Canadian School Administrators' Statistical Reasoning about Probability, Effect, and Representativeness
Bibliographic record
Abstract
How do Canadian school leaders interpret data to inform their decisions? How do they reason with probability concepts? These are the questions we are investigating in the first year of this longitudinal bilingual project conducted in Alberta, British Columbia, and Ontario. Our theoretical framework is inspired by the semiotic perspective of Charles Sanders Peirce (1839-1914) which suggests that interpretation is a triadic process integrated in a social context that puts in relation a sign, an object, and an interpretant. To this end, we conducted two individual interviews in which we asked 10 English-speaking school leaders and 9 French-speaking school leaders some questions about data presented in a tabular form (mock data on class level student performance and school level health data), line graph (PISA 2018 report on reading scores from 2009 to 2018) and box plots (mock data on student performance in reading in different countries). Our preliminary results reveal that principal’s reason abductively when it comes to interpreting statistics and want to know the context or the story behind the numbers before making any decisions. Also, they prefer to interpreting data collaboratively with their colleagues and feel more comfortable with data grouped in tables and line graphs. They considered themselves "data-driven" but not statisticians and use verbal terms rather than ratios or percentages (e.g., high probability, high likelihood, high odds) to express probabilistic ideas. In the next years, we will study how their professional experiences influence their conceptions of causality and how they reason about sampling and representativeness.
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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 | 0.063 | 0.143 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.007 |
| Science and technology studies | 0.024 | 0.019 |
| Scholarly communication | 0.016 | 0.004 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".