Differentiating Instruction in Elementary Mathematics

Bay School DistrictJuly 14 - 15, 2008

"In the end, all learners need your energy, your heart and your mind. They have that in common because they are young humans. How they need you however, differs. Unless we understand and respond to those differences, we fail many learners." *

* Tomlinson, C.A. (2001). How to differentiate instruction in mixed ability classrooms (2nd Ed.). Alexandria, VA: ASCD.

Dr. Nanci Smith, Ph.D.Educational ConsultantCurriculum and Professional DevelopmentCave Creek, AZnanci_mathmaster@yahoo.com

Thinking About Your StudentsUse the categories below to cluster your students according to their learning needs. Feel free to add

or disregard categories. Some students may fit into more than one category.

• Needs Extra Practice on Basic Skills

• Needs Extra Time to Complete Tasks

• Has Strong Interests Often Not Reflected in School Tasks

• Works Better Independently

• Works Better Collaboratively

• Likes Practical, Relevant, Hands-On Tasks

• Has a Highly Creative Approach to Learning

• Needs to Work Ahead (Advanced Work)

• Needs Additional Teaching

MyAppointment Clock

Round the Clock Learning BuddiesRound the Clock Learning Buddies

Make an appointment with 12 different people – one for each hour on the clock. Be sure you both record the appointment on your clocks. Only make the appointment if there is an open slot at that hour on both of your clocks.

Tape this paper inside a notebook, or to something that you will

bring to class each day.

What is Differentiation?

• Look at the following 7 slides in the packet and reflect on what you know and have heard about differentiation.

• Ponder on your own: – What does this tell me about differentiation?– If this statement were true, what would I see in a classroom? – What would a teacher say? – What would students be doing?

(Jot down your thoughts and observations – 4 minutes)

• Pair with someone and share your ideas. (4 minutes)• Share with others

(4 minutes)

What Differentiated Instruction…IS

• Differentiated instruction is more QUALITATIVE than quantitative.

• Differentiated instruction provides MULTIPLE approaches to content, process, and product.

• Differentiated instruction is STUDENT CENTERED.

• Differentiated instruction is a BLEND of whole class, group, and individual instruction.

• Differentiated instruction is "ORGANIC".

IS NOT• Individual instruction • Chaotic• Just another way to provide

homogenous instruction (You DO use flexible grouping instead)

• Just modifying grading systems and reducing work loads

• More work for the "good" students and less and different for the "poor" students

Differentiated Instruction

Defined

“Differentiated instruction is a teaching philosophy based on the premise that teachers should adapt instruction to student differences. Rather than marching students through the curriculum lockstep, teachers should modify their instruction to meet students’ varying readiness levels, learning preferences, and interests. Therefore, the teacher proactively plans a variety of ways to ‘get at’ and express learning.”

Carol Ann Tomlinson

“Differentiation is making sure that the right students get the right learning tasks at the right time. Once you have a sense of

what each student holds as ‘given’ or ‘known’ and what he or

she needs in order to learn, differentiation is no longer an

option; it is an obvious response.”Assessment as Learning: Using Classroom Assessment to Maximize Student Learning

Lorna M. EarlCorwin Press, Inc. – 2003 – pp. 86-87

Differentiation

Is a teacher’s response to learner’s needs

Guided by general principles of differentiation

Respectful tasks Flexible grouping Continual assessment

Teachers Can Differentiate Through:

Content Process Product Environment

According to Students’

Readiness Interest Learning Profile

Through a range of strategies such as:

Multiple intelligences…Jigsaw…4MAT…Graphic Organizers…RAFTSCompacting…Tiered assignments…Leveled texts…Complex Instruction…

Learning Centers

What’s the point of differentiating in these

different ways?Readiness

Growth

InterestLearning Profile

Motivation Efficiency

for

Interest – Readiness – Learning Profile

by

Self – Peers - Teachers

Key Principles of a Differentiated Classroom

Key Principles of a Differentiated Classroom

• The teacher is The teacher is clear about what mattersclear about what matters in subject matter. in subject matter.

• All students participate in All students participate in respectful workrespectful work..

• The teacher understands, appreciates, and The teacher understands, appreciates, and builds upon builds upon student differences.student differences.

• AssessmentAssessment and and instructioninstruction are are inseparableinseparable..

• The teacher adjusts The teacher adjusts content, process, and productcontent, process, and product in in response to student response to student readiness, interestsreadiness, interests, and , and learning learning profile.profile.

• Students and teachers are Students and teachers are collaboratorscollaborators in learning. in learning.

• Goals of a differentiated classroom are Goals of a differentiated classroom are maximum growthmaximum growth and and individual successindividual success..

• FlexibilityFlexibility is the hallmark of a differentiated classroom. is the hallmark of a differentiated classroom.

• The teacher is The teacher is clear about what mattersclear about what matters in subject matter. in subject matter.

• All students participate in All students participate in respectful workrespectful work..

• The teacher understands, appreciates, and The teacher understands, appreciates, and builds upon builds upon student differences.student differences.

• AssessmentAssessment and and instructioninstruction are are inseparableinseparable..

• The teacher adjusts The teacher adjusts content, process, and productcontent, process, and product in in response to student response to student readiness, interestsreadiness, interests, and , and learning learning profile.profile.

• Students and teachers are Students and teachers are collaboratorscollaborators in learning. in learning.

• Goals of a differentiated classroom are Goals of a differentiated classroom are maximum growthmaximum growth and and individual successindividual success..

• FlexibilityFlexibility is the hallmark of a differentiated classroom. is the hallmark of a differentiated classroom.Source: Tomlinson, C. (2000). Differentiating Instruction for Academic Diversity. San Antonio, TX: ASCD

There are two keys to differentiation:

1.Know your kids2.Know your

content

There are two keys to differentiation:

1.Know your kids

2. Know your content

READINESS

What does READINESS mean?

It is the student’s entry point relative to a particular understanding or skill.

C.A.Tomlinson, 1999

BRAIN RESEARCHReticular Activating System

RAS = “Toggle Switch”

HIGH MIDDLE LOW

Hot (EEG) Mild (EEG) Cold (EEG – sleeplike)

Limbic aroused Cortical arousal Sleep (depression)

Flight / Fight Problem Solving Relaxation

Out of Control In Control Off Duty

Carbohydrates Proteins Carbohydrates/Dairy

Burnout Achievement Depression

Extreme Challenge Moderate Challenge No Challenge

Only one of these three states is activated (aroused) at a time:

“Certain motivational states which interfere with learning condition are especially dangerous: anxiety and boredom. Anxiety occurs primarily when teachers expect too much from students; boredom occurs when teachers expect too little.” – Howard Gardner

Learning only happens when the toggle switch is in the middle position

Advanced Learners♦ Advanced learners can become mentally lazy, even though they do well in school.

♦ Advanced learners may become “hooked” on the trappings of success.

♦ Advanced learners may become perfectionists.

♦ Advanced learners may fail to develop a sense of self-efficacy.

♦ Advanced learners may fail to develop study and coping skills.

Pre-Assessment• What the student already knows about what is

being planned• What standards, objectives, concepts & skills

the individual student understands• What further instruction and opportunities for

mastery are needed• What requires reteaching or enhancement• What areas of interests and feelings are in the

different areas of the study• How to set up flexible groups: Whole,

individual, partner, or small group

What Do You Know About Proportional Reasoning?

DescriptionDefinition Information

Examples Non-examples

ProportionalReasoning

Pre-Assessment• What the student already knows about what is

being planned• What standards, objectives, concepts & skills

the individual student understands• What further instruction and opportunities for

mastery are needed• What requires reteaching or enhancement• What areas of interests and feelings are in the

different areas of the study• How to set up flexible groups: Whole,

individual, partner, or small group

THINKING ABOUT ON-GOING ASSESSMENT

STUDENT DATA SOURCES1. Journal entry2. Short answer test3. Open response test4. Home learning5. Notebook6. Oral response7. Portfolio entry8. Exhibition9. Culminating product10. Question writing11. Problem solving

TEACHER DATA MECHANISMS

1. Anecdotal records2. Observation by checklist3. Skills checklist4. Class discussion5. Small group interaction6. Teacher – student

conference7. Assessment stations8. Exit cards9. Problem posing10. Performance tasks and

rubrics

Yes/No Cards• Using a 4x6 index card the student writes YES on one

side and NO on the other.• When a question is asked the students hold up YES or

NO.1. Ask the students if they know the following vocabulary

words and what they mean.2. Call out a word. If a student is holding a YES they may

be called on to give the correct answer.3. Remind them that if they don’t know the words it is OK

because they will be learning them.4. You can do the same thing with conceptual ideas, etc.

Y

E

S

NO

Thumb It!

• Have students respond with the position of their thumb to get an assessment of what their current understanding of a topic being studied.

• Where I am now in my understanding of ______?

Up Sideways DownI know a lot I know some I know very little

Exit Cards

List

• 3 things you learned today

• 2 things you’d like to learn more about

• 1 question you still have

Exit Cards

Explain the difference between an expression and

an equation. Give some examples of each as part of

your explanation.

Circle VocabularyCreative

Find a way to help us remember all this vocabulary! You can create a skit by becoming each term, and talking about who you are and how you relate to each other, draw pictures, make a collage, or any other way of which you can think.

ORRole Audience Format Topic Diameter Radius email Twice as niceCircle Tangent poem You touch me!Secant Chord voicemail I extend you.