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Preparing Teachers to Lead Mathematics Discussions


by Timothy A. Boerst, Laurie Sleep, Deborah Loewenberg Ball & Hyman Bass ó 2011

Background/Context: Discussion is central to mathematics teaching and learning, as well as to mathematics as an academic discipline. Studies have shown that facilitating discussions is complex work that is not easily done or learned. To make such complex aspects of the work of teaching learnable by beginners, recent research has focused on approaches to teacher education that decompose practice into smaller tasks or routines that can be articulated, unpacked, studied, and rehearsed.

Purpose/Objective/Research Question/Focus of Study: Drawing on the elements of Grossman et al.ís (2009) framework for pedagogies of practice in professional education, this article describes an approach to analyzing teaching practice that supports the design of teacher education in which novices to learn how to engage in high-leverage teaching practices and simultaneously develop a sense of why the work is done.

Setting: The context for the study is a mathematics methods course for prospective elementary teachers.

Research Design: The study involved qualitative analysis of both the design of the course and its implementation.

Conclusions/Recommendations: Results from this study suggest that: (1) Decomposing teaching into nested practices of varying grain sizes that maintain the connection between techniques and domains can support beginning teachers in attending simultaneously to the how and the why of practice, as well as provide a map of teaching that teacher educators can use to support the learning of teaching. (2) Nesting early approximations of practice inside subsequent ones is a way to support beginning teachers in building toward recomposed teaching practice. As practices are nested, teacher educators can increase the complexity of the approximations by adjusting the content and authenticity of the context of practice as well as by decreasing the amount scaffolding provided. (3) Assessment is vital to pedagogies of practice. Decompositions, approximations, and representations of practice need to be developed in ways that support assessment for the array of teacher education purposes. (4) Because subject matter is at the heart of teaching, it is crucial to attend to the ways in which the content interacts with pedagogies of practice.



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Cite This Article as: Teachers College Record Volume 113 Number 12, 2011, p. 2844-2877
http://www.tcrecord.org ID Number: 16496, Date Accessed: 7/24/2014 10:43:36 AM

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About the Author
  • Timothy Boerst
    University of Michigan
    E-mail Author
    TIMOTHY BOERST is a clinical associate professor at the University of Michigan School of Education. In 15 years of elementary school teaching, Tim earned National Board Certification, held multiple leadership positions in the National Council of Teachers of Mathematics, and developed scholarship focused on mathematics teaching practice through the Center for Proficiency in Teaching Mathematics at UM and the Carnegie Foundation. He studies teacher preparation and professional development through engagement in program and course design, teaching mathematics methods courses, and leading projects focused on the assessment of teaching practice. He has a Ph.D. in teacher education and a masterís in mathematics education from UM.
  • Laurie Sleep
    University of Michigan
    LAURIE SLEEP is a research investigator at the University of Michigan. Her research interests build on her experience as an elementary teacher and include studying the teaching and learning of elementary mathematics, the mathematical demands of teaching, and the preparation of teachers. She develops assessments of teachersí mathematical knowledge for teaching, designs and studies innovative curriculum and materials for teacher education and professional development, and teaches mathematics content and methods courses for elementary teachers. She has a Ph.D. in mathematics education and a masterís in mathematics from the University of Michigan.
  • Deborah Ball
    University of Michigan
    E-mail Author
    DEBORAH LOEWENBERG BALL currently serves as dean of the University of Michigan School of Education, where she is also the William H. Payne Collegiate Professor. She taught elementary school for over 15 years and continues to teach regularly. Her research focuses on mathematics instruction and on interventions designed to improve its quality and effectiveness. Ball has authored or coauthored over 150 publications and has lectured and made numerous major presentations around the world.
  • Hyman Bass
    University of Michigan
    HYMAN BASS is the Samuel Eilenberg Distinguished University Professor of Mathematics and Mathematics Education at the University of Michigan. Following a long research career in mathematics, in diverse aspects of algebra, with applications to geometry, he has turned his attention increasingly over the past 15 years to mathematics education, largely in collaboration with Deborah Ball. This work focuses notably on mathematical knowledge for teaching and the teaching of reasoning and proving, especially in the early grades.
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