Decimal Number System: Knowledge of Quebec Students Educated Under the 2001 and 1981 Programs and Teaching Situations
Bibliographic record
Abstract
Decimal Number System (DNS) is fundamental in the teaching of arithmetic.Although several scholars have studied the system, it was mostly the studies carried out in the 80s-90s that brought out its complexity and also the difficulties students encounter with its learning.In some of them, the scholars saw the students' difficulties through the prism of the earlier program's behaviourist and objective foundation structure.However, the current curriculum in Quebec, based on social constructivism and structured according to competences is a departure from the past.In this context, this study, inspired by a doctoral dissertation, is intended to explore the strategies and knowledge in solving tasks on the DNS of 154 third grade students from six schools as well as teaching situations in two classes, more than 30 years after the studies were carried out in Quebec.The main data collected for the study included audio interviews with 18 students, a questionnaire (n=154), videotape of lessons and documentation.First, we outlined the strategies and knowledge of pupils on the DNS as well as teaching situations, and then we compared them with earlier studies as well as the current program's competence-based structuring.We also discussed the scope of the task and class effects.We used the DNS frame of reference and the Theory of didactical situations for the analyses.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".