Mathematics teachers’ knowledge for teaching problem solving
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In recent years, considerable attention has been given to the knowledge teachers ought to hold for teaching mathematics. Teachers need to hold knowledge of mathematical problem solving for themselves as problem solvers and to help students to become better problem solvers. Thus, a teacher’s knowledge of and for teaching problem solving must be broader than general ability in problem solving. In this article a category-based perspective is used to discuss the types of knowledge that should be included in mathematical problem-solving knowledge for teaching. In particular, what do teachers need to know to teach for problem-solving proficiency? This question is addressed based on a review of the research literature on problem solving in mathematics education. The article discusses the perspective of problem-solving proficiency that framed the review and the findings regarding six categories of knowledge that teachers ought to hold to support students’ development of problem-solving proficiency. It concludes that mathematics problem-solving knowledge for teaching is a complex network of interdependent knowledge. Understanding this interdependence is important to help teachers to hold mathematical problem-solving knowledge for teaching so that it is usable in a meaningful and effective way in supporting problem-solving proficiency in their teaching. The perspective of mathematical problem-solving knowledge for teaching presented in this article can be built on to provide a framework of key knowledge mathematics teachers ought to hold to inform practice-based investigation of it and the design and investigation of learning experiences to help teachers to understand and develop the mathematics knowledge they need to teach for problem-solving proficiency.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.006 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it