Excellence in mathematics: teaching practices of four exemplary secondary school mathematics teachers
Bibliographic record
Abstract
The teaching practices of four exemplary secondary school mathematics teachers are examined in the context of the current education reform in Ontario. This thesis examines the teachers' conceptions of mathematics and their affective, cognitive and managerial teaching behaviours. Although there has been some research investigating conceptions of mathematics and mathematics teaching practices at the elementary school level, research at the secondary school level appears to be limited. Qualitative methods are used to explore the teaching practices and the teachers' underlying conceptions of mathematics. Participants were interviewed and observed in their respective educational settings. The teachers' views on learning and teaching mathematics include teaching strategies, evidence of students' knowledge and skill in mathematics, ways of enhancing student performance, methods of dealing with barriers encountered in teaching mathematics and opportunities for professional development. Teachers gave students the opportunity to learn in a variety of ways: individually, co-operatively, with teacher direction and by hands-on experience. Teaching for understanding of mathematics was demonstrated by examples of problem solving involving the students' making connections with previously learned material in mathematics, integrating mathematics with other subject disciplines, making applications of mathematical concepts to practical, everyday examples, and by gaining further experience in the use of technology as a means of learning mathematical concepts. Variation in assessment and evaluation of student work was also supported. Positive personal relationships between student and teacher, as well as the challenge to develop their skills, further inspired the students and helped them gain confidence and achieve good results in mathematics.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.009 | 0.005 |
| Scholarly communication | 0.003 | 0.001 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 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 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".