Examining Curricula within the Scope of Algebraic Thinking: Examples from Turkiye, Singapore, England and Canada (Ontario)
Bibliographic record
Abstract
The purpose of this research is to compare the Century of Türkiye Education Model, which has been implemented since the 2024–2025 academic year, and the Türkiye (2018, 2024) secondary school mathematics curriculum, which is still ongoing, with the mathematics curricula of Singapore, England, and Canada (Ontario) in the field of algebraic thinking and algebra learning, revealing similarities and differences. The curricula of Singapore, England, and Ontario have been considered data sources due to their higher average scale scores in internationally recognized assessments such as TIMSS and PISA compared to Turkiye and their geographical diversity across different continents. The algebra learning area at the class levels corresponding to grades 5–8 has been examined through document analysis using three distinct dimensions based on various concepts and processes alongside the components of generalized arithmetic, functional thinking, and modeling languages associated with algebraic thinking. The similarities and differences between the sub-learning areas and achievements related to the algebra learning area have been delineated through horizontal comparisons. As a result of the comparison, it was found that the Ontario and the Century of Türkiye Model curricula present a balanced distribution among generalized arithmetic, functional thinking, and modeling languages. The Singapore curriculum, on the other hand, emphasizes functional thinking and problem solving through patterns and relations, while the England curriculum integrates algebra with reasoning and real-life applications. Overall, the provision of algebraic concepts at each grade level, the support of various processes, the inclusivity of mathematical expressions, and the presence of guiding descriptions and exemplary applications are notable across the curricula.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".