How elementary students learn to mathematically analyze word problems: the case of addition and subtraction
Bibliographic record
Abstract
Mathematical problem solving, and more specifically the ability to mathematically analyze and model a situation, is one of the most important aspects of teaching and learning mathematics in school. Today, researchers agree that the problem-solving and mathematizing phenomena are extremely complex and that research is needed to better understand the cognitive processes involved at a phenomenological level. The lack of nuanced understanding of the ways of reasoning students might employ to analyze and model a problem prevents teachers from effectively meeting their needs. Within the context of a larger study on the development of mathematical reasoning in early grades of elementary school, I studied how grade two elementary school students solve additive problems to answer the following questions:1.What kind of mathematizing do students use to solving additive word problems? 2.What are the relationships between the instruction implemented and students' development of mathematizing processes?Applying the grounded theory methodology, I analyzed multiple observations of students solving additive problems throughout one school year. I suggest models for six strategies of mathematizing, which I describe in detail. I describe the dynamics of change in the learners' ways of reasoning and the relationships between this change and the teaching implemented.
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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 | 0.013 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| 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".