A longitudinal investigation of the codevelopment and bidirectional relations among whole number arithmetic and conceptual and procedural fraction knowledge.
Bibliographic record
Abstract
How do conceptual and procedural fraction knowledge influence the development of each other over time? Is their pattern of development a reflection of instruction? In the present study we conducted a four-wave longitudinal investigation of the co- and bidirectional development of whole number arithmetic, and conceptual and procedural fraction knowledge during a critical phase of fraction learning. Chinese students (N = 1,055, Mage = 9.8, SD = 0.7) educated through a linear curriculum completed whole number arithmetic, and conceptual and procedural fraction assessments during the first and second terms in Grade 4 and Grade 5. Cross-lagged panel analysis, controlling for students’ non-verbal reasoning skills, revealed that conceptual and procedural fraction knowledge did not influence the development of one another prior to Grade 5. However, starting in Grade 5, a unidirectional pattern emerged, where conceptual fraction knowledge supported the development of procedural fraction knowledge. This unilateral conceptual-to-procedural pattern of development contrasts with findings from studies with students in the U.S., suggesting that educational experiences may shape the co-development of these two types of fraction knowledge. Furthermore, proficiency in whole number arithmetic predicted the development in both conceptual and procedural fraction knowledge, highlighting its important role alongside conceptual knowledge in supporting the acquisition of fraction procedures. Our findings emphasize the need to consider educational experiences and foster meaningful connections between concepts and procedures during fraction instruction while promoting mastery of whole number arithmetic to promote students’ development of fraction knowledge.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".