differentiating mathematics instruction session 1: underpinnings and approaches adapted from dr....
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Differentiating Mathematics Instruction Session 1:
Underpinnings and Approaches
Adapted from Dr. Marian Small’s presentation August, 2008
Goals for Series• Develop familiarity with the principles of
differentiated instruction (DI)• Learn about specific strategies and structures • Practise using these strategies• Consider Big Ideas for topics you teach• Make connections between instruction and
assessment• Reflect on your own practice of DI
Goals for Session 1
• Recognize your own starting point• Consider what differentiating instruction (DI)
means• Learn about some generic structures• Think about how students differ
mathematically
Anticipation Guide
• Identify your current viewpoint for each statement on the Anticipation Guide.
• Add three of your own statements regarding differentiating instruction.
Four Corners
The best way to differentiate instruction is to:
• teach to the group, but differentiate consolidation
• teach different things to different groups
• provide individual learning packages as much as possible
• personalize both instruction and assessment
Reflect
• Have you changed your mind about the best strategies?
• What new ideas have you heard that you had not thought of before?
Visualization Activity
• Visualize four very different students
to think about as you consider
how you will differentiate instruction.
• Name and briefly describe these students. You will return to these students throughout the sessions.
Current Knowledge
• What differentiated instruction (DI) is
• Leading Math Success Report
• DI considerations: - interest, learning style, readiness - content, process, product
Current Knowledge
Accepted principles:• Focus on key concepts• Choice• Pre-assessment
Differentiation Strategies
• Menus
• Tiering
• Choice Boards (Tic-Tac-Toe or Think-Tac-Toe)
• Cubing
• RAFT
• Stations (Learning Centres)
Sample Menu
• Main Dish: Use transformations to sketch each of these graphs: h(x) = 2(x- 4)2,
g(x) = -0.5(x + 2)2,….• Side Dishes (choose 2) - Create three quadratic functions that pass
through (1,4). Describe two ways to transform each so that they pass through (2,7).
- Create a flow chart to guide someone through graphing f(x) = a(x –h)2 + k….
Menu (sample)
• Desserts (optional) - Create a pattern of parabolas using a
graphing calculator. Write the associated equations and tell what makes it a pattern.
- Tell how the graph of f(x) = 3(x +2)2 would look different without the rules for order of operations….
Tiering (Sample)
• Calculate slopes given simple information about a line (e.g., two points)
• Create lines with given slopes to fit given conditions (e.g., parallel to … and going through (…))
• Describe or develop several real-life problems that require knowledge of slope and apply what you have learned to solve those real-life problems.
Tic-Tac-Toe (sample)
Complete question # …. on page …. in your text.
Choose the pro or con side and make your argument:The best way to add mixed numbers is to make them into equivalent improper fractions.
Think of a situation where you would add fractions in your everyday life.
Make up a jingle that would help someone remember the steps for subtracting mixed numbers.
Someone asks you why you have to get a common denominator when you add and subtract fractions but not when you multiply. What would you say?
Create a subtraction of fractions question where the difference is 3/5. • Neither denominator you use can be 5. • Describe your strategy.
Replace the blanks with the digits 1, 2, 3, 4, 5, and 6 and add these fractions:[]/[] + []/[] + []/[]
Draw a picture to show how to add 3/5 and 4/6.
Find or create three fraction “word problems”. Solve them and show your work.
Cubing (sample)
• Face 1: Describe what a power is.• Face 2: Compare using powers to
multiplying. How are they alike and how are they different?
• Face 3: What does using a power remind you of? Why?
• Face 4: What are the important parts of a power? Why is each part needed?
• Face 5: When would you ever use powers?• Face 6: Why was it a good idea (or a bad
idea) to invent powers?
RAFT (sample)
ROLE AUDIENCE FORMAT TOPIC
Coefficient Variable Email We belong together
Algebra Principal of a school
Letter Why you need to provide more teaching time for me
Variable Students Instruction manual How to isolate me
Equivalent fractions
Single fractions Personal ad How to find a life partner
Stations (sample)
• Station 1: Simple “rectangular” or cylinder shape activities
• Station 2: Prisms of various sorts
• Station 3: Composite shapes involving only prisms
• Station 4: Composite shapes involving prisms and cylinders
• Station 5: More complex shapes requiring invented strategies
How do students differ?
• How do student responses differ with respect to solving problems:
- in algebra
- involving proportional reasoning?
• How do their responses differ in spatial problems?
• How do students differ with respect to problem solving and reasoning behaviours?
What to do …
• Choose one of the four topics (algebra, proportional reasoning, spatial, problem solving and reasoning behaviours).
• Form four groups (or more sub-groups) based on your choices.
• Be ready to articulate what “big picture” differences you are likely to find as a classroom teacher.
Sharing Thoughts
• Is there one approach as the goal for all students to use?
• Is it appropriate that some students always solve a problem using other approaches?
Home Activity
1. Journal prompt:
How do the differences we discussed relate to your four students?
2. Select one of the DI Research Synopsis Supports for Instructional Planning and Decision Making (p. 9-22) posted at
http://www.edu.gov.on.ca/eng/studentsuccess/lms/ResearchSynopses.pdf
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