Application of Information Visualization Techniques to the Design of a Mathematical Mindtool: A Usability Study
Bibliographic record
Abstract
One of the goals of information visualization is to support human thinking through the use of external visual aids. Mathematical mindtools can act as visual cognitive aids to enhance thinking and reasoning about mathematical objects and concepts. Although some mathematical mindtools incorporate information visualization techniques, the systematic use of these techniques in the design of these tools and their effect on users’ thinking and reasoning need to be investigated. A mathematical mindtool called PARSE (Platonic-Archimedean Solids Explorer) is presented in this paper. PARSE is intended to support the exploration and learning of a subset of geometric shapes. The mathematical objects and concepts embedded in PARSE have been enhanced using information visualization techniques. A usability study of PARSE and its information visualization techniques have been conducted and reported. The study shows that information visualization techniques enhance and support learning and exploration of mathematical concepts. The findings reported in this paper suggest that mathematical mindtools provide a fertile ground for investigating different information visualization techniques and their effectiveness in supporting learning tasks.
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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 | 0.016 | 0.071 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".