Using Virtual Math Manipulatives To Support Math Learning For Secondary Students With Significant Math Difficulties: A Professional Development Resource Guide
Bibliographic record
Abstract
Virtual math manipulatives are digital educational tools that have been demonstrated to support the learning of all students, especially those with learning disabilities and/or other significant difficulties in math (Bouck et al., 2017; Bouck, Shurr, et al., 2020; Moyer-Packenham, & Westenskow, 2013). However, these tools are used far less frequently in secondary math classrooms than in elementary-level classes (Reiten, 2021; Swan & Marshal, 2010). This may be due to the lack of professional training that secondary math teachers receive on these tools (O’Meara et al., 2020). Therefore, the purpose of this project is to provide secondary math educators with an accessible professional development resource guide on the topic of virtual math manipulatives and how they can be integrated into secondary-level math courses. This guidebook contains information on virtual manipulatives and how they can benefit students with significant math difficulties, while also describing how they can be incorporated into lessons through the virtual representational abstract instructional sequence. This guide also includes two analytic frameworks that encourage educators to evaluate virtual manipulatives and related learning tasks. An annotated list of virtual math manipulatives is also provided. Finally, this guidebook also provides educators with several virtual manipulative tasks to use and/or critique within an example unit plan for Ontario’s new ninth grade math course. By support educators in incorporating virtual math manipulatives into their lessons, this guide seeks to improve math learning for all students- particularly those with significant math difficulties.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.040 | 0.032 |
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".