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Differentiating in MathMargaret AdamsMelrose Public Schools

+Please join….

Please sit with your grade level colleagues…

Diana Browning Wright, Teaching and Learning Trainings, 2003

How We Teach Makes A Difference!

+Objectives

Define differentiation and how it applies to math instruction.

Plan for differentiation in math instruction. Name assessments to determine students’ interests

and readiness. Discuss strategies to transform mathematical tasks and

provide for student choice.

+Agenda

Self-Assessment What is differentiation? Planning for Differentiation Assessment: Know Your Students Transform your Task Incorporating Student Choice

Sharing

Write a definition of differentiation that you believe clarifies its key intent, elements

and principles---in other words—a definition that could clarify

thinking in your school or district

1. Pick a column2. Write or think silently3. Be ready to share

Explain to a new teacher what

differentiation is in terms of what he/she

would be doing in the classroom—and why. The definition should help the new teacher develop an

image of differentiation in

action

Develop a metaphor, analogy or visual symbol that you think represents and clarifies what’s

important to understand about

differentiation

Myths About Differentiated Instruction

Individualized instruction a la special education

Chaotic

Homogenous grouping all the time

Tailoring the same suit of clothes

Expecting more of advanced learners and less of struggling learners

New

It’s formulaic; there are a finite number of “correct” strategies that always work

+ 8

A proactive decision-making process that considers critical student learning differences and the curriculum. Differentiated instruction decisions are made by teachers and are based on: (1) formative assessment data, (2) research-based instructional strategies, and (3) a positive learning environment.

Differentiated Instruction Is…

+What are ways we already differentiate?Review the list of math core instructional practices.

Which ones would match our definition for differentiation?

+Self-Assessment on DifferentiationTake the self-assessment on differentiation in math.

+Differentiation in Action

What do you see happening in the clip that differentiating instruction is part of these classrooms?

What surprises you?What questions do you have?

+Differentiation Planning

Content Process Product

Readiness

Interest

Learning Profile

How

to diff

erentiate?

What to differentiate?

+

Readiness

Interest

Learning Profiles

How

to diff

erentiate?

Tasks should reflect or matchthe student’s skill levels.

Readiness

InterestTasks “ignite” curiosity or passion no matter the readiness level.

Learning Profile/Preference

Tasks encourage students towork in a student-preferred manner.

Differentiate by Student:

+Readiness To differentiate according to readiness,

teachers: Identify the content students are to

learn at their grade level. Become familiar with state standards for mathematics.

Assess what students already know. A decision to adapt content should be based on what you know about your students’ readiness. Embed assessments into your instructional practices.

Evaluate the assessment data to determine the levels of content that students can investigate and the pace at which they can do so.

+Interest

To differentiate according to interest, teachers:Identify their students’ favorite books, activities, and pastimes.

Identify ways to link mathematical content to a variety of real world contexts.

Support student choice through interest centers, technology, and assignments with built-in choices.

+Learning ProfilesTo differentiate according to learning profiles, teachers:Determine the circumstances in which

students learn best and provide opportunities to work alone or with others, in quiet and less quiet environments, and in a variety of locations.

Include visual, auditory, and kinesthetic modes of learning.

+Develop understanding of fractions as numbers

MA.3.NF.1.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts…

~Uses halves, fourths

~Uses teacher model

~Works with equivalent fractions with different

denominators

~Works on computer-based game

~Plays board gamewith one peer

~Uses favorite candy fortask

~Color-codes fractional parts~Uses song to

identify “whole vs. part”~Works in mixed ability

group

Readiness Interest Learning Profile

Examples in the Math Class:

+Differentiation Planning

Content Process Product

Readiness

Interest

Learning Profile

How

to diff

erentiate?

What to differentiate?

+

Content Process

Product

What to differentiate?

+Content, Process, and Product

What will students learn (content)? How the students will learn it (process)? How the students will demonstrate their knowledge

(product)?

WHAT we want students tolearn and HOW we give themaccess to it.

Content

Process HOW a student makes senseof the learning.

ProductWHAT a student makesor does that SHOWS he/she has the knowledge, understanding, and skillsthat were taught.

Differentiate by Content:

+Develop understanding of fractions as numbers

MA.3.NF.1.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts…

~Teaches meaning of “equal parts”

using models or pictures~Scaffold standard by

giving quick hints aboutkey points

~”I do it, We do it, You do it”~Cooperative learning

groups ~Use Concrete-

Representational-Abstractlesson

~Create 2 ways topartition equal sets of

jelly beans~Write a word problem

about fractions andequal parts

Content Process Product

Examples in the Math Class:

+Differentiation Planning

Content Process Product

Readiness

Interest

Learning Profile

How

to diff

erentiate?

What to differentiate?

+qContent Process Product

Readiness Pre-teach comparative length terms to Mei and Sasha.Is anyone read for yards yet?

Make inch and foot strips so that some can use multiple units to measure lenght

What sentence stems would support Mei and Sasha?

Interest Let students choose items to measure in the classroom.

Create interest centers that require students to measure.

Write about ways measurement is used in a favorite activity.Make a poster.

Learning Profile

Have Jon and Carla make rulers by pasting inch strips.

Velcro models of inch and foot strips for Jake to feel

Use gestures, oral language, or written descriptions to show how to estimate lengths. Second Grade Example

Measurement

+Content Process Product

Readiness Zach and Micki need to review area model for multiplication

Could I tier some homework assignments

Could students create a video on how to multiply fractions?

Interest Give choices of leveled word problems to solve.

Adapt favorite food recipe for a larger group.

Write word problems for others to solve with real world applications.

Learning Profile

Have completed examples for models.

Connect to reading music?Could Ned, Casey, and Nardia work in the hallway to avoid distractions?

Complete a graphic organizer for multiplying fractions.Create extensions for Sam, Arturo, and Kiki.

Fifth Grade Example Multiplying Fractions

+Planning for Differentiation

Content Process Product

Readiness

Interest

Learning Profile

How

to diff

erentiate?

What to differentiate?

+ASSESSMENT Know Your Students

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+Questionnaires and Interviews for Getting to Know Students Parent or Guardian Questionnaire What Interests You? Questionnaire Who Are You as a Learner? Questionnaire What Do You Think About Mathematics? Questionnaire A Mathematical Autobiography Interviewing Students During Class

+Carosuel Examples

Choose a poster with an example of a questionnaire or interview.

Four to five participants per poster. Annotate the questionnaire. Use the following stems:

We love… We wonder… We disagree… Another idea is…

+Interviewing Students During Class What structures are in place to make it possible for the

teacher to conduct these interviews? What would you recommend the teacher’s action plan

be moving forward? How could you include students in their own action plan?

In your own classroom, how could interviewing your students inform your instruction to make the math accessible to each student?

+Open-Ended Problems Provide insights into student thinking.

Kindergarten: Show the number five in many different ways.

First Grade: Your younger sister wants to learn how to tell time. Make a list of the most important things she needs to know. Or, describe how you would teach her to tell time using pictures, numbers, and words.

Second Grade: What do you know about 12? Show 12 in as many different ways as you can.

Third Grade: What do you know about 100? Fifth Grade: What do you know about ¾? Grades 3-5: What do you know about shapes? Write

and draw to communicate your ideas.

Quick Assessments

Pick one quick assessment that you

could use tomorrow. Be ready to explain how you

would use it.

1. Pick a column2. Write or think silently3. Be ready to share

Explain to a new teacher one of the quick assessments you think best fits the math program.

Pick one quick assessment that you have used.

Explain how you have used it.

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Transform Your Tasks

+Open Up Problems

Tasks can be opened up to allow for one or more solutions and wide range of responses and understandings. Give students choice over the difficulty level Problems with more than one answer What’s the Questions Open Ended Problems

+Give Students Control Over the Difficulty Level Students Provide the Numbers in the Problem

Nora had ____ stamps in her stamp book. There were ____ stamps on each page. Them Nora’s uncle came to visit and gave her stamps to fill _____ more pages in her book and add stamps to the next page. Now Nora had _____stamps.

+Problems with More Than One AnswerDanny had some pennies and nickels. He has 5 coins.How much money could Danny have?

Jocelyn has 15 pencils.Some are sharpened and some are not. How many of each type of pencil could Jocelyn have?

Use graph paper. Draw 6 different quadrilaterals with an area of 6 square units.

+What’s the Question? Problems

Here are the answers, but some many need the cents sign: 4, 22, 2, 48, 26.

Number Story

Colin had 3 nickels and 7 pennies.

Lisa has 9 nickels and 3 pennies.

What could be the questions?

+Open Ended Problems

What are some different triangles that you can draw? Dana added 26 and 47 an got a sum of 63. What could

you show and tell Dana to help her find the correct sum?

What are some patterns you see on the hundreds chart?

How could you describe a parallelogram to someone who has never seen one?

How is measurement used in your home? The answer is 5.25. What could the question be?

+Partners Working on Open Ended Task What skills does each learner demonstrate? What misconceptions did you notice? What questions would you want to ask to check each

students’ understanding of the mathematics?

Place the numbers: 3,4,6,15, 20 and 30, so that the product of each side is 360.

Write one more problem like this one and trade it with a classmate.

+Vary the Challenge

Tiered Tasks Students focus on the same general concept

but do so according to their level of readiness.

Identify the important mathematical ideas.

+Sample Tiered Assignments

By grade, review the tiered task. What are the mathematical concepts students are applying in the task?

What makes each task different?

+Math Projects

Extend learning for students with math projects that support students’ application of the math concepts to the real world.

Review the math projects by grade. Divide the packets so each person gets one. Review the

projects. Present your project to your group.

+Student Choice

+Providing Student Choice

Math Menu Math Projects Think Dots Think Tac Toes

+Math Menu

Several activities are listed and, just as you were in a restaurant, you can choose what you order.

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+Think Dots

Students begin ThinkDots by sitting with other students using activity cards of the same color.

Students roll the die and complete the activity on the card that corresponds to the dots thrown on the die.

If the first roll is an activity that the student does not want, to do a second roll is allowed.

Teachers can create an Activity Sheet to correspond to the lesson for easy recording and management.

+Think Dots

+Think Dots

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+

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+Think Tac Toe

A 3 by 3 matrix with nine cells, resembling a tic-tac-toe.

Organized in different ways. For example, rows could offer increasingly more challenging tasks and students cold choose a row at the right level for them.

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+Think Tac Toe: In Action

How does the teacher help the students make sense of the problems on the Think Tac Toe choice board?

Why is it important? In your own words, what strategies do you use to help

students make sense of problems?