Supporting Teachers’ Learning about Mathematical Modeling
Bibliographic record
Abstract
In the United States, one of the Standards for Mathematical Practice of the Common Core Curriculum (Common Core State Standards Initiative, 2010) is Model with mathematics. This standard requires that students be taught in a manner that will enable them to “apply the mathematics they know to solve problems arising in everyday life, society, and the workplace” (p. 7). However many prospective and practicing teachers acquire a pedagogical style that does not support this standard. To promote higher levels of student thinking associated with mathematical modeling, teachers must thus be taught not only what mathematical modeling is, but how it can be effectively incorporated in their lessons and presented to their classes. Teacher training should also include how to develop rubrics for assessment, among which are rubrics that enable students to demonstrate mathematical modeling proficiency in different ways. In this research, the topics addressed include ways professional development can help in-service teachers appreciate the importance of mathematical modeling tasks; concerns about teacher backgrounds in mathematical modeling; and the most effective ways for improving in-service teachers’ knowledge of mathematical modeling and their teaching of mathematical modeling. While the primary focus of this research is on teacher education and training in the United States, the findings from both domestic and international research are clearly significant for those who are responsible for various aspects of teacher preparation worldwide. Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics (CCSSM). Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
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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 | 0.007 | 0.024 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.002 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.002 | 0.008 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.015 | 0.007 |
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".