Towards a Methodology for the Characterization of Teachers’ Didactic-Mathematical Knowledge

Abstract

This research study aims at exploring the use of some dimensions and theoreticalmethodological tools suggested by the model of Didactic-Mathematical Knowledge (DMK) for the analysis, characterization and development of knowledge that teachers should have in order to efficiently develop within their practice. For this purpose, we analyzed the activity performed by five high school teachers, in relation to an activity about patterns suggested in the framework of the Master of Mathematics Education Program at University of Los Lagos, Chile. As a result of the analysis, it becomes evident that teachers can indeed solve items related to the common content knowledge, but have certain difficulties when they face items that aim at exploring other dimensions of their knowledge, for example, about extended content knowledge, of resources and means, or of the affective state of students.

Meta Didactic-Mathematical Knowledge of Teachers: Criteria for The Reflection and Assessment on Teaching Practice

“…Within the Onto-Semiotic Approach (OSA) of mathematical knowledge and instruction (Godino, Batanero & Font, 2007), a theoretical model of the mathematics teacher"s knowledge (Pino-Fan, Assis & Castro, 2015;Pino-Fan, Godino & Font, 2016), known as the DidacticMathematical Knowledge model (DMK model), has been developed. As stated by these authors, one of the aspects of the development of said model is the interconnectedness of the notion of the teacher"s "knowledge" with that of their "competence".…”

“…Within the DMKC model it is considered that the two key competences of the mathematics teacher are: 1) the mathematical competency; and 2) the didactical analysis and intervention competency, whose fundamental nucleus (Font, 2011;Pino-Fan, Assis & Castro, 2015) consists of designing, applying and assessing the sequences of one"s own learning, and that of others, by means of didactic analysis techniques and criteria of quality, in order to establish cycles of planning, implementation, evaluation and to put forward proposals for improvement. In order to develop such competence, the teacher requires, on one hand, knowledge that allows them to describe and explain what has happened in the process of teaching and learning -the didactical dimension of the DMK model (Pino-Fan, Assis & Castro, 2015), as a component of the DMKC model-and, on the other hand, they require knowledge to assess what has taken place and to make suggestions for the improvement of future implementations -the meta didactic-mathematical dimension of the DMK model (Pino-Fan, Assis & Castro, 2015)-.…”

“…Similarly, Pino-Fan, Assis and Castro (2015) put forward a model for the teacher"s didactic-mathematical knowledge, which enables the characterization of the teacher"s knowledge on the basis of three dimensions: mathematical, didactical and meta didacticmathematical. For this investigation, we focused on the third dimension, which refers to: "the knowledge needed by teachers to: reflect on their own practice, identify and analyze the set of norms and meta-norms that regulate the teaching and learning processes of mathematics, and assess the didactic suitability in order to find potential improvements in the both design and implementation stages of such processes of study".…”

A Proposal to Enhance Preservice Teacher’s Noticing

“…We have chosen the didactic-mathematical knowledge (DMK) model (Pino-Fan, Assis, & Castro, 2015;PinoFan, Godino & Font, 2016;, to conduct this research. The DMK model is based in the Onto-Semiotic Approach to Research in Mathematics Education (OSA) (Godino, Batanero & Font, 2007).…”

“…This phenomenon is called contingency (Rowland, Huckstep, & Thwaites, 2005). The didacticmathematical knowledge model (Pino-Fan, Assis & Castro, 2015) propose dimensions, and sub-dimensions, where the knowledge of the mathematics teachers is organized to help them identifying and developing key skills to carry contingency processes. Star, Lynch, and Perova (2011), report that teachers have trouble identifying relevant features, both in the didactic-mathematical tasks and in the mathematical content.…”