Transforming Pedagogical Practice in Mathematics: Moving from Telling to Listening.
Bibliographic record
Abstract
The research reported in this article is part of a larger study that examines an initiative to expand teacher expertise in facilitating mathematical problem solving within the framework of developing and field-testing pedagogical resources. We focus on one year of the study and report on the complex process of professional development as teachers move from traditional pedagogies of teacher explanation of mathematical operations followed by student practice to a pedagogy of teacher and student exploration of number operations within a problem-solving environment. We see that, in this initiative, teachers, consultants, and professional developers explored new mathematical and pedagogical ideas, creating a collective that provided a supportive environment that served as a model for classroom settings where teachers and students, in turn, investigated mathematical ideas. International Journal for Mathematics Teaching and Learning 1 Transforming pedagogical practice in mathematics: Moving from telling to listening “The depressing thing about arithmetic badly taught is that it destroys a child’s intellect and, to some extent, his integrity. Before they are taught arithmetic, children will not give their assent to utter nonsense; afterwards they will. Instead of looking at things and thinking about them, they will make wild guesses in the hopes of pleasing a teacher.” (W.W. Sawyer, Mathematician’s Delight) For more than three decades perspectives in mathematics education have strongly promoted developing an understanding of mathematical concepts, procedures, connections, and applications through problem solving (National Council of Teachers of Mathematics [NCTM], 1989, 2000; National Research Council, 1989; Silver, Ghousseini, Gosen, Charalambous, & Font Strawhun, 2005). However, facilitating the development of mathematical understanding through problem solving remains a challenge for teachers. The study reported in this article discusses the complex task of working with elementary teachers as they move from traditional pedagogies of teacher explanation to a pedagogy of teacher and student exploration of mathematical ideas within a problem-solving environment.
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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 | 0.011 | 0.022 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.006 | 0.022 |
| Scholarly communication | 0.010 | 0.013 |
| Open science | 0.001 | 0.010 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".