Designing Manipulatives as Microworld-Making: A Reflective Approach to Enhancing a Course through Pre-Service Teachers’ Contributions
Bibliographic record
Abstract
This paper establishes a foundation for a teacher education course through a reflective approach to its development, viewing it as a dynamic process shaped by students’ experiences, knowledge construction, and manipulative design. This perspective reimagines teacher education beyond content delivery, promoting a vision in which both teacher educators and pre-service teachers are simultaneously practitioners, designers, and learners. Consistent with constructionist principles, the study analyses the design work of one student to explore how her contributions informed refinements to course structure and pedagogical framing. The pre-service teacher’s manipulative is examined through the lens of Symbolically Structured Environments (SSEs) – conceptually aligned with microworlds – highlighting how physical action interacts with mathematical symbols to deepen understanding. Framing manipulative design as microworld-making, the second iteration of the course incorporated key SSE elements to empower pre-service teachers to design manipulative that actively engage students in mathematical thinking.
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".