Differentiating Mathematics Instruction

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Differentiating Mathematics Instruction

• Session 2
• Focusing on Important Mathematics Big Ideas

Adapted from Dr. Marian Smalls presentation
August, 2008
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but also the big picture
Thinking about the pieces
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Goals for Session 2

• Develop an understanding of the notion of
  instructional trajectories
• Become more knowledgeable about big ideas in
  mathematics
• Make connections between big ideas in Ontario
  mathematics courses and instructional
  trajectories
• Appreciate the value of big ideas for planning
  and teaching

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Differentiated Instruction Synopsis

• Stand Up/Hand Up/ Pair Up
• Discuss the synopsis you chose to read about.
• Highlight something you found interesting, new,
  not sure of, or
• Find a new sharing partner and repeat the
  activity.

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Integer Addition and Subtraction

• Individually write down the big ideas on stick-on
  notes.
• In your groups create a concept map, linking
  your ideas.
• Post your concept maps.
• Do a Gallery Walk to review others work.
• Share your observations in a group discussion.

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Big Ideas - Planning Instructional Sequences

• Instructional trajectories/learning
  landscapes/knowledge packages
• A description, usually visual, of the development
  that helps you see where students come from and
  where they go to

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Landscape of Learning

• Big ideas or key ideas (ovals)
• Strategies (rectangles)
• Models or representations (triangles)

Fosnot, 2002
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Mathematics Knowledge Package
Ma, 1999
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Integer /- trajectory
M Small
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Big Ideas

• Plan instructional path
• Identify connections and learning pathways

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Specific Expectations

• Construct tables of values, graphs and equations
  using a variety of tools to represent linear
  relations derived from descriptions of realistic
  situations
• Describe a situation that would explain the
  events illustrated by a given graph of a
  relationship between two variables or

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Examples

• With certain relations, all you need to know are
  two pieces of data and you can describe the whole
  relation.
• With certain kinds of relations, a specific
  increase in one variable always results in a
  specific increase in the other.

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What are the big ideas you teach?

• Move to a table with teachers who teach one of
  the same courses you do.
• What is a big idea in that course?
• What is important to teach, but not a big idea?
• Create an instructional trajectory for your Big
  Idea.

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Share Your Thinking

• Post your instructional trajectories.
• Do a Gallery Walk to review others work.
• What observations did you make?

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Exit Card

• Consider and write a response to
• Something you learned that would be useful
• A question you still have or something you have
  doubts about

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Home Activity

• In your reflection journal, write about
• something you learned that you think might be
  useful in your teaching.
• something with which you disagree with or have
  doubts about.
• why considering Big Ideas helps in
  differentiating learning.