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Differentiation in Mathematics
Transcript of Differentiation in Mathematics
Apps for Students
Pre-K to Grade 1
Small, M. (2012). Great Ways to Differentiate Mathematics Instruction. New York, NY: Teachers College Press.
Tomlinson, C. A. (1999). The Differentiated Classroom: Responding to the Needs of All Learners. Alexandra, VA: Association for Supervision and Curriculum Development.
Tomlinson, C. A., & Edison, C.C. (2003). Differentiation in Practice, K-5: A Resource Guide for Differentiating Curriculum. Alexandra, VA: Association for the Supervision and Curriculum Development.
Tomlinson, C.A., & Allan, S.D. (2011). Leadership for Differentiating Schools and Classrooms. Alexandria, VA: Association for the Supervision of Curriculum Development.
Westphal, L. E. (2011). Differentiating Instruction with Menus: Math. Waco, TX.
Websites for Students
"Consistently using a variety of instructional approaches to modify content, process, and/or products in response to learning readiness and interest of academically diverse students." (Tomlinson, 1999)
"In the context of education, we can define differentiation as a teacher's reacting responsively to a learner's needs." (Tomlinson & Allan, 2011)
"...differentiated instruction refers to a systematic approach to planning curriculum and instruction for academically diverse learners. It is a way of thinking about the classroom with the dual goals of honoring each student's learning capacity." (Tomlinson & Edison, 2003)
Differentiated instruction creates a variety of entry points to ensure students are able to access the curriculum meaningfully.
Content is what we want students to know, understand, and be able to do.
Process is how lessons are taught and how activities are designed to help students develop an understanding of content.
Products are the items used to demonstrate knowledge, understanding, and/or ability to apply or extend skills.
Present information through visual, tactile, and auditory means.
Provide small group or individual instruction to reteach concepts or extend thinking.
Utilize varying levels of examples during mini-lessons.
"A question is open when it is framed in such a way that a variety of responses or approaches are possible" (Small, 2012, p. 6)
Strategies for Open Questions
Turning Around a Question
Asking for Similarities and Differences
Replacing a Number with a Blank
Creating a Sentence
Using "Soft" Words
Changing the Question
What is half of 20?
10 is a fraction of a number.
What could that number be?
*Give the answer and ask for the question.
What is the hypotenuse of a right triangle if the legs are 3 units and 4 units long?
One side of a right triangle is 5 units long. What could the other side lengths be?
*Teacher chooses two items and asks how they are similar and different.
How is number 10 similar to number 2?
How are a cube and a square similar?
* Replace a number with a blank and allow students to choose the number to use.
Choose two numbers for two class sizes and determine the total number in both classes.
*Ask students to create a sentence that includes certain words and numbers.
Create a sentence that includes the number 2 and 3 and the words "and" and "more."
*Use words that are somewhat vague to allow for less precision in order to foster richer, more interesting conversation.
What are two numbers that add to something close to 75?
*Begin with a question already available, such as a question from a text resource.
Jack has 4 packages of gum. There are 5 pieces in each package. How many pieces of gum does Jack have in all?
Jack has some packages of gum. There is one more piece in each package than the number of packages. How many pieces of gum does Rodney have in all?
A cookie has a diameter of 1.75 inches. Express the diameter as a fraction in simplest form.
The diameter of a cookie is between 1 and 2 inches. Express the diameter as a fraction in two different ways.
Varying time for activities
Varying length of assignments
*"Parallel tasks are sets of tasks, usually two or three, that are designed to meet the needs of students at different developmental levels, but that get at the same big idea and are close enough in context that they can be discussed simultaneously" (Small, 2012, p. 10)
There were 483 students in the school in the morning. 99 students left for a field trip. How many students are left in the school?
There are 71 students in 3rd grade in the school. 29 of them are in the library. How many are left in their classroom?
Differentiate the types of required individual or group projects.
Use different rubrics
Give options on how to express overall mastery of concepts
*Menus can be used to provide choice and to differentiate instruction.
Three -Shape Menu
Point-Based List Menu
Give Me Five Menu
Grades 4 +
Grades 2 to 3
Heacox, D. (2012). Differentiated Instruction "in the Regular" Classroom: How to Reach and Teach All Learners, Grades 3-12. Minneapolic, MN: Free Spirit Publising Inc.
Diller, D. (2011). Math Work Stations: Independent Learning You Can Count On, K-2. Portland, ME: Stenhouse Publishers.