Distinctive characteristics of mathematical thinking in non-modelling friendly environment
Bibliographic record
Abstract
We first discern three different sources to describe the non-modelling-friendly environment in Taiwan: the background of mathematics teachers and students, examinations and textbooks. Under such unfriendly circumstances, how one can implement the teaching and learning of mathematical modelling is explored. In this paper, we focus on the analysis of distinctive characteristics of high school studentsapos; thinking of modelling. The changes required of the participating teacher and the evolution supporting these changes will be written in another article. Three kinds of Taiwanese students' modelling processes are identified, and the finding shows that the common feature of mathematical thinking of modelling is that, in practice, students do not solve mathematical models. We further conjecture that provoking students to explore mathematical solutions during modelling activities will benefit their situational reasoning, mathematizating, interpreting and communicating. On one hand, teachers can design model-exploring activities based on characteristics of students' thinking during modelling activities, and provide settings where conflicts between models and situations are confronted and the need to justify the validity of models and solutions is considered. On the other hand, students may elaborate their models and learn alternative approaches or tools for rethinking previously studied mathematical models during model-exploring activities.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 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".