A practice based agenda for teacher content knowledge
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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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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

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.


Knowing multiplication

49

X 25

Knowing multiplication


Knowing multiplication for teaching analyzing errors

How did students get each of these answers?

Knowing multiplication for teaching:Analyzing errors


Knowing multiplication for teaching analyzing correct answers

Knowing multiplication for teaching: Analyzing correct answers

Is there a method? Would it work to multiply any two whole numbers?


Other tasks of teaching mathematics

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)


Modeling

Modeling

  • Red “pies” to represent negative numbers

  • Green “pies” to represent positive numbers


Viewing focus

Viewing focus:

What mathematical work for teaching is suggested?


Implicit model of influences on student achievement1

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.


Sample item writing story problems

Sample item:Writing story problems

10


Sample item choosing examples for ordering decimals

Sample item:Choosing examples for ordering decimals

  • .5 7.0111.4

  • .60 2.533.12.45

  • .64.25 .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?

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