A collaborative Study on innovations for teaching and learning mathematics in different cultures among the APEC member economies

Figure 3. Lesson Study Challenge in Singapore with 21 Japanese teachers supported by the National Institute of Education, Singapore.

2. Difficulties and Challenges for the Lesson Study Movement

Known difficulties for introducing lesson study are basically coming from the custom (or culture). Researchers as scientists usually want to be observers. Teachers usually like their ways and do not want to show their practices to others. Governors want to have soonest statistical evidence before considering various efforts for improvement. Because researchers have to contribute to research journals, teachers have to teach many hours, governors have to set the grants for next year, and all of them try to do their best on their jobs within their culture, we cannot change the ways.

Nevertheless, it is problematic that we tend to find the cause in others and do not easily reflect on ourselves. Teachers usually explain students fail by the problems originated from curriculum, textbooks, parents and students. Researchers usually find problems through the observation, and recommend improvements but most of them do not concern the implementation of their recommendations.

On the other hand, the keywords for introducing lesson study are "challenges beyond the custom"・ For overcoming custom, some cultural impacts given by good lesson study experience will be necessary. Our introductory way for Lesson Study movement in the project is to show and share our challenges for developing good practice on the theme within researchers, teachers and governors. In our case, Japanese teachers show their lesson study challenge in countries around the world such as US, Singapore (Figure 3), Chile and Thailand. There, students talk in local language and Japanese teachers talk in Japanese. Even if the lesson is done through translation, students share mathematical ideas with teachers and learn mathematics beyond difficulty. This has strong cultural impact because until that moment, the participants do not have experience to observe the lesson even if they are parents of children. From the lesson study on theme, they knew that the lessons deeply depended on the teacher and the plan of the lesson. Through the discussion on the theme of the lesson study after the lesson, they learn that the major issues of lesson study are not limited only to learning from one lesson but also include developing new ideas for each participant and wishes for challenges.

Figure 4. APEC project activities through the year

For giving a cultural impact and pushing challenges based on the theme, to show the model lesson study including a demonstration lesson and a panel after demonstration is (are) necessary for knowing what it is and enabling participants to consider the next step by themselves. For considering, the panel must be organized by the theme of the lesson study. The panelists must discuss what they observed in relation to the theme, and ask why-question to the teacher and propose how-question depending on his/her answers. The discussion aims at making clear what is important and necessary for developing fruitful ideas on the theme of the lesson study, and not for evaluation of the teacher, a challenger, even if the critical discussion included some evaluations of the lesson based on the aim of the lesson which was proposed by the challenger and the theme of the lesson study which could be defined by the challenger and panelists.

3. The ways for sharing good Lesson Study practice

In the project, specialists from APEC economies works for developing model teaching approaches with videos through the process.(See Figure 4).

Firstly, we shared the lesson study conference through the live broadcasting on the Internet. Figure 5 are numbers of access from the world in two days at the Third APEC-Tsukuba Conference: Europe-Africa-America were at midnight-night.

Thirdly, we develop local theories of teaching approaches for developing good practice (figure 7) through lesson studies and use videos and theories for teacher education (figure 8). Teachers' pedagogical content knowledge which is necessary for developing good practice is embedded into the local theory. In relation to developing local theories for mathematics teaching through lesson study, we are expecting following publications;

• Problem Solving Teaching Approaches as for a Developing Model Practice
• How to Develop Mathematical Thinking in Classroom
• How to Develop Mathematical Argumentation in Classroom

Figure 6. A Product of APEC Lesson Study on the website.

Figure 7. Local Teaching Theory developed through Lesson Study (Koeno Gravemeijer, Third Tokyo conference, 2007)

Figure 8. Pedagogical Contents Knowledge developed through Lesson Study (Masami Isoda, Third Tokyo conference,2007)

Reference

Isoda,M., Arcavi,A., Mena, A. L., (2007). El Estidio de Clases Japonés, Chile: Ediciones Universitarias de Valparaíso en Mathematicás
Isoda, M., Stephens, M., Ohara, Y., Miyakawa,T. (2007), Japanese Lesson Study in Mathematics, Singapore: World Scientific

URL

http://math-info.criced.tsukuba.ac.jp/