An analysis of the relationship between high-school pre-calculus and university calculus grades
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
First-year mathematics instructors at universities across North America and the globe have been noticing a decline in the mathematics skills and preparation of their incoming students, who have been failing out of first-year mathematics courses at alarming rates. Though some universities have implemented placement or diagnostic tests to measure students’ preparedness, many still use high school grades as the only indicator of readiness for university mathematics. However, researchers have questioned how effective these high school grades are at predicting success in university mathematics classes due to factors such as mis-aligned teaching methods, curriculum, and grade inflation. This study analyzes the relationship between grade 12 Pre-Calculus grades and first year university Calculus grades at a large Canadian university over the period from 2001–2015 in an attempt to quantify previous research in a large-scale, longitudinal manner. Results show that there is a significant disconnect between these grades, that the disconnect has been growing over time, and that it is is quite significant for students who are not performing well at the Calculus level. Recommendations moving forward include the implementation of placement examination in a wide-scale manner, and increased communication and collaboration between K-12 and university mathematics educators and administrators.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.039 | 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