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

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