This paper presents the model, The Mathematics Teacher's Specialised Knowledge (MTSK). It acknowledges earlier contributions to understanding and structuring teachers' knowledge, in particular, the special debt owed to Shulman's notion of pedagogical content knowledge and to Ball and collaborators' Mathematical Knowledge for Teaching (MKT) influential for the specialised nature of one of its sub-domains. Our research with teachers has led us to explore the characteristics of MKT and to refine the descriptors relating to its sub-domains, a task which has underlined the difficulty involved in unambiguously delimiting the boundaries which separate these. As a result, and taking into consideration a broader view of the specialised nature of the teacher's mathematical knowledge, we propose a framework which, whilst respecting the major domains of Content Knowledge and Pedagogical Content Knowledge, regards the specialisation in respect of mathematical knowledge as a property which is inherent to the model and extends across all sub-domains.
Al considerar un paradigma de acción en el aula, como lo es el Aprendizaje Basado en Proyectos (ABP), lo que es explorado y evidenciado desde el punto de vista académico, a veces está lejos de ser comprendido y retomado en el actuar diario del profesor. Perrenoud (2000) menciona que, dentro del método ABP, no hay un estándar, ya que todos tienen su propio entender y modos de ejecutarlo. Por esta razón, construimos una entrevista como instrumento para abordar la comprensión del profesor de matemáticas que generalmente trabaja con ABP y así elaboramos un instrumento con categorías y subcategorías basadas en distintos elementos, lo cual permite tener una mirada amplia y exhaustiva de la comprensión del profesor acerca del ABP. Palabras clave: Aprendizaje Basado en Proyectos, Caracterización del ABP, Comprensión del profesor Resumo Ao considerar um paradigma de aula, como é a Aprendizagem Baseada em Projetos (ABP), aquilo que é explorado e evidenciado desde o ponto de vista acadêmico às vezes está longe de ser compreendido e retomado na ação cotidiana do professor. Perrenoud (2000) menciona que dentro do método ABP não há um padrão, já que todos têm seu próprio modo de entender e de executá-lo. Por isso, construímos uma entrevista como instrumento para acessar a compreensão do professor de matemática que geralmente trabalha com ABP e, assim, elaboramos um instrumento com categorias e subcategorias baseadas em distintos elementos, o qual nos permite ter uma visão ampla e exaustiva da compreensão do professor sobre o ABP. Palavras-chave: Aprendizagem Baseada em Projetos; caracterização do ABP; entendimento do professor.
Resumen En este trabajo indagamos sobre las posibles relaciones entre los resultados del análisis de una sesión de clase con dos modelos teóricos: el modelo Mathematics Teacher’s Specialised Knowledge (MTSK) y los Espacios de Trabajo Matemático (ETM). De este modo, discutimos el conocimiento especializado (MTSK) que evidencia en una sesión sobre la multiplicación de matrices un profesor universitario de álgebra lineal y el espacio de trabajo matemático (ETM) idóneo del profesor en esta sesión. El conocimiento evidenciado por el profesor parece explicar las génesis que el profesor prima en el trabajo matemático que propone. Así, el análisis con ambos modelos permite comprender mejor la actividad matemática que propicia el profesor y cómo se explica desde su conocimiento.
The aim of this study is to deepen our understanding of the practice of a lecturer in linear algebra by exploring the connections he makes between his content knowledge and his pedagogical content knowledge while working on the topic of matrices. Data were collected through video recordings of his classes and semi-structured interviews, and were analysed with the Mathematics Teacher’s Specialised Knowledge model. Instances of classroom performance, supported by the teacher’s own affirmations, provided evidence relating to the categories comprising the model, and enabled us to establish connections between the lecturer’s knowledge, his understanding of his students’ learning capabilities, and his knowledge of teaching mathematics, which together account for his classroom practice: the use of varied examples to introduce new content, the highlighting of the most salient aspects of the topic, and alerts about potential errors and difficulties. The contribution that these results could make to the training of university teachers, which would be done with the knowledge of the areas of difficulty shown by the teacher in mind, could be used to deepen other elements of their pedagogical content knowledge. The interconnections between areas of knowledge identified by the study also serve to validate the usefulness of a theoretical model for studying teachers’ knowledge.
En este documento mostramos un análisis sobre el conocimiento que evidencia un profesor de matemáticas de secundaria al resolver el problema de las cuerdas (se colocan n puntos sobre una circunferencia, ¿es posible determinar el número de todas las cuerdas que pueden trazarse?), usando el modelo analítico de conocimiento profesional mathematics teacher’s specialised knowledge (MTSK). Los resultados muestran la potencialidad del modelo como herramienta de análisis para profundizar en la comprensión y caracterización del conocimiento del profesor de matemáticas, en particular del conocimiento de los temas. Mathematics teacher’s specialised knowledge detected in the circle chord problem solution In this paper we show an analysis of the knowledge that evidences a secondary teacher to solve the circle chord problem (if there are n points in a circumference, is it possible to determine the number of all the possible cords?) using the analytical model of professional knowledge: mathematics teacher's specialised knowledge (MTSK). The results show the potential of the model as an analytical tool to deep in the comprehension and characterization of the mathematics teacher’s knowledge, especially the knowledge of topics.Handle: http://hdl.handle.net/10481/37190WOS-ESCINº de citas en WOS (2017): 1 (Citas de 2º orden, 0)Nº de citas en SCOPUS (2017): 1 (Citas de 2º orden, 0)
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