Miguel Montes

The mathematics teacher’s specialised knowledge (MTSK) model

ABSTRACT This paper presents the Mathematics Teacher’s Specialised Knowledge (MTSK) model. 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. The authors’ research with teachers has led them 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, the authors 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.

Reflecting Upon Different Perspectives on Specialized Advanced Mathematical Knowledge for Teaching

Teachers’ knowledge assumes a major role in practice and in the students learning and achievement. In particular, the construct of horizon knowledge or, what can be termed specialized advanced mathematical knowledge for teaching (in order to capture the overall perspectives we are dealing with within this proposal) has been the focus of attention from some researchers with different foci of attack (e.g., Carrillo, Climent, Contreras, & Muñoz-Catalán, 2013; Jakobsen, Thames, Ribeiro, & Delaney, 2012; Wasserman & Stockton, 2013; Zazkis & Mamolo, 2011). In that sense, and aiming to deepen our understanding of such a construct, the aim of this working group is to discuss and reflect upon, different theoretical perspectives, methodological approaches and analytic methods used when focusing on such specialized advanced mathematical knowledge for teaching. In particular, we consider the activities of analysing and conceptualizing situations where access and development of such teachers’ knowledge is of primary importance.

Mathematic Teachers' Specialized Knowledge about Infinity

Esta investigacion aborda el conocimiento especializado que el profesor de matematicas de secundaria puede movilizar, en pos de su identificacion, caracterizacion y categorizacion. Para ello, nos basamos en el modelo de ‘Conocimiento Especializado del Profesor de Matematicas’-MTSK-. El estudio sigue el enfoque metodologico de la Grounded Theory, encuadrado en un paradigma interpretativo, con un diseno de estudio de caso. Las herramientas usadas y desarrolladas para obtener los datos fueron un cuestionario exploratorio y una entrevista, asistiendo tambien a las clases del profesor objeto del estudio de caso para anadir elementos de discusion a la entrevista. Se analizaron los datos en varias ocasiones, desde diferentes enfoques, de manera que pudieramos obtener un mayor grado de triangulacion. Las conclusiones que se establecen en esta investigacion reflejan la naturaleza compleja del conocimiento del profesor, particularizada en el caso del infinito.

Arithmetic Knowledge of prospective teachers. Strengths and Weaknesses

Los medios de comunicacion han alertado recientemente a la opinion publica acerca de una realidad que la investigacion en educacion matematica llevaba evidenciando las dos ultimas decadas: la deficiente formacion matematica de los maestros. Estas deficiencias, que habiamos venido constatando de manera informal en nuestras universidades con los estudiantes para Maestro (EPM), son el objeto de estudio de nuestra investigacion. En ese contexto, este articulo describe un estudio exploratorio tipo survey sobre el conocimiento matematico necesario para la ensenanza que tienen 737 estudiantes para Maestro de tres centros de formacion de maestros de universidades andaluzas, realizado en el contexto de un Proyecto de Innovacion Docente de una de ellas. Usando el marco de conocimiento especializado del profesor de Matematicas (MTSK) y, dentro de el, el subdominio relativo al conocimiento de los temas matematicos, se elaboro un cuestionario que contenia items relativos a fracciones, decimales y porcentajes, contenidos que fueron elegidos tanto por su trascendencia intrinseca como por su aplicacion a otros contenidos matematicos y a otras disciplinas en el ambito de la Educacion Primaria. Esto nos ha permitido explorar el conocimiento que estos futuros profesores poseen sobre esos contenidos. Los resultados han mostrado un numero importante de debilidades, algunas de las cuales ya habian sido descritas por la literatura de investigacion, y tambien algunas fortalezas. En ambos casos, la informacion obtenida supone un referente para explorar la realidad de otros centros de formacion de maestros; un elemento de reflexion para las autoridades academicas acerca de los procesos de seleccion para el acceso a la universidad y, mas concretamente, a estos centros de formacion; y un punto de partida para el rediseno de sus programas de formacion.The social media have recently warned to public opinion about a truth that the research in mathematics education has been pointing up the last two decades: the poor mathematical training of primary teachers. These deficiencies, that we have being noticing in our universities with the prospective primary teachers (PPT), are our object of study. In this context, this paper describes a survey-type study on the mathematical knowledge required to teach of 737 prospective primary teachers from three universities in Andalusia. Based on the Mathematic Teacher Specialized Knowledge (MTSK), we have carried out a questionnaire addressing items related to fractions, decimals and percentages, contents chosen by its intrinsic transcendence, as by their application to other mathematical contents and other disciplines, in the ambit of primary school. This questionnaire has allowed us to explore the knowledge that these future teachers posses about these contents. The results of the study show an important number of weaknesses, some of them already described in research literature, and also some strengths. In both cases, the obtained information gives a base to explore other teacher training centers, elements of reflection to the academic authorities about the selection process to the access to university and, more concretely, to this training centers, as a starting point to redesign their training programs.