Mathematical Modeling Through the Eyes of Elementary and Middle Preservice Teachers
Bibliographic record
Abstract
Mathematical modeling is a useful pedagogy in mathematics education, but preservice teachers (PSTs) conceptualization of the teaching and learning of modeling practices is an ongoing concern. This research study examined 31 elementary and middle grades PSTs’ conceptualization of mathematical modeling and their experiences with such modeling. The study participants were recruited from two, four-year university mathematics methods courses located in northeastern and midwestern United States. Data for this study was collected through a questionnaire and analyzed using qualitative and quantitative methods. Results indicated that most of the PSTs had little understanding of the intersection of mathematical modeling, and the teaching and learning of mathematics. As such, many perceived mathematical modeling as an exclusive action reserved for teachers. Additionally, the results revealed that most participants had minimal, if any, experience with mathematical modeling. These limited experiences portrayed mathematical modeling as a show and tell method or step-by-step explanation. Our results expand the inadequate research into elementary and middle grades PSTs’ knowledge of and experiences in mathematical modeling and warrant the exigency for the inclusion of extensive mathematical modeling practices into methods and content courses for PSTs. The directions for future research and implications for researchers and teacher education programs are also discussed.
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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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.004 | 0.005 |
| Scholarly communication | 0.006 | 0.005 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 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".