Virtual Manipulative Materials in Secondary Mathematics: A Theoretical Discussion.
Why this work is in the frame
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Bibliographic record
Abstract
With the increased use of computer manipulatives in teaching there is need for theoretical discussions on the role of manipulatives. This article reviews theoretical rationales for using manipulatives and illustrates how earlier distinctions of manipulative materials must be broadened to include new forms of materials such as virtual manipulatives which are also useful tools in a larger collection of learning tools. applying a theoretical lens to a specific material—polynomial tiles—this article demonstrates the following: (a) a complementary relationships between virtual and concrete manipulatives, (b) two or more theories can appropriately justify the same material, and (c) exploration of a specific manipulative may generate novel theoretical rationales. This exploration has proven to be helpful in the process of designing, selecting, categorizing and evaluating learning tool.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it