Examining the effectiveness of the numeracy course ‘Numbers for Life’ at McMaster University
Bibliographic record
Abstract
This paper reports on our study of the effectiveness of the course instruction in the numeracy course ‘Numbers for Life’, offered at McMaster University, Canada, and taught by one of the co-authors. In this course students explore the ways to reason with numbers in a variety of contexts important not only for their individual lives and their community, but broader – it helps them understand the world they live in, and the challenges they will face. To answer important questions about students’ learning and their development of quantitative reasoning skills, we designed a two-year research project, for which we secured government funding. We combined quantitative and qualitative data analysis methods to assess the gains in student learning and skills development using a number of instruments, including pre-test and post-test surveys, class activities, course assessments and teaching evaluations. Our research suggests that the “Numbers for Life” course instruction improves most students’ numeracy knowledge and skills. We detected improvements in students’ ability to understand numbers, ability to engage with logical constructions and reasoning, and ability to engage with multiple-step problems which require quantitative reasoning. The largest learning gains were detected among students who had inadequate background, as determined by their pre-test performance. We were not able to detect pre- to post-test improvements in communication (explaining what a numeric answer represents, providing a logical argument, creating a narrative about a situation involving numbers, and so on). We believe that part of the reason for this lies in the fact that students were probably not as serious, nor as patient in their approach to completing their post-test (at the end of the semester) as they were in completing a pre-test (at the start of the semester).
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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 | 0.007 | 0.034 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".