Elementary Mathematics Teacher Preparation in an Era of Reform: The Development and Assessment of Mathematics for Teaching
Bibliographic record
Abstract
Teachers’ understanding of the elementary school mathematics curriculum forms part, but not all, of the newly emerged field of mathematics for teaching, a term that describes the specialised mathematics knowledge of teachers. Pre‐service teachers from a one‐year teacher preparation program were studied in each of three years, using a pre‐test/post‐test survey of procedural and conceptual knowledge of mathem‐ atics required by elemtary teachers . Beliefs about mathematics were also examined through post‐test interviews of 22 of the participants from one of the cohorts. Each cohort of teacher‐candidates was consistently found to be initially weak in conceptual understanding of basic mathematics concepts as needed for teaching. The pre‐service methods course, which included a strong focus on specialised mathematical concepts, significantly improved pre‐service teachers’ understandings, but only to a minimally acceptable level. Program changes, such as extra optional course in mathematics for teaching, together with a mandatory high‐stakes examination in mathematics for teaching at the end of the methods course, have been subsequently implemented and show some promise. Keywords: mathematics teacher education, pre‐service teacher education, teacher mathematics knowledge, conceptual knowledge, teacher preparation, mathematics for teaching La compréhension qu’ont les enseignants du curriculum de mathématiques au pri‐ maire fait partie d’un nouveau domaine de recherche – les mathématiques en prati‐ que d’enseignement – axé sur les notions mathématiques spécialisées dont les ensei‐ gnants ont besoin. Des étudiants en pédagogie inscrits dans un programme de forma‐ tion à l’enseignement d’un an pour le primaire ont fait l’objet d’une étude sur trois ans à l’aide d’une enquête pré‐test et post‐test portant sur leurs connaissances des méthodes et concepts liés aux mathématiques au primaire. Les croyances d’une ving‐ taine des participants au sujet des mathématiques ont également été analysées à l’aide d’entrevues post‐test. L’auteure a constaté qu’au départ la compréhension des concepts mathématiques pour enseigner au primaire était faible dans chaque cohorte enseignant‐étudiants. Le cours de méthodologie, fortement axé sur des notions ma‐ thématiques spécialisées, a amélioré nettement la compréhension des étudiants, mais seulement à un niveau tout juste acceptable. Des changements ont été par la suite apportés au programme, comme un choix plus vaste de cours optionnels de mathé‐ matiques en pratique d’enseignement et l’ajout d’un examen de mathématiques en pratique d’enseignement obligatoire et à enjeux élevés à la fin du cours de méthodo‐ logie. Ces changements semblent prometteurs. Mots clés: formation à l’enseignement des mathématiques, formation à l’enseignement, connaissances mathématiques de l’enseignant, connaissance concep‐ tuelle, mathématiques en pratique d’enseignement
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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 | 0.006 | 0.029 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".