COMMUNICATION IN MATHEMATICS: A CASE FOR CONCPTUAL QUESTIONING IN ONTARIO MIDDLE SCHOOLS
Bibliographic record
Abstract
In mathematics education, communication is one of the foundational cornerstones. The Ontario Ministry of Education and Training has placed a significant emphasis on communication in the mathematics classroom. In The Ontario Curriculum, Grades 1-8:\nMathematics Revised (2004), communication is highlighted as one of the seven mathematical processes as well as one of the four categories for assessment on the achievement chart. Communication takes many forms in the mathematics classroom including questioning, written response, and discourse. Despite all of the emphasis on communication, the employment of quality communication in mathematics is somewhat elusive. One method for eliciting quality communication in mathematics is through conceptual questioning. The question then arises, can a generalist intermediate teacher create and implement conceptual questions, and assess student responses in terms of conceptual understanding and communication. Using the action research format known as learning study I investigate two teachers. Learning study provided the opportunity for the teachers to examine the creation and application of conceptual questioning through the development and implementation of the rate and ratio unit. The data collected, some of which contains a narrative format, was viewed through a variation theory and phenomenography lens. The data revealed that within certain specific conditions, the creation and employment of conceptual questions can be accomplished by generalist teachers, albeit to varying degrees of success.
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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 | 0.021 | 0.046 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.034 | 0.033 |
| Scholarly communication | 0.009 | 0.007 |
| Open science | 0.004 | 0.008 |
| Research integrity | 0.007 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 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".