Teaching and learning mathematics through error analysis
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
For decades, mathematics education pedagogy has relied most heavily on teachers, demonstrating correctly worked example exercises as models for students to follow while practicing their own exercises. In more recent years, incorrect exercises have been introduced for the purpose of student-conducted error analysis. Combining the use of correctly worked exercises with error analysis has led researchers to posit increased mathematical understanding. Combining the use of correctly worked exercises with error analysis has led researchers to posit increased mathematical understanding. A mixed method design was used to investigate the use of error analysis in a seventh-grade mathematics unit on equations and inequalities. Quantitative data were used to establish statistical significance of the effectiveness of using error analysis and qualitative methods were used to understand participants’ experience with error analysis. The results determined that there was no significant difference in posttest scores. However, there was a significant difference in delayed posttest scores. In general, the teacher and students found the use of error analysis to be beneficial in the learning process.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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