Quantitative Reasoning and Conceptual Analysis as a Framework for Teaching and Learning Probability
Bibliographic record
Abstract
Thompson’s theory of quantitative reasoning and von Glasersfeld’s approach to conceptual analysis are underutilized tools in probability and statistics education. Both are valuable frameworks for researching how individuals conceptualize and reason about/with uncertainty as well as helping to inform instructional design around the same topics. We describe both conceptual analysis and the theory of quantitative reasoning and how they have shaped mathematics education. Further, we provide some instances where they have successfully been used in probability and statistics education. Sharing these useful tools from mathematics education has profound implications for the field given its tight linkages. Thus, presenting this framework has potential to provoke reflection within the field regarding what constitutes foundational probabilistic and statistical ideas and how instruction might support students’ understanding of them.
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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 | 0.039 | 0.038 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.007 | 0.004 |
| Science and technology studies | 0.004 | 0.038 |
| Scholarly communication | 0.014 | 0.019 |
| Open science | 0.004 | 0.007 |
| Research integrity | 0.003 | 0.010 |
| 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".