Thursday and Friday last week, we had the pleasure of arranging a seminar with Danish colleague Jeppe Skott here in Stavanger. The focus of the seminar was on research concerning teachers' beliefs and their impact on their teaching of mathematics. About 20 people attended the seminar, and I enjoyed it very much!

Skott started off with a session on the historical background of research on beliefs in mathematics education research. He talked about the development of teacher training in the Scandinavian countries, and he pointed to some of the major international studies in recent years. Then he lead us back to the OEEC study from the early sixties, and in this connection, he introduced Bauersfeld's three levels:

As a further theoretical background for the discussion, he introduced theories concerning constructivism (radical and social) and other.

Skott then introduced us with some of his own research in this field, and he introduced the case of Christopher as an example. (See his 2001 article for more on this!) In relation to this example, Skott introduced some of his own concepts: school mathematics images (SMI) and critical incidents of practice (CIP).

On Friday, Skott brought up the difficult and interesting discussion about the nature and existence of beliefs, and how we investigate them. His initial claim was that "traditional beliefs research" had made it impossible to give a reasonable answer to the question about the

relationship between a teacher's conceptions about a subject on the one hand, and the teaching practice on the other hand. The main reason for that is that the answer has already been given as a premise for the research: there is a strong relationship between the two. This has not

been based on empirical evidence, Skott claims.

He then introduced a discussion about methods in beliefs research, and he pointed to the study he and Tine Wedege made of the Nordic KappAbel contest as an example (PDF version of the report). In a discussion of data analysis, Skott introduced the constructivist version of grounded theory presented by Charmaz (2006) as an example.

In the final round, Skott made a strong emphasis on the importance of context in beliefs research, and the implications this has on choice of research methods, etc. Some of his main points were:

Skott started off with a session on the historical background of research on beliefs in mathematics education research. He talked about the development of teacher training in the Scandinavian countries, and he pointed to some of the major international studies in recent years. Then he lead us back to the OEEC study from the early sixties, and in this connection, he introduced Bauersfeld's three levels:

- Matter meant
- Matter taught
- Matter learnt

Significant changes in school mathematics will only be achieved if there are marked changes in the perceptions and attitudes of these teachers and if they are assisted to develop necessary new skills.A strong focus was thereby put on the teachers' perceptions and attitudes. The focus on the teacher as the main problem in the implementation process was thereby presented, and much of the research did (and still do) refer to Ernest's model of the relationship between the espoused and enacted beliefs of the mathematics teacher. A main issue here, according to Skott, is that the premise for this research is taken for granted, and it is not based on analysis of data!

As a further theoretical background for the discussion, he introduced theories concerning constructivism (radical and social) and other.

Skott then introduced us with some of his own research in this field, and he introduced the case of Christopher as an example. (See his 2001 article for more on this!) In relation to this example, Skott introduced some of his own concepts: school mathematics images (SMI) and critical incidents of practice (CIP).

On Friday, Skott brought up the difficult and interesting discussion about the nature and existence of beliefs, and how we investigate them. His initial claim was that "traditional beliefs research" had made it impossible to give a reasonable answer to the question about the

relationship between a teacher's conceptions about a subject on the one hand, and the teaching practice on the other hand. The main reason for that is that the answer has already been given as a premise for the research: there is a strong relationship between the two. This has not

been based on empirical evidence, Skott claims.

He then introduced a discussion about methods in beliefs research, and he pointed to the study he and Tine Wedege made of the Nordic KappAbel contest as an example (PDF version of the report). In a discussion of data analysis, Skott introduced the constructivist version of grounded theory presented by Charmaz (2006) as an example.

In the final round, Skott made a strong emphasis on the importance of context in beliefs research, and the implications this has on choice of research methods, etc. Some of his main points were:

- Inconsistency between beliefs and practice is from the point of view of the observer
- Consistency is situated in practice
- It is NOT the teacher's practice

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