Implementing KeyMath approach for assessment, learning, and teaching for an inclusive middle school classroom in British Columbia
Bibliographic record
Abstract
Mathematical pedagogy has a large body of research as it pertains to both typically achieving students and learners with special needs, particularly math disabilities. The label of mathematical disability is dependent on several types of assessments that measure various aspects of cognition related to mathematical skill. Rural school districts, such as the one where this project started, have limited resources to assess and instruct learners with mathematical disabilities. This project made use of the KeyMath-3 diagnostic assessment in the construction of classroom math units using the KeyMath-3 diagnostic assessment that guides diagnosis of math disability. This diagnostic assessment was used as a focus for the language and types of questions used in various mathematical units. The British Columbia Ministry of Education math curriculum, KeyMath-3 diagnostic assessment, and IXL.com math program were all analyzed to find common language and goals as the focal points for the lessons. Probability, Pythagorean Theorem, Algebraic Expression, and Surface Area units were constructed at the Grade 8 middle school level using this approach to make learning accessible to learners with math disabilities while simultaneously allowing stronger math learners to fully express their levels of mathematical understanding. The combined use of diagnostic assessment, curricular goals, and support programs analyzed in this project allows for the construction of math units that could improve the understanding of all math learners, especially those students with math disabilities.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.006 | 0.001 |
| Scholarly communication | 0.003 | 0.001 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".