The World's a Stage@@@Structure and Insight: A Theory of Mathematics Education

https://dspace.library.uu.nl/bitstream/handle/1874/25945/korthagen-the%20teacher%20educator.pdf?sequence=1

The Teacher Educator as a Role Model.

Preservice mathematics teacher education is a complex process which involves many interacting elements. These elements include the kinds of knowledge, competencies, attitudes, and values that teacher candidates should develop, the context in which learning takes place (university, school, and other settings), and the roles, interests, and characteristics of the participants in the process (preservice teachers, university instructors, school mentors, and students). Other elements are program options and conditions such as pedagogical approaches, the relationship of preservice teachers and instructors, access to resources, and use of information and communication technology (ICT). Preservice teacher education also faces issues associated with bridging theory and practice and transforming the identity of preservice teachers from that of student to that of teacher. Other issues include confl icts between what is considered important for preservice teachers to learn and what they actually learn, between university and school contexts, and among the perspectives of the direct participants in the teacher education process and other interested parties such as ministries of education, school administrators, parents, media, and the public. Research also adds a layer of complexity in understanding teacher education in that studies can place emphasis on different aspects of the mathematics curriculum as well as of preservice teachers’ learning and related learning opportunities. Figure 11.1 provides one way of viewing the relationships of key components of this complex landscape of preservice mathematics teacher education. At the center of it are the development of the preservice teachers’ knowledge of mathematics and knowledge of mathematics teaching. While these two components can be considered independently, there is an important overlap in which the mathematics and teaching knowledge have inherent connections. Development of the identity of the preservice teacher is shown as embodying both knowledge of mathematics and mathematics teaching. In addition, it deals with factors such as values, habits, norms, dispositions, and in general, ways of being a teacher. The development of identity is nested in, or done in reference to, the group identity of the teachers’ professional community, for example, the established values and norms of the profession and the processes of professional interactions. The fi nal component of this landscape consists of several elements that can infl uence the nature of preservice teacher education programs in different ways. These include:

Preservice mathematics teachers’ knowledge and development

Teacher educators seem to agree that, to be able to support their student teachers' learning, they themselves should be good models of the kind of teaching they are trying to promote. However, it is clear from the literature that this congruent teaching is not self‐evident in teacher education. In the present article, we describe a small in‐depth study, in which we attempted to establish whether teacher educators begin to teach more congruently when supported, and the factors influencing the occurrence or non‐occurrence of such congruent teaching. To do so, we organised a workshop on the subject. Before and after the workshop, we interviewed the participating teacher educators, using videotapes of their lessons. To discover the possible contribution of the workshop to their congruent teaching, we later compared both interviews. We found that a particularly important aspect of congruent teaching, i.e. the teacher educators' ability to link their own teaching to theory, had improved. Our conclusion is that ...

Preach what you teach! Teacher educators and congruent teaching

Scholars of decades past, current researchers, and various reform documents all deal, directly or indirectly, with the question of what constitutes good mathematics teaching. Often good teaching is situated in the context of broader educational goals, such as preparing literate citizenry. Researchers generally define good teaching implicitly with attention to various processes such as reasoning and problem solving. In a series of three interviews, we examined nine experienced and professionally active teachers’ views of good mathematics teaching and how it develops. The interviews were couched in the context of the teachers mentoring student teachers. In general, these teachers thought good teaching requires a sound knowledge of mathematics, promotes mathematical understanding, engages and motivates students, and requires effective management skills. Furthermore, the teachers felt that good teaching is developed from experience, education, personal reading and reflection, and interaction with colleagues. Experience was considered the primary contributor. The article compares and contrasts the teachers’ notions of good teaching with those of various scholars and researchers and positions stated in various reform documents.

What Constitutes Good Mathematics Teaching and How it Develops: Nine High School Teachers’ Perspectives

A shift in mathematics education in the Netherlands towards the so-called realistic approach made it necessary to prepare prospective teachers for a type of curriculum different from what they experienced as pupils. This article describes the characteristics of a preservice programme aiming at this goal and presents an analysis of the development of the student teachers' views of mathematics and mathematics education during the programme as well as their classroom behaviour. This analysis is based on two research studies. The first was a longitudinal study in which the student teachers were followed during 
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 years by means of questionnaires and interviews. The second was a study in which graduates from this programme were compared with graduates from a more traditional preparation programme by means of two teacher questionnaires and a pupil questionnaire, the latter measuring the pupils' perceptions of the actual teaching behaviour of the graduates. The teacher education programme appeared to be successful in changing the student teachers' views of mathematics education, especially in the direction of a more inquiry oriented approach, and in promoting effective teacher behaviour in the classroom. As far as their facilitating role as a teacher is concerned, the student teachers seemed to go through a two-stage learning process. Most of them reached the first stage, in which they realize that pupils have different preferences for learning and that a variety of possible explanations for problems should be offered. However, only a small number of student teachers seem to reach the second stage, in which they recognize the principle of building on pupils' own constructions, an important feature of realistic mathematics education. Possible explanations for the low impact of the programme, as well as solutions are discussed.

Harrie Broekman

Papers

Preparing teachers for realistic mathematics education