KNOWING AND USING MATHEMATICS IN TEACHING: CONCEPTUAL AND EPISTEMOLOGICAL CLARIFICATIONS
Notice bibliographique
Résumé
The body of research on teachers' mathematical knowledge for teaching has been growing in importance in recent years in the international research community (Adler & Davis, 2006; Ball & Bass, 2003; Davis & Simmt, 2006; Margoli nas, Coulanges & Bessot, 2005). These studies, grounded in empirical data and theoretical reflections about teachers' mathematical knowledge, offer new ways of thinking about teachers' mathematical education. They challenge the math ematics teacher education structures prevalent in most universities, where an emphasis is placed on university aca demic mathematical training something that has been argued to be quite disconnected from the mathematical prac tices teachers enact in their classrooms (see, e.g., Moreira & David, 2008; Proulx & Bednarz, 2008). That said, as francophones who work in the field of didac tique des mathematiques in Quebec (Canada) [2], we admit to having been surprised by the excitement that the body of research on teachers' mathematical knowledge, pioneered by Ball and Bass, has recently provoked in the scientific community. We were under the impression that this discourse (and the examples given to explicate this new field) had been present for a number of years in francophone communities, at least in Quebec, around the various developments enacted by mathematics teacher educators in pre-service teacher edu cation (see, e.g., Bednarz, 2001; Bednarz, Gattuso & Mary, 1995; Bednarz & Proulx, 2005; Janvier, 1996; Janvier & Hosson, 1999). However, this brought us to realize that these interventions and developments, and their underpinning principles, had not been theorized as well and as recent work in the domain of teachers' mathematical knowledge. [3] We thus perceive an opportunity to explain our conceptu alizations about knowing and using mathematics in teaching. We hope to contribute to the current reflections on teachers' mathematical knowledge for teaching and stim ulate discussions around this significant component of teachers' knowledge. We ground our discourse in mathematics teachers' actual practices, using vignettes taken from a collaborative study with a teacher. Our work has been refined through collabo rative studies with teachers (see, e.g., Bednarz, 2004,2009), which enabled us to better understand the knowledge enacted by teachers in mathematics teaching/learning situa tions. This theorization is also inspired from a posteriori reflections on the interventions developed in our secondary level mathematics teacher education program, established in the 1970s at the Universite du Quebec a Montreal (UQAM). Our discussion combines these two complementary axes: (1) theorizations about knowledge teachers enact in their mathe matics teaching practices and (2) illustrations, drawn from our program, of efforts to develop this professional knowledge.
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Comment cette classification a été obtenuedéplier
Prédiction distillée sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,001 | 0,001 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,000 |
| Études des sciences et des technologies | 0,000 | 0,000 |
| Communication savante | 0,000 | 0,000 |
| Science ouverte | 0,000 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,000 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,000 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule tête enseignante, pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».