1. International Workshop On Graduate Program for Secondary Mathematics and Science Teachers: What Qualities are Needed?

2. Group Discussion I Common Issues and Trends in Mathematics Teacher Education Situations & Issues of in Each Country Case of U.K. Case of U.S. Case of Chaina Case of Japan

3. Situations & Issues in Each Country Acquire and guarantee excellent students (influence of the economy recession) Accept foreign students (from China, Asia region…) on graduate schools Decreasing the numbers of children Post-doctor program Similar situations & issues in Japan Case of U.K.

4. Situations & Issues in Each Country How to train the excellent teachers But,,,Qualities’’ level is different between U.S. and Japan [Background for Qualities] Depends on talented/gifted Not-consider growth as teacher Acquire/Gather the excellent students All teacher training/education on undergraduate Trains to the excellent teachers Case of U.S.

5. Situations & Issues in Each Country Need the viewpoint of global Expand curriculum categories/job market (e.g. statistics education) Employment examination and authority of school principal Using Technology (e.g. using graphing calculator is influenced by AP calculus) School teachers (especially, elementry school teachers) can’t solve mathematics Difference between Ph.D. and Ed.D. Case of U.S.

6. Situations & Issues in Each Country Huge influences from U.S. Increasing the numbers of children Need one million teachers for each grade Mathematics contents for teaching in schools are too many Academic background of school teachers is too many college or teacher college level Most students have graphing calculator without using it Case of China

7. Situations & Issues in Each Country Elementary school teacher can’t solve mathematics Upper secondary school teacher like/love mathematics, but don’t like education. Students can get school teacher licenses at graduating university Tendency to get some licenses Differences between master of education and professional degree course (e.g. employment examination, necessary conditions…) Case of Japan

8. Group Discussion II What Qualities are Needed among Mathematics Teachers? Abilities/Competencies of mathematics Knowledge or practices of teaching methods Curriculum Some Aspects Difference between MKT and PCK Research methods Lesson study

9. What Qualities are Needed among Mathematics Teachers? Problems of upper secondary level Target is entrance examination in Japan (e.g. statistics) Students have to know mathematics well What is know mathematics well? Difference subjects between mathematics education students and mathematics proper students (e.g. history of mathematics) Need to understand system of mathematics from school level to academic level Abilities/Competencies of mathematics

10. What Qualities are Needed among Mathematics Teachers? Abilities of developing materials (c.f. aspect of MKT and PCK) Background of problems (When? Why? How?) Lack of concept for studying materials in U.S. Abilities of interpreting Interpretation of pupils/students ideas Interpretation of text Abilities of designing lessons Connections between school mathematics and academic mathematics (e.g. projective geometry, number theory…) Knowledge or practices of teaching methods

11. What Qualities are Needed among Mathematics Teachers? Not desirable to know specific teaching method Observing good lesson practice Developing abilities to observe lesson (c.f. aspect of lesson study) Cultural difference for Teaching method Art of teaching (e.g. Professional Development (Phase I) is a stage to master knowledge, and Professional Development (Phase II) is a stage to use/apply the knowledge and raise abilities) Craft of teaching (e.g. approach good practices through imitation) Knowledge or practices of teaching methods

12. What Qualities are Needed among Mathematics Teachers? Changes of,,Course of study’’ and aims Curriculum development study is not useful (c.f. aspect of lesson study) Not needed to develop curriculum, but needed to understand curriculum Not needed the question: What to teach? (e.g. teachers’ guides are edited by textbook companies and some excellent teachers) Lack of curriculum senses What is,,Curriculum’’ ? Planed curriculum, implemented curriculum… Curriculum

13. Difference between MKT(Mathematical Knowledge for Teaching) and PCK(Pedagogical Content Knowledge) MKT is needed to interpret contents mathematically, and PCK is in-service teacher training in Japan. (c.f. aspect of lesson study) Distinguish MKT from PCK is dificult What is background both MKT and PCK? Aspect of MKT and PCK

14. What is basic of research method? Implementing research from perspective of systematic made public Perspective of systematic made public is lack in action research. Absorbing only the method is not good Writing documents or papers by English Aspect of Research Method

15. Difference lesson study based on cultural background Held on teacher center in U.S. Autonomy in school level independently in old Japan Observing the attached schools in both graduate of education and professional degree course Difference between instructional reader and Principal ship Difference system of administrator(e.g. principal) in schools Aspect of Lesson Study