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California State University - Northridge
Professional Development Workshop
Wednesday, February 28, 2007, 4:30 - 6:00 pm
Oviatt Library Presentation Room

Deborah Ball, Hyman Bass, Imani Masters-Goffney, Laurie Sleep, Mark Thames
How Does Mathematical Language Figure in the Work of Teaching? What Does This Imply for the Mathematical Knowledge Needed for Teaching?
Abstract:
Mathematical language plays a central role in mathematics teaching and learning. To start, it is a foundation of mathematical reasoning, essential for constructing mathematical knowledge and providing resources for developing and justifying claims. Furthermore, mathematical language is not only something that students must learn to understand and use; it is also the primary medium of instruction. What is surprising, however, is that although mathematical language clearly matters for mathematics teaching and learning, exactly what teachers need to know about mathematical language remains underexplored. Using video records of classroom practice, this talk investigates the work of carefully attending to and using mathematical language in teaching, and the implications for mathematical knowledge for teaching and teaching with sensitivity to issues of equity.

California State University - Northridge
Workshop and Public Lecture
February 23-24, 2006

Public lecture, Feb. 23:
Deborah Ball, Hyman Bass, Laurie Sleep, Mark Hoover Thames, University of Michigan
Mapping the Domain of Mathematical Knowledge for Teaching: Knowing and Using Mathematics as a Teacher
Although widespread agreement exists that content knowledge is essential for effective instruction, what is actually meant by "content knowledge" varies. Terms such as "mathematical knowledge" and "pedagogical content knowledge" are used in different ways by different people, often without anyone noticing the confusion. We suggest that efforts to design opportunities for teachers to learn mathematics are hampered by this lack of specification and discrimination, and the lack of shared definitions for terms and ideas about "content knowledge." In this session, we will explore a set of distinctions that our research group has developed to "map" the territory of "mathematical knowledge for teaching" and consider what might be involved in helping teachers learn these different domains of content knowledge. The session will involve participants in direct engagement in artifacts of practice, taken directly from the work of teaching mathematics.

Workshop, Feb. 24:
Deborah Ball, Hyman Bass, Laurie Sleep, Mark Hoover Thames, University of Michigan
Learning to Do Mathematics in Teaching
In this session, participants will explore ways to develop teachers' skills with the mathematical work of teaching. Several core tasks of teaching mathematics will be examined, together with tasks and structures that can support teachers learning to do the mathematical work of the profession. Examples include analyzing student errors, selecting numerical examples, choosing and using representations, and developing definitions. In each case, we will frame and set up a task of teaching that will give participants the opportunity to understand the work, try it, analyze how it went, and compare their work with others'.