Examining the Effect of Position in the Program on Performance in Discrete Mathematics
Bibliographic record
Abstract
The discrete mathematics component common to computer science programs is often a source of difficulty for students. Two common approaches have been to integrate the mathematics with computer science in a computer science course or requiring students to complete a discrete mathematics course from the mathematics department. Different approaches to instruction have been attempted with varying success. This paper reports the result of an investigation of student performance in discrete mathematics on the basis of the position in the program at which the student first attempts the discrete mathematics course offered by the mathematics department. The major sample includes 739 students over an 8-year period who first attempted the mathematics course in their first year, second year, or third year of the program. The analysis of the data indicated that there was a significantly better performance record for students who first attempted the course in their second or subsequent year. Analysis including 52 students in Spain found no significant difference between performance of first-year students in that country as compared to Canada. The conclusion reached is that position in the program is important and the increased maturity of students in second and subsequent years would indicate that the discrete mathematics course might best be placed in the second year rather than in the first.
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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 | 0.003 | 0.019 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".