The role of co-construction of the clock model in the development of fractional understanding in a grade 4/5 classroom
Bibliographic record
Abstract
The focus of this case study was to determine the impact of the co-construction and use of the clock model in the development of fractional understanding in a Grade 4/5 classroom. A pretest, instruction, midtest, intervention, posttest, retention test sequence was used. The teaching unit was developed to address six areas of student difficulty with fractions identified in the literature: factional parts are equal size portions, fraction symbols, improper fractions, size of unit fractions, estimation and comparison, and equivalent fractions. The clock model was co-constructed by the students with the teacher in the second half of the unit. Students used the clock model in four different forms: as an area model, as whole numbers of minutes, as equivalent fractions, and as an open clock. Although some students did not adopt the clock model, others used it with great success. Most students moved beyond using only landmark fractions of an hour to being able to work with thirds and sixths of an hour. The clock model helped some students to better understand the relationship between equivalent fractions. Recommendations are discussed.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".