Norma08 - Day 1

Plenary - J. Skott
The Norma 08 Conference takes place in Copenhagen this week, and I am attending. I will therefore have a focus on this conference this week. The first plenary lecture was presented by Danish researcher Jeppe Skott, and here are my notes from the presentation (which was very interesting by the way). I also plan on covering the conference on twitter, so take a look there as well for live reports!

Title: "The education and identity of mathematics teachers"
Research on mathematics teachers has grown tremendously during the past 20-30 years. Skott starts with a presentation about publications, journals, monographs, etc.
Two main concerns:

• Teachers' knowledge
• Teachers' beliefs

In the 1980s - a shift in the view of learning, mathematics, etc. changed the whole field of school mathematics (fallibilism, social constructivism). Teachers placed in a new role, as opposed to before. Teachers supposed to understand what students are doing, and to guide their learning. New role: planned unpredictability (interesting concept!)

Teachers' knowledge
Displays a couple of examples from the literature that displays teachers' (lack of) knowledge about mathematics (for teaching). Perhaps pre-service education is not what it should have been?
The importance of Shulman's work. The article "Those who understand..." A main idea: content matters! Two of Shulman's concepts important:

• Content knowledge
• Pedagogical content knowledge

What is it that teachers' should know about? (content knowledge)
What is it that makes a topic difficult? (pedagogical content knowledge)

The mathematics of the classroom - the mathematics of the mathematician.
Liping Ma - asked teachers in China and the US lots of questions concerning basic mathematics. Many teachers (esp. the US teachers) weren't able to solve the problems. A basic question for her - What is the relevant knowledge needed by teachers? American teachers - list of disconnected procedures. Chinese teachers - alle these procedures were related. "Understanding with bredth."
D. Ball, H. Bass et al. Classroom based approach. Mathematical challenges from the classroom. (Elements from the LMT measurements) D. Ball calls it "unpacking mathematical knowledge" - digging deeply into the conceptual issues.

A shift in the area of developing a knowledge base for teaching:

• From - number of courses
• to - knowledge of school mathematics (L. Ma)
• to - knowing in action (D. Ball)

Beliefs research in math education
In order for any reform to have an impact there needs to be a change in the teachers' beliefs.
Developing and changing beliefs. Several suggestions and attempts (see points in slide).
Relationship between beliefs and practice.

A moral so far: There is a need for contextualizing mathematics education to the act of teaching.

Discussion of the relationship (or expected relationship) between development of curriculum and curriculum material and teaching practice.
As researchers, a main issue is the one of theorizing practice.

Poses an interesting question: In what sense is mathematics education an applied field?
Points at an interesting quote by P. Cobb about the issue of mathematics education (research).
Interesting model about the dimensions of research (by Stokes).

A main issue for research in math education is maybe not about theorizing, but about having impact on practice.

The end of the talk filled with intriguing questions and interesting metaphors. (Thaetetus' ship - if you replace a plank, and then another plank, when is it no longer Thaetetus' ship, but a new one?)

All in all a very interesting presentation! Hopefully these notes could be deciphered by others as well...