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
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.
How this classification was reachedexpand
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".