1. International Symposium for Pre- and In-Service Mathematics and Science Teachers Tad Watanabe Kennesaw State University, Georgia, USA twatanab@kennesaw.edu What Qualities Are Needed for Mathematics Teachers in the Next Decades

2. L. Shulman (1987) Shulman (1987) articulated a framework for teacher knowledge base that included knowledge of: content context general pedagogy curriculum learners educational ends pedagogical content knowledge.

3. Mathematics Knowledge for Teaching Hill, Ball, & Schilling (2008)

4. Subject Matter Knowledge Common Content Knowledge: knowledge that is used in the work of teaching in ways in common with how it is used in many other professions or occupations that also use mathematics. Specialized Content Knowledge: mathematical knowledge that allows teachers to engage in particular teaching tasks, including how to accurately represent mathematical ideas, provide mathematical explanations for common rules and prcedures, and examine and understand unusual solution methods to problems.

5. Developing MKT Through formal education processes, i.e., undergraduate and graduate teacher education programs, professional development opportunities offered by schools and districts, etc.

6. Undergraduate & Graduate Mathematics Courses What mathematics should prospective teachers study? What mathematics should in-service teachers study? How should mathematics courses for prospective teachers be taught? (and by whom?) How much mathematics should be included in a teacher education program?

7. Developing MKT Through formal education processes, i.e., undergraduate and graduate teacher education programs, professional development opportunities offered by schools and districts, etc. From each other and reflecting on own teaching

8. Facilitating Teachers Learning from Each Other We need a knowledge building system

9. Characteristics of Knowledge Building Systems (outside of education) Shared goals across the system: Shared goals are clearly articulated and accepted by all members of the profession. Visible, tangible, changeable products: Artifacts that embody the goals of the system are jointly constructed and steadily improved by incorporating the growing knowledge of the system. Small tests of small changes:The professional artifacts, and the information generated to produce them, are vetted for quality and usefulness by collecting just enough data about small-scale changes. Multiple sources of innovation from throughout the system: All members contribute to the construction of artifacts based on their special expertise, ensuring multiple sources of innovation from throughout the system.

10. Morris & Hiebert (2009)

11. Developing MKT Through formal education processes, i.e., undergraduate and graduate teacher education programs, professional development opportunities offered by schools and districts, etc. From each other and reflecting on own teaching Knowledge Building System Shared Goals Tangible Products: lesson plans, journal articles, conference presentations, books, etc. Disposition and capacity to share and collaborate

12. Disposition & Capacity Making teaching more public Making teaching more intentional Ability to articulate own intentions – both verbally and through writing Ability to observe students Ability to observe teaching etc.

13. Challenges to Japanese Education System Japan appears to have a well-functioning knowledge building system for teaching (mathematics, science, and other subject areas) In spite of many cultural and societal differences, teacher knowledge held by Japanese teachers may be informative to teachers in the United States (and perhaps elsewhere). In addition, know how of knowledge building system WITHIN education may be useful to the education community in the US. Transmit knowledge to the world: both to inform others and to add another layer of vetting in the knowledge building system.

14. Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 39 (4), 372-400. Morris, A. K., & Hiebert, J. (2009). Intorduction: Building knowledge bases and improving systems of practice. The Elementary School Journal, 109 (5), 429-441. Shulman, L.S. (1987). Knowledge and teaching: foundations of the new reform. Harvard Educational Review, 57 (1), 1-22.