International Symposium for Pre- and In-Service

Mathematics and Science Teachers

Tad WatanabeKennesaw State University, Georgia,

USAtwatanab@kennesaw.edu

What Qualities Are Needed for Mathematics Teachers in the Next

Decades

L. Shulman (1987)Shulman (1987) articulated a framework

for teacher knowledge base that included knowledge of:contentcontextgeneral pedagogycurriculumlearnerseducational endspedagogical content knowledge.

Mathematics Knowledge for Teaching

Hill, Ball, & Schilling (2008)

Subject Matter KnowledgeCommon 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.

Developing MKTThrough formal education processes,

i.e., undergraduate and graduate teacher education programs, professional development opportunities offered by schools and districts, etc.

Undergraduate & Graduate Mathematics CoursesWhat 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?

Developing MKTThrough 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

Facilitating Teachers Learning from Each OtherWe need a knowledge building system

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.

Morris & Hiebert (2009)

Developing MKTThrough 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 teachingKnowledge Building System

Shared GoalsTangible Products: lesson plans, journal articles,

conference presentations, books, etc.Disposition and capacity to share and collaborate

Disposition & CapacityMaking teaching more publicMaking teaching more intentionalAbility to articulate own intentions – both

verbally and through writingAbility to observe studentsAbility to observe teachingetc.

Challenges to Japanese Education SystemJapan 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.

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.