Using Variation Theory to Analyze and Extend a Resource: Three Lessons on Fractions from JUMP Math
Bibliographic record
Abstract
In this article, we report on our experiences of using the variation theory of learning (Marton 2015) to analyze and extend lessons from JUMP Math, a widely used resource in mathematics classrooms throughout Canada. JUMP Math is a comprehensive K–8 resource developed using the principles of structured inquiry. To access the available free and paid resources, users have to create an account and choose one of the four membership types depending on their need of the resources. Our work focuses on three individual JUMP Math lessons on comparing and ordering fractions, ranging from Grades 3 to 5. In what follows, we briefly describe the principles of variation theory and elaborate on our motivation for this work. We then present analyses informed by variation theory of the three JUMP Math lessons, each of which is accompanied by a task we designed to supplement the lesson. We conclude by reflecting on some successes and challenges we experienced in pairing variation theory with a classroom resource in a mathematics curriculum and an instruction course for elementary mathematics teachers. We then discuss implications for professional learning.
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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 | 0.005 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.007 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".