The Impact of Structured Practice on Fifth Grader’s Fraction Knowledge
Bibliographic record
Abstract
The present study investigated whether Grade 5 students, who are learning a procedure for a whole number by a fraction using repeated addition, would develop conceptual knowledge of fractions. The study aimed to answer three questions: 1 – Does practicing a procedure to multiply a whole number by a fraction through repeated addition result in acquiring greater procedural accuracy in fraction multiplication? 2 - Does practicing a procedure to multiply a whole number by a fraction through repeated addition result in greater conceptual knowledge? and 3 - Does self-explaining contribute to developing conceptual knowledge when practicing a procedure to multiply a whole number by a fraction through repeated addition? For this pretest-intervention-posttest study, 56 Grade 5 students were selected from two schools located in the greater Montreal area (two classes from each school) Three randomly-selected groups were created within each class. Two groups received instruction on how to use the procedure: one was prompted while the other was not. The third group explored geometry notions without receiving any instruction on fractions. As expected, the results demonstrate that after the 4-week intervention period, practicing exercises involving the multiplication of whole numbers by fractions enhanced procedural accuracy, whereas those who did not receive such instruction did not. In contrast to expectations, students' conceptual understanding of fraction magnitude was not enhanced by practicing a procedure for multiplying whole number by fractions. To clearly identify the mechanisms that would facilitate this transfer, more research is necessary.
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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 | 0.001 | 0.006 |
| 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 | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".