The work was focused on the papers of Santos, Koichu, Hodgen and Even at the first part of the group sessions, the papers Ravel, Gal, Kaldrimidou and Medici at the second part of the group sessions and the papers Rowland, Prestage, Goulding, Malara and Deulofou at the third part of the group sessions.

The group leaders formulated four questions based on the papers that were used as overarching issues in the sessions.

Some questions concerned where we were aiming in the group. How can we create an overview of the knowledge in a certain area and where do we want to expand our knowledge? How are the findings in the papers related to each other. Are they consistent or do we have contradictory results? How can the findings influence teacher education in the future? There are parts of the model that is not touched upon in the papers. Why is that? Do we have blind spots to cover? Of course some of the papers concern more than one part of the model. For example the papers of Kaldrimidou and Even have something to do with teachers’ professional language and there are other similar cases.

These are the questions we decided to bear in mind during the work in group 12:

1) What is the nature of the relationships between what we know about teaching practices and what is done or studied in teacher education? What do we know or need to know about teaching practices to develop better teacher education programs/to study different aspects? What do we know or need to know about using our knowledge about teaching practices to conduct better teacher education/study different aspects?

2) What do we know or need to know about the opposite direction: from a study of teacher education to issues in teaching practices? Or, what might be the relationships between teacher education and teaching practice? What kind of evidence can we provide to show that teacher education is worth the time and money invested in it? What kind of evidence do we not have but need to have in order to communicate with different people, like policy makers?

3) What is the connection between teachers' development of a teaching practice and pupils’ learning in mathematics. Is there a link between teachers' learning during teacher education and pupils’ learning during the teaching practice? How can we learn more about the relation between pupils' learning and teachers' teaching in order to assist both groups to improve the result? What do we mean by improving the result of teacher education or teaching practice or pupils' learning of mathematics?

4) What does evidence mean in the field of research on teacher education? What kind of evidence can we get in it?

A. How can we get evidence?

B. How have the authors of the papers in our group dealt with evidence in them?

During the group work there were two concepts that came up more often than others: teacher identity and teacher roles. In the discussion participants tried of argue for one or the other of these concepts. Several of the papers used on or the other of the concepts.

The following questions were raised in WG3 in CERME2 (reported by Fulvia Furinghetti and Barbro Grevholm):

• A lot of different and complex issues came up but no issue stood out as of primary importance.
• Relations between pre-service and in-service training. Is the difference going to disappear when we get life-long learning?
• The role of mathematical knowledge and the balance between subject knowledge and pedagogical knowledge.
• Relations or differences in issues at primary and secondary level.
• Would the discussions in our group have been different if we were educators only and not researchers?
• Relationships with institutions and the political influences on our behalf.
• The need to define in every paper a local meaning of central concepts (like reflection, improvement, changes, and development).
• The effect on teachers of stimuli like writing, reading, and technology.
• Teachers’ awareness, teacher students’ awareness.
• The role of discussion, conversation, communication in promoting professional growth.
• Is the role of technology less strong than in earlier phases?

Some of these questions were included in the discussions in CERME3 but not all of them. On the other hand additional questions were raised by the papers and participants in CERME3. The picture of research in mathematics teacher education that evolved during the working group is complex and built by many nested problem areas. Further work is obviously needed before we can discover areas where consistent and well founded results inform us about theories and practices in teacher education.

The invitation for group 12 in CERME3 was for research- or development based papers on the study of teaching practices to issues in teacher education, including questions concerning the teachers work from all aspects.

Particular interest was expressed in theoretical, empirical or developmental papers that address one or more of the following themes:

• The nature and development of teacher knowledge.
• The relationship between teaching and learning in mathematics.
• The role of computer-based tools in teacher education and teachers’ work.
• The elaboration of theoretical frameworks that may provide insightful models for interpreting evidence from research on pre- and in-service education and teachers work.

The third aspect of these four did not take up much interest in the group work. One reason for that might be that other groups were dealing with this issue. Theoretical frameworks that could provide insightful models were not common either. Many of the studies were carefully looking at one specific issue and trying to go deep into it. As a result of this fact it is not easy to see a broader picture or fit the different studies together in a coherent overview. There is a need for further work in CERME4 on issues on teacher education and development.

This introduction was written by Barbro Grevholm and it is based on the collaborative work of the coordinator and the group leaders of TG-12 in planning and implementing the working group.

List of contributions

List of Thematic Groups