Differentiating Instruction Using a Virtual Environment: A Study of Mathematical Problem Posing Among Gifted and Talented Learners
Bibliographic record
Abstract
Meeting the needs of mathematically gifted and talented students is a challenge for educators. To support teachers of mathematically gifted and talented students to find appropriate solutions, several innovative projects were conducted in schools using funds provided by the New Brunswick, Canada, Department of Education. This article presents one such initiative: a collaborative project we developed with two middle school teachers to enrich the mathematical experience of their most advanced students. We worked with 40 students from both schools, involving them in creating mathematics problems using multimedia tools for the CAMI (Communauté d’apprentissages multidisciplinaires interactifs)1 website. We analyzed the richness of the problems created by the participants (Manuel, 2010), as well as students’ perceptions of their experiences, collected through semi-structured interviews. Students appreciated the experience, and recommended that the project be continued in following years. Most of the problems created by students were moderately rich, and included multiple steps, but were similar to those used in classrooms. Some students stated that they were more comfortable solving problems than creating new ones, which suggested that they found the task challenging. Our results showed that specific programs for students interested in mathematics could provide positive experiences and challenges. Our research also suggested that problem posing in mathematics classrooms needs to be investigated in more depth.
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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 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.007 | 0.006 |
| Scholarly communication | 0.007 | 0.004 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 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".