TSG27 complements and is focused differently from the work of Topic Study Groups 28 and 29. These groups are more generally concerned with pre- and in-service teacher education. We are concerned with teacher content knowledge and its relationship to teaching skill. This implies that mathematical knowledge for teachers and mathematical knowledge for professional mathematicians have similarities and also important differences. What are these differences? These differences are not restricted to different amounts and different areas of mathematical knowledge. The differences have to be understood on the basis of different epistemological views on the nature of mathematical knowledge in different contexts and on the function for which the mathematical knowledge is used. The call for papers below is indicative of this focus. We are not concerned with teacher beliefs, the relationship between beliefs and practice, nor with teacher education practice and approaches that do not focus on knowledge of mathematics and its use in teaching. These aspects of mathematics teacher education, although important, are in the background for this Topic Study Group, whereas they are likely to be more in focus on TSG28 and 29.

TSG 27’s work is framed by the following focus questions:

Q1. What are (and have been) different perspectives about mathematical knowledge for teaching? What are the bases––theoretical or empirical––for these perspectives? Where are areas of overlap and agreement? Where and what are major differences? Do these represent substantially conflicting views, or do they simply reflect giving attention to different aspects of the question?

Q2. What are (and have been) different methods of studying mathematical knowledge for teaching ––what teachers know and use, or what they need to know and know how to use? What are key common and distinct aspects of the methods used to answer these questions?

Q3. What are (and have been) different empirical research fields or contexts e.g. in primary or secondary classrooms, with or without digital technologies, with or without teachers as co-researchers, in mathematics or maths method classes for teachers? How have these shaped the research questions pursued?

Q4. How could research results gained by different research methodologies (quantitative, qualitative, interpretative research methods) support teachers developing their mathematical knowledge and their professional view on the nature of mathematics in teaching?

Q5. What are some distinct approaches to helping teachers develop the mathematical knowledge they need to know and know how to use? What kinds of evidence are there about how these function and with what effects?

PROGRAMME

Day 1, MONDAY 7 July 1 hour: Framing the work of the group

Major issues in the terrain of maths knowledge for teaching -Jill Adler, Deborah Ball An epistemological orientation to the problem of MKT ...Heinz Steinbring

Day 2: WEDNESDAY 9 July 90 mins.

Work in smaller groups on a selection of themes informed by the submitted papers.

We ask that all participants read the papers prior to the Congress. Some of the papers speak to more than one of the themes. We think these are interesting themes that can both inform the discussion, and give scope for those who have contributed papers to talk about their work within a larger theme.

Provisional themes * Are MKT and its components most effectively described and grasped by topic? Big ideas? Mathematical use? (Yasuhiro Sekiguchi and Mercy Kazima) * Are categories or distinctions within MKT useful and for what? (Li Jianhua, Dany Huillet) * Is MKT teachable and in what forms? (Craig Pournara, Raven McCrory). * Is MKT measurable? If so, what kinds of measures are in use and in what contexts, for what purposes? How do such measures interact with environments of high stakes assessments. (Mark HooverThames, Stefan Krauss)

Day 3. FRIDAY 11 JULY, 1 Hour.

Synthesis: What do we seem to agree on, what not, and why?

Brent Davis and Tim Rowland

Day 4 SATURDAY 12 July 90 Mins: Ways forward for this line of work; critical next steps

1. Greater shared understanding of breadth of question, ranging and developing methodologies (approaches and methods and how they shape the work) as well as emerging knowledge/understanding

2. Exemplars of practice

3. Post–ICME report/publication

Thirty papers have been received and accepted. See details below. We welcome other participants to the sessions at the Congress.

The papers listed alphabetically below have all been accepted for discussion in the Topic Study Group TSG27.

(Please note the paper by Thames et al. is not in alphabetical order. It has just been received and uploaded on to the site. The paper can be found at the end of the list. Message posted-20 Jun 08.)

(Please note that the papers by Heid and Senk et al. are not in alphabetical order. They have just been received and uploaded on to the site. The papers can be found at the end of the list. Message posted-30 Jun 08.)

(Please note that the paper by Kristjansdottir is not in alphabetical order. It has just been received and uploaded on to the site. The paper can be found at the end of the list. Message posted-05 Jul 08.)