Teachers' Conceptions of Mathematical Word Problems: A Basis for Professional Development.
Bibliographic record
Abstract
Olive Chapman University of Calgary This paper reports on a study of mathematics teachers’ thinking in the teaching of contextual or word problems [WP] with particular focus on teachers’ conceptions of WP and the relationship to teaching. The 20 participants included Grades 1-12 preservice and inservice teachers. Data consisted of interviews and classroom observations. The findings indicated 8 ways in which the teachers conceptualized WP, e.g., WP as object and experience, and a model of WP as a nesting of mathematics and social contexts. These conceptions played a significant role in framing their teaching of WP in terms of 4 teaching perspectives, including a paradigmatic and a phenomenological approach. Implications for teacher development based on the findings are also discussed. Recent reform recommendations in mathematics education (e.g., NCTM 1989, 2000) assign a significant role to problem contexts in developing meaning for mathematics and to a problem-solving perspective of teaching and learning mathematics. Implementing such recommendations suggests an increase in importance in the use of a range of contextual problems or word problems [WP], “routine” or “non-routine”, in the classroom. This paper considers the teacher as a basis for understanding the teaching of WP. The paper is based on a 3-year project that investigated teacher thinking in the teaching of WP. In particular, it reports on inservice teachers’ conceptions of WP, the relationship to their teaching and implications for professional development. BACKGROUND AND THEORETICAL PERSPECTIVE
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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 | 0.004 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.005 | 0.019 |
| Scholarly communication | 0.006 | 0.004 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| 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".