1. Differentiating Mathematics Instruction Session 1: Underpinnings and Approaches Adapted from Dr. Marian Small’s presentation August, 2008

2. 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

3. 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

4. Anticipation Guide Identify your current viewpoint for each statement on the Anticipation Guide. Add three of your own statements regarding differentiating instruction.

5. 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

6. Reflect Have you changed your mind about the best strategies? What new ideas have you heard that you had not thought of before?

7. 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.

8. Current Knowledge What differentiated instruction (DI) is Leading Math Success Report DI considerations: - interest, learning style, readiness - content, process, product

9. Current Knowledge Accepted principles: Focus on key concepts Choice Pre-assessment

10. Differentiation Strategies Menus Tiering Choice Boards (Tic-Tac-Toe or Think-Tac- Toe) Cubing RAFT Stations (Learning Centres)

11. 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….

12. 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….

13. 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.

14. 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.

15. 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?

16. RAFT (sample) ROLEAUDIENCEFORMATTOPIC CoefficientVariableEmailWe belong together AlgebraPrincipal of a school LetterWhy you need to provide more teaching time for me VariableStudentsInstruction manualHow to isolate me Equivalent fractions Single fractionsPersonal adHow to find a life partner

17. 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

18. 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?

19. 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.

20. 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?

21. 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/ResearchSy nopses.pdf