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

Abstract

The objective of this study is to demonstrate that the criteria of didactical suitability, proposed by the theoretical framework known as the Onto-Semiotic Approach (OSA) of mathematical knowledge and instruction, are powerful tools for organizing the reflection and assessment of instruction processes carried out by mathematics teachers. To this aim, the results of a multiple case study are presented which prove that when teachers are faced with the task of evaluating processes of instruction, they employ-either implicitly or explicitly-the OSA criteria of didactical suitability (epistemic, cognitive, affective, mediational, interactional and ecological). Therefore, the explicit application of said criteria in teachers' education cycles contributes to the development of the didactic analysis competence that is necessary for teachers to be able to reflect on their own practices.

Case Study on Mathematics Pre-service Teachers’ Difficulties in Problem Posing

“…They confessed that they did not have suitable resources or tools. This idea was also described in studies by Sriraman (2005) and Breda et al (2017), who stated that pre-service teachers must develop the competence of assessing the problems they could use, and that this competence must be developed in teacher education. A way of teaching this competence is with tasks that involve managing the educational analysis, for example, posing problems by varying a given problem or by creating a new problem, whether a certain situation is faced or due to a specific request (Malaspina, Mallart & Font, 2015).…”

“…We consider that a teacher must not only be able to solve mathematical problems, but also choose, modify and pose problems for educational purposes (Tichá & Hošpesová, 2013). Teachers must develop analysis and intervention skills to evaluate the problems they use (Breda, Pino-Fan & Font, 2017). These skills involve reflecting on the mathematical practice of problem solving and problem posing, and assessing problems based on certain educational criteria.…”

A Proposal to Enhance Preservice Teacher’s Noticing

“…Table 1 shows the different indicators of the Didactical Suitability suggested by Breda et al (2017) which were suggested in the "Meta" dimension of the DMK for reflection on the practice. The indicators set conforms the Guide for Didactical Reflection that researchers discussed with the preservice teachers after each one of them taught a class to the girls.…”

Spatial thinking from didactic sequences with the use of 3d paper folding in the study of regular polygons in seventh grade students

“…By reviewing the term of the didactic sequences as a reference, it can be stated that they are consecutive and uninterrupted events that lead to an understanding of a specific topic [6]. A fundamental aspect in the didactic sequences destined to form competences is to consider a significant problem [7], this is due to the fact that education not only forms, but also is a scenario to solve problems of the context where different components are involved [8].…”