Miguel Ribeiro

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.