on so that students don’t make any more mistakes when working on math problems. Student errors in solving mathematics problems are (1) errors in connecting concepts, (2) errors in operations and (3) errors in constructing concepts. The problem is what is the structure of students’ mathematical misconceptions in solving mathematical problems based on cognitive style. The method in this research, namely an exploratory descriptive approach, aims to determine the structure of students’ errors based on cognitive style in solving mathematical problems. Analysis of research data, namely: (1) Data reduction, (2) Data exposure, (3) data triangulation and (4) drawing conclusions. The cognitive styles referred to are field dependent and independent. The conclusions are (1) the structure of conceptual errors with an applied field dependent cognitive style begins with disequilibrating, then solving by linking applicable concepts, and (2) the structure of conceptual errors with a field independent cognitive style begins with disequilibrating, then solving using analyse.
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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 | 0.000 | 0.003 |
| 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