Understanding Dimensions of Student Readiness from a Calculus Baseline Assessment Through Semi-Automatic Text Analysis and Clustering
Bibliographic record
Abstract
In this article, we introduce a diagnostic tool that is intended to gauge the level of preparedness for students who are beginning their first undergraduate calculus course. The results gathered by this tool form a multi-dimensional view of student readiness through the qualitative coding of “explain your reasoning” prompts that are paired with multiple choice questions (MCQs). The codes are categorized into a taxonomy that gauge and observe various student skill sets. Manually coded responses are used as a training set for the fitting of a gradient boosting machine (GBM) model, which automatically codes responses at a fixed cost. Compared against a manual coder’s assessment of a held-out validation, the automatic coder averaged over 80% matching accuracy. Using these qualitative codes as vector dimensions, k-clustering of student demographic allows for the visualization of distinct snapshots of diverse student skill sets that exist within a large first-year undergraduate math class. These visualizations are generated as spider plots.
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How this classification was reachedexpand
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 | 0.000 |
| 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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".