Differentiating Tasks Math 412 February 11 2009 Differentiating

Differentiating Tasks Math 412 February 11, 2009

Differentiating Instruction o “…differentiating instruction means … that students have multiple options for taking in information, making sense of ideas, and expressing what they learn. In other words, a differentiated classroom provides different avenues to acquiring content, to processing or making sense of ideas, and to developing products so that each student can learn effectively. ” Tomlinson 2001

Differentiating Instruction Some ways to differentiate instruction in mathematics class: n n Open-ended Questions Common Task with Multiple Variations Differentiation Using Multiple Entry Points Example Spaces

Diversity in the Classroom o Using differentiated tasks is one way to attend to the diversity of learners in your classroom.

Open-ended Questions o Open-ended questions have more than one acceptable answer and/ or can be approached by more than one way of thinking.

Open-ended Questions o o o Well designed open-ended problems provide most students with an obtainable yet challenging task. Open-ended tasks allow for differentiation of product. Products vary in quantity and complexity depending on the student’s understanding.

Open-ended Questions o An Open-Ended Question: n should elicit a range of responses n requires the student not just to give an answer, but to explain why the answer makes sense n may allow students to communicate their understanding of connections across mathematical topics n should be accessible to most students and offer students an opportunity to engage in the problem-solving process n should draw students to think deeply about a concept and to select strategies or procedures that make sense to them n can create an open invitation for interest-based student work

Open-ended Questions Method 1: Working Backward 1. 2. 3. Identify a topic. Think of a closed question and write down the answer. Make up an open question that includes (or addresses) the answer. Example: 1. 2. 3. Multiplication 40 x 9 = 360 Two whole numbers multiply to make 360. What might the two numbers be?

Open-ended Questions Method 2: Adjusting an Existing Question 1. 2. 3. Identify a topic. Think of a typical question. Adjust it to make an open question. Example: 1. 2. 3. Money How much change would you get back if you used a toonie to buy Caesar salad and juice? I bought lunch at the cafeteria and got 35¢ change back. How much did I start with and what did I buy? Identify a topic. Today’s Specials Green Salad Caesar Salad Veggies and Dip Fruit Plate Macaroni Muffin Milk Juice Water $1. 15 $1. 20 $1. 15 $1. 35 65¢ 45¢ 55¢

Common Task with Multiple Variations o o A common problem-solving task, and adjust it for different levels Students tend to select the numbers that are challenging enough for them while giving them the chance to be successful in finding a solution.

Plan Common Tasks with Multiple Variations o o The approach is to plan an activity with multiple variations. For many problems involving computations, you can insert multiple sets of numbers.

An Example of a Common Task with Multiple Variations o Marian has a new job. The distance she travels to work each day is {5, 94, or 114} kilometers. How many kilometers does she travel to work in {6, 7, or 9} days?

Plan Common Tasks with Multiple Variations o o When using tasks of this nature all students benefit and feel as though they worked on the same task. Class discussion can involve all students.

Measurement Example o o Outcome D 2 – Recognize and demonstrate that objects of the same area can have different perimeters. Typical Question (closed task, no choice): n n Build each of the following shapes with your colour tiles. Find the perimeter of each shape. Which shape has the greater perimeter?

Measurement Example (continued) o o New Task (open, choice in number of tiles): Using 8, 16, or 20 colour tiles create different shapes and determine the perimeter of each. Record your findings on grid paper. n n What do you think is the smallest perimeter you can make? What do you think is the greatest perimeter you can make? Prepare a poster presentation to show your results. Sides of squares must match up exactly. Allowed Not Allowed

Differentiation Using Multiple Entry Points o o Van de Walle (2006) recommends using multiple entry points, so that all students are able to gain access to a given concept. Diverse activities that tap students’ particular inclinations and favoured way of representing knowledge.

Multiple Entry Points Based on Five Representations: Concrete Real world (context) Pictures Oral and written Symbols - Based on Learning Modalities: - Verbal Auditory Kinesthetic Based on Multiple Intelligences: - Logical-mathematical Bodily kinesthetic Linguistic Spatial Musical Naturalist Interpersonal Intrapersonal

Sample – 3 D Geometry p. 11

Example Spaces: Quadrilaterals o o o Draw a figure that has four sides Draw another. Draw one that is really different than the first two. Share your three pictures with three other classmates. Sort your pictures in a way that everyone can agree on. Prepare a flip chart with your sorted pictures and be prepared to explain how you sorted them to the class.

Example Spaces: Operations o o o o Think of an number sentence that gives an answer of 12. Think of another. Think of one that is really different than the first two. Share your examples with a partner and see if you have any similar examples. Try to find new examples that are different than the ones you have. List a few more. Partner with another pair and share again. As a group try to find all the numbers sentences you can think of that give an answer of 12. (This could go on forever so decide as a group when you think you have enough).