Strategies to Promote Motivation in the Mathematics Classroom

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Strategies to Promote Motivation in the
Mathematics Classroom

• TASEL-M August Institute 2006

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Motivation in the Math Classroom

• In pairs discuss
• What, ideally, does student involvement in
  learning mathematics look and feel like from
• your perspective as a teacher?
• the perspective of your students?

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Research on Motivation

• Guiding question What factors promote (or
  discourage) students involvement in thinking
  about and developing an understanding of math?
• Involvement is more than being physically
  on-task
• Focused concentration and care about things
  making sense
• Intrinsically motivated to persist
• Cognitively engaged and challenged
• Two areas of focus
• Cognitive Demand of Mathematical Tasks
• Discourse Strategies
• References
• Henningsen Stein (1997). Mathematical tasks and
  student cognition. Journal for Research in
  Mathematics Education, 28(5), 524-549.
• Turner et al. (1998). Creating contexts for
  involvement in mathematics. Journal of
  Educational Psychology, 90(4), 730-745.

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Mathematical Tasks

• What is cognitive demand?
• Focus is on the sort of student thinking
  required.
• Kinds of thinking required
• Memorization
• Procedures without Connections
• Requires little or no understanding of concepts
  or relationships.
• Procedures with Connections
• Requires some understanding of the how or why
  of the procedure.
• Doing Mathematics

Lower level
Higher level
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Examples of Mathematical Tasks (1)

• Memorization
• Which of these shows the identity property of
  multiplication?
• A) a x b b x a
• B) a x 1 a
• C) a 0 a
• Procedures without Connections
• Write and solve a proportion for each of these
• A) 17 is what percent of 68?
• B) 21 is 30 of what number?
• Too much of a focus on lower level tasks
  discourages student involvement in learning
  mathematics.

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Examples of Mathematical Tasks (2)

• Procedures with Connections
• Solve by factoring x2 7x 12 0
• Explain how the factors of the equation relate to
  the roots of the equation. Use this information
  to draw a sketch of the graph of the function
  f(x) x2 7x 12.
• Doing Mathematics
• Describe a situation that could be modeled with
  the equation y 2x 5, then make a graph to
  represent the model. Explain how the situation,
  equation, and graph are interrelated.
• Higher level tasks, when well-implemented,
  promote involvement in learning mathematics.

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Characteristics ofHigher-Level Mathematical Tasks
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The Border Problem

• Without counting 1-by-1 and without writing
  anything down, calculate the number of shaded
  squares in the 10 by 10 grid shown.
• Determine a general rule for finding the number
  of shaded squares in any similar n by n grid.

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Video CaseBuilding on Student Ideas

• The Border Problem
• What might be the lessons goals and objectives?
• What is the cognitive demand of the task (as
  designed)?
• As you watch, consider
• Who is doing most of the thinking?
• How does the teacher support student
  involvement?
• After watching, think about
• What sort of planning would this lesson require?
• From Boaler Humphreys (2006). Connecting
  mathematical ideas. Portsmouth, NH Heinemann.

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Discourse Strategies (less involvement) I-R-E

• Initiation-Response-Evaluation (I-R-E)
• Ask a known-answer question
• Evaluate a student response as right or wrong
• Minimize student interaction through prescribed
  turn taking
• Establish the authority of the text and teacher
• Examples
• What is the answer to 5?
• What are you supposed to do next?
• What is the reciprocal of 3/5? 5/3. Very good!
• That is exactly what the book says.

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Discourse Strategies (less involvement)
Procedures

• Procedures
• Give directions
• Implement procedures
• Tell students how to think and act
• Examples
• Listen to what I say and write it down.
• Take out your books and turn to page 45.

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Discourse Strategies (less involvement)
Extrinsic Support

• Extrinsic Support
• Superficial statements of praise (focus is not on
  the learning goals and objectives)
• Threats to gain compliance
• Examples
• You have such neat handwriting.
• These scores are terrible. I was really shocked.
• If you dont finish up you will stay after class.

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Discourse Strategies (more involvement)
Intrinsic Support

• Intrinsic Support
• View challenge/risk taking as desirable
• Respond to errors constructively
• Comment on students progress toward the learning
  goals and objectives
• Evoke students curiosity and interest
• Examples
• That's great! Do you see what she did for 5?
• This may seem difficult, but if you stay with it
  you'll figure it out.
• Good. You figured out the y-intercept. How
  might we determine the slope here?

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Discourse Strategies (more involvement)
Negotiation

• Negotiation
• Adjust instruction in response to students
• Model strategies students might use
• Guide students to deeper understanding
• Examples
• What information is needed to solve this problem?
• Try to break the problem into smaller parts.
• Here is an example of how I might approach a
  similar problem.

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Discourse Strategies (more involvement) Transfer
Responsibility

• Transfer responsibility
• Support development of strategic thinking
• Encourage autonomous learning
• Hold students accountable for understanding
• Examples
• Explain the strategy you used to get that answer.
• You need to have a rule to justify your
  statement.
• Why does Normas method work?

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Reflecting on Instructional Practices Creating a
Self-Inventory Rubric

• How you can strengthen the ways student
  involvement and motivation are promoted and
  supported in your classes?
• Write 3-5 statements about specific strategies
  youd like to work to improve this year.
• Draw ideas from On Common Ground, TARGET TiPS,
  motivation data, and Motivation in the Classroom
  presentation
• Examples
• I give students tasks that require them to think
  about mathematical relationships and concepts.
• I provide feedback to students that promotes
  further thinking and improved understanding.
• I allow opportunities for students to be an
  authority in mathematics.
• Identify where you are now and where you want to
  be.