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A Practice-Based Agenda for Teacher Content Knowledge

A Practice-Based Agenda for Teacher Content Knowledge. Laurie Sleep, Mark Thames, Deborah Ball, and Hyman Bass University of Michigan Developing Working Knowledge of the NMP Report Center on Instruction • Long Beach, CA • December 10, 2008. Implicit model of influences on student achievement.

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A Practice-Based Agenda for Teacher Content Knowledge

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  1. A Practice-Based Agenda for Teacher Content Knowledge Laurie Sleep, Mark Thames, Deborah Ball, and Hyman Bass University of Michigan Developing Working Knowledge of the NMP Report Center on Instruction • Long Beach, CA • December 10, 2008

  2. Implicit model of influences on student achievement Teacher knowledge Instruction Student achievement We need to know more about what mathematical knowledge matters for the work teachers do and how that knowledge impacts instruction. We need better measures to test these hypotheses and to support improvement efforts.

  3. 49 X 25 Knowing multiplication

  4. How did students get each of these answers? Knowing multiplication for teaching:Analyzing errors

  5. Knowing multiplication for teaching: Analyzing correct answers Is there a method? Would it work to multiply any two whole numbers?

  6. Other tasks of teaching mathematics • Responding to students’ “why” questions • Unpacking and decomposing mathematical ideas • Explaining and guiding explanation • Using mathematical language and notation • Generating examples • Sequencing ideas • Choosing and using representations • Analyzing errors • Interpreting and evaluating alternative solutions and thinking • Analyzing mathematical treatments in textbooks • Making mathematical practices explicit • Maintaining the cognitive demands of problems • Matching teaching strategies to student learning goals • Attending to issues of equity (e.g., language, contexts, mathematical practices)

  7. Modeling • Red “pies” to represent negative numbers • Green “pies” to represent positive numbers

  8. Viewing focus: What mathematical work for teaching is suggested?

  9. Implicit model of influences on student achievement Teacher knowledge Instruction Student achievement We need to know more about what mathematical knowledge matters for the work teachers do and how that knowledge impacts instruction. We need better measures to test these hypotheses and to support improvement efforts.

  10. Sample item:Writing story problems 10

  11. Sample item:Choosing examples for ordering decimals • .5 7 .01 11.4 • .60 2.53 3.12 .45 • .6 4.25 .565 2.5 • These lists are all equally good for assessing whether students understand how to order decimal numbers. Which of the following lists would be best for assessing whether your students understand decimal ordering? 11

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