Licentiate student Yukiko Asami-Johansson
Linköpings universitet/Högskolan I Gävle
My project is about a study of using a Japanese mathematics teaching method in Swedish classroom discourse. After the beginning of the 80´s, particularly since the recommendation from the NCTM ‘s
Agenda for Action arrived, classroom discourse centered on problem solving has been the focus of many Japanese educators (Miwa, 1992). The current Japanese teaching pattern is considered to be a good form of mathematics lesson among educators in Japan (Iida, 2000). Kazuhiko Souma is one of the Japanese educators/researchers who has introduced and practiced classroom discourse centered on problem solving. The books of his describe teaching methods and have generally a practical perspective with many explicit lesson plans.
There are two main intentions in my project. First, to describe and analyse Kazuhiko Souma’s method, especially compared to other Japanese methods in the same tradition, second, to analyse the possibility of adopting his method to Swedish classrooms in order to develop the mathematical discourse.
Souma’s method stresses that the teacher should present only partial problems to encourage a group discussion concerning alternatives before the presentation of mathematical theory. In particular, the teacher should allow the students to guess answers, make conjectures and reach solutions by discussion before advancing to methods and definitions. He emphasizes that the teacher carefully needs to prepare the problems and subjects, so that students can relate and distinguish the problem from previous knowledge and so that these problems can lead to a multitude of answers and thoughts.
Souma underlines that problem oriented classes should be about mathematics and mathematical theory, not primarily about applied text problems. Through communicating mathematical ideas and by retelling what one’s idea is, one constructs and assimilates one’s thought (Sfard, 2008). Students’ individual mathematical experience is moreover linked to verbal communication (Björkvist, 1993).
The processing of solving such well-crafted problems as regular classroom activities supports the developing students’ mathematical thinking (Silver, Kilpatrick & Schlesinger, 1990). It appears that
Souma’s method is similar to those mathematical researches.
I think there are some conditions to use the Souma’s method: First, the teacher must be confident in his/her mathematical knowledge and thus being able to detect equivalence in mathematical methods and representations of mathematical objects (Cobb, 1988; Wood, 1993). Second, the teacher must establish a social classroom norm so that the students feel totally safe to express and justify their actual thought. It is important that the students have a positive attitude towards listening to their peers’ explanations of mathematical topics. (Yackel & Cobb, 1996; Cobb, et al., 1997; Wood, 1993)
I will make an empirical study together with a teacher of mathematics in an upper secondary school in
Sweden, using Souma’s method in a class focusing on the content area algebra and geometry. I am going to analyse the result from video films and interviews of the teacher and the students with respect to several criteria, for example, problem solving, reasoning, proof, communication, connections and representation.

References:
Björkqvist, O. (1993), Social konstruktivism som grund för matematikundervisning, Nordisk
Matematikkdidaktikk, Vol. 1, nr.1, 8-17.
Cobb, P. (1988). The tension Between Theories of Learning and Instruction in Mathematics
Education. EDUCATIONAL PSYCHOLOGIST,23(2), 87-103.
Iida, S. (2000). Teaching Problem Solving. In Nakahara, T. (Ed.), Sansuu suugakuka juuyouyougo
300 no kisochishiki, Meijitosho, Tokyo. In Japanese, 161.
Miwa, T. (1992), Nihon to amerika no suugakuteki mondaikaiketu no shidou. Toyokan, Tokyo.
Sfard, A. (2008). Thinking as communicating: Cambridge University Press.
Silver, E. A., Kilpatrick, J. and Schlesinger, B. (1990) Thinking Through Mathematics:
New York, NY: College Entrance Examination Board,
Souma, K. (1997) Suugakuka Mondaikaiketu no jugyou” (The teaching of problem solving - the subject of mathematics), Meijitosho, Tokyo. in Japanese.
Wood, T. (1993). CREATING AN ENVIROMENT FOR LEARNING MATHEMATICS: SOCIAL
INTERACTION PERSPECTIVE. Journal for Research in Mathematics Education, vol 6, 15-20.
Yackel, E., Cobb, P. (1996). SOCIOMATHEMATICAL NORMS, ARGUMENTATION, AND
AUTONOMY IN MATHEMATICS. Journal Research in Mathematics Education, vol. 27(4), 458-
477.