Transcript Motivation in the Math Classroom

Strategies to Promote
Motivation in the
Mathematics Classroom
TASEL-M August Institute 2006
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?
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.
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
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.
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.
Characteristics of
Higher-Level Mathematical Tasks
Higher-level tasks require students to…
 do more than computation.
 extend prior knowledge to explore unfamiliar
tasks and situations.
 use a variety of means (models, drawings,
graphs, concrete materials, etc…) to represent
phenomena.
 look for patterns and relationships and check
their results against existing knowledge.
 make predictions, estimations and/or
hypotheses and devise means for testing them.
 demonstrate and deepen their understanding
of mathematical concepts and relationships.
The Border Problem
1. Without counting 1by-1 and without
writing anything
down, calculate the
number of shaded
squares in the 10 by
10 grid shown.
2. Determine a general
rule for finding the
number of shaded
squares in any
similar n by n grid.
Video Case:
Building on Student Ideas
• The Border Problem
• What might be the lesson’s 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.
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.
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.
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 don’t finish up you will stay after class.
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?
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.
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 Norma’s method work?
Reflecting on Instructional Practices:
Creating a Self-Inventory Rubric
1. How you can strengthen the ways student
involvement and motivation are promoted and
supported in your classes?
2. Write 3-5 statements about specific strategies
you’d 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.”
3. Identify where you are now and where you want to be.