Supporting Rigorous Teaching and Learning of Mathematics

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Supporting Rigorous Teaching and Learning of
Mathematics

• Diagnosing and Questioning Tools for Surfacing
  Student Errors and Misconceptions

Disciplinary Literacy September 1, 2009
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Diagnosing and Questioning

• Why is it important to think about the
  misconceptions or errors that are likely to
  surface as students work on a task?
• Why is it important to anticipate assessing and
  advancing questions that may address errors and
  misconceptions? Why not just tell them what
  they are doing wrong?

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Rationale
the depth of students misunderstandings or the
nature of their misconceptions become obvious
only when they were asked to explain their
thinking
Wagner Parker, 1993
unless students are asked to explain their
thinking, a teacher may no know which concepts
the students understand
Manouchehri Lapp, 2003
The teachers questions must give learners an
opportunity to communicate their reasoning
processes. These types of questions allow the
teacher to gather detailed data on how students
think
Manouchehri Lapp, 2003
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Overview of Activities

• Solve the Wheel of Theodorus task.
• Identify misconceptions and errors that might
  arise as students engage in the task.
• Develop questions to assess and advance students
  who exhibit these misconceptions.
• Recommend modifications to the Wheel of Theodorus
  Lesson Plan to better prepare teachers to
  anticipate, and address, student difficulties.
• Discuss the value of considering student
  misconceptions and of developing questions to
  address them.

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Solving the Wheel of Theodorus Task
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Solving the Wheel of Theodorus Task
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Lesson Goals

• Use the Pythagorean Theorem to determine
  hypotenuse lengths in right triangles.
• Describe and generalize visual and numeric
  patterns.
• Demonstrate and discuss understandings about the
  need and advantage of irrational numbers
  expressed in radical form in certain problem
  situations.

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Key Concept with Content and Performance
Expectations

• Key Concept
• Algebraic expressions can be used to describe,
  represent and analyze number patterns, visual
  patterns and patterns that underlie real-world
  situations.

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Anticipating Errors and Misconceptions

• Identify the misconceptions or errors that you
  think are likely to surface as students work on
  the task.

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Diagnosing and Questioning Tools for Surfacing
Errors and Misconceptions

• Review the possible student responses labeled
  Student A through Student E.
• For each response, diagnose the problem the
  student may be having. Use the Diagnosing and
  Addressing Student Difficulties table to record
  your diagnoses.
• Determine what questions you will ask to assess
  and/or advance each students understanding.

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Diagnosing and Questioning Tools for Surfacing
Errors and Misconceptions

• Review the ways that the lesson plan addresses
  student misconceptions and errors.
• At your table, discuss ways in which the lesson
  plan could be enhanced to better prepare teachers
  to anticipate and address student misconceptions
  and errors.

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Diagnosing and Questioning Tools for Surfacing
Errors and Misconceptions

• Why is it important to think about the
  misconceptions or errors that are likely to
  surface as students work on a task?
• Why is it important to anticipate assessing and
  advancing questions that may address errors and
  misconceptions? Why not just tell them what
  they are doing wrong?