Bibliographic record
Abstract
How do students make sense of fractions?Formal fraction knowledge begins when students start mapping fractions shown visually (e.g., area models), with symbols (e.g., ¾) and with words (e.g., three-quarters).Students were recruited from three schools that service rural and smalltown communities.Participating students in grade 4 (N=64) and grade 6 (N = 66) completed measures of cognition, language, and three novel measures developed for this study: mathematical vocabulary, orthography (i.e., the conventions for writing symbolic math), and fraction mapping.Five months later, their conceptual fraction skills (i.e., mapping, word problems and number line) were measured.I used two analytical approaches to examine the role of fraction mapping as students acquire conceptual fraction knowledge.In Study 1 (Chapters 4 and 5), I tested a path model in which mathematical vocabulary and orthography predicted fraction mapping, and fraction mapping predicted conceptual fraction skills.The model was largely supported for both grade 4 and grade 6.Moreover, mathematical vocabulary also predicted conceptual fraction skills for sixth graders.Thus, once students have sufficient knowledge of fraction mappings, other skills such as mathematical vocabulary may contribute more strongly to students' knowledge of fraction concepts.In Study 2 (Chapter 6), I used latent profile analysis to group students based on their fraction number line estimation.Three groups emerged.Relational estimators had the most advanced fraction concepts because they viewed the fraction as a unit.Compared to the other groups, relational estimators were more likely to be in sixth grade, have better mapping skills and more accurate whole number line estimation.Whole-component and denominator estimators, respectively, interpreted the fraction based on the magnitudes of both components (i.e., the numerator and denominator) or just the denominator.Only fraction mapping skills
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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 | 0.002 | 0.041 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".