Bibliographic record
Abstract
This paper reports part of a larger study and examines one teacher’s use of problem-solving teaching approaches in Years 7 and 9. Thirteen problem-solving lessons were observed over an 18 month period during which the teacher devised and used 7 different problem-solving tasks. Three tasks are described in detail and analysed in terms of task structure and implementation, and how the teacher managed whole-class discussions. Analysis highlights changes in the design and use of the tasks. They became more open-ended and the teacher improved the quality of whole-class discussions to promote student learning and reflection. Anderson and White (2004) distinguish between problem solving, “the process of students exploring non-routine questions, using a range of strategies to solve unfamiliar tasks, as well as developing the processes of analysing, reasoning, generalising and abstracting ” (p. 127), and problem-solving teaching approaches, “investigations, open-ended questions, and modelling tasks, as well as providing opportunities for students to pose questions and explore new ideas ” (p. 127). Problem-solving teaching is therefore an approach in which “teachers see themselves as guides, listeners, and observers rather than authorities and answer givers” (Norton, McRobbie, & Cooper, 2002, p. 39). Problem solving is an important part of what it means to do mathematics and students require frequent
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.024 | 0.002 |
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".