Differentiation - What Works?

Jim MilesInternational Center for Leadership in Education

It’s All About Math!

Welcome to the Middle School Mathematics Initiative!

Institute Theme:

Closing the Achievement Gap – Strategies to Support Struggling Learners

It’s All About Math!

Sponsored by:

Florida Department of Education

Florida and the Islands Comprehensive Center at ETS (FLICC)

In Partnership with:

The International Center for Leadership in Education

ESCORT

Florida Council of Teachers of Mathematics

PAEC

It’s All About Math!

Objectives:

•Identify and define struggling learners

•Become aware of innovative and practical strategies to use with students who are struggling academically in math

•Utilize Rigor and Relevance materials and resources to address the needs of struggling learners

•Develop a lesson using differentiated instruction strategies to use with struggling learners

It’s All About Math!

Agenda at a Glance:

Day 1

•Registration, Continental Breakfast

•Welcome, Introductions

• Ice Breaker and Jump Start Activity

•Defining and Identifying the Struggling Learner

•Break

•Theory of Practice and Differentiated Instruction

•Lunch

•Theory of Practice and Differentiated Instruction (cont.)

•Learning Styles

•Examples of Differentiated Instruction – Breakout rooms

It’s All About Math!

Agenda at a Glance:

Day 2

•Continental Breakfast – Large Room

•Examples of Differentiated Instruction – Breakout Rooms

•Sharing of Quad D Lesson Revisions – Large Room

•Break

•Vocabulary Strategies – Large Room

•Lunch – Large Room

•Assessment Strategies - Large Room

•Action Plan Revisions – Breakout Rooms

It’s All About Math!

Standards Database:

Model Lessons - Peer Review

Survey Questions:

1. What is the name of the lesson you reviewed?

2. What learning opportunities does this lesson provide for math students?

3. Does the math content of this lesson fit the associated benchmark?

It’s All About Math!

Standards Database:

Model Lessons - Peer Review

4. How well does this lesson address the following teaching and learning process standards? [each will have a text box to request justification]

Problem SolvingReasoning and ProofCommunicationConnectionsRepresentations

5. What modifications did or would you make to this lesson plan?

6. Do you recommend this lesson for publication in the Standards Database: (select one)

As is With modifications

Not recommended

AGENDA Differentiated Instruction Differentiation Math Strategies Learning Styles Vocabulary Strategies

Critical Questions

What is differentiation?

What does and does not work in differentiation initiatives?

What I know I know about Differentiation

What I think I know about Differentiation

What I want to know about Differentiation

What I have learned about Differentiation

Characteristics of a Differentiated Classroom

All students explore, apply, and understand the same benchmarks

Continuous assessment is an integral part of the curriculum.

Flexible grouping is used consistently Students are active explorers

All Students

Why Differentiation Does Not Succeed in Schools…

Lack of trust and climate issues Insufficient staff development Focus is on teaching and not on learning Focus is on methodology and not on

meeting diverse student needs Teachers work in isolation More than a lesson plans is needed

Problem Solving Problem representation

Pictorial versus Schematic representationGoal: develop schematic representations:

relationship among the problem parts

Problem execution Stations

Same concepts taught differently: algebra

Differentiating a 6th Grade math Classroom

Differentiated InstructionContent

Learn how to subtract using two-digit numbers versus larger numbers in the context of word problems

ProcessAccessing the material through centers (stations)

versus the web

ProductDemonstrate understanding of a geometric concept

by solving a problem set versus building a model

Differentiated Instruction

30 different ways to teach the same lessonLinking student readiness to differentiation

Through relevanceStudent learning mode

Our Math Students

English Language Learners Gifted students Struggling students

English Language LearnersHelping English Learners acquire math language

How can math teachers help them acquire academic language they need?

ESL teachers may not have strong math skills

What needs to be doneAccelerate learning that is grade-level

appropriate.Give students challenging work with the

support they need to be successful.

Collaborative GroupsCreate a math classroom with rich language development activities students speaking, reading, and writing heterogeneous groups of students at

varying levels of English acquisition students talking to peers, in groups

and in classroom discussion

Differentiation in the Classroom

There are four supporting systems that interact to make differentiation a natural next step.

Supporting Structures

For Natural Differentiation

1. Aligned Curriculum and Assessments

2. Strategy Toolkit

3. Personal Connections

4. Diagnostic Thinking

Aligned Curriculum and Assessments

Rigor / RelevanceAligned Formative

and Summative Assessments

Performance-basedConcept-basedCritical questionsPowerful standards

Literacy: Thinking and communicating DTQ Literacy Critical thinking Brain friendly Multiple intelligences

or learning styles Research-based Subgroup specific

Quick Write Quick Write

Strategy Toolkit

Selection of Strategies

Data Collection: Areas for Focus and Support

Thinking Process, product or performance Content Relationship and Reflection Independence

Standards Basis: Areas for Focus and Support

RigorousRelevantLeverageEnduranceReadiness for next level

Researched-based Best PracticesResearched-based Best Practices

Categories of Instructional Strategies That Affect Student Achievement

Percentile Gain

Identifying similarities and differences, using metaphors and analogies

45

Summarizing and notetaking 34

Reinforcing effort and providing recognition 29

Homework and practice 28

Nonlinguistic representations 27

Cooperative learning 27

Setting objectives and providing feedback 23

Generating and testing hypotheses 23

Questions, cues, and advance organizers 22

Marzano, R., Pickering, D., & Pollack, J., Classroom Instruction That Works, 2001

Personal Connections

For students and staff Relationships Reflection Trust Coaching

and mentoring Involvement Learning communities

In a Culture of Learning, Students

Exhibit purposeful action Can describe next steps Appropriately ask for assistance Questions are about aspects of complex

thinking rather than procedure Adhere to class norms Attitude and demeanor are positive Collaborate as needed without prompts Positively reinforce each other Can self-evaluate work in progress

Student Engagement

Cultivate one-on-one relationshipsLearn and use new skills and habitsUse effective instructional strategiesEngage ALL students in activities/discussions Promote School wide culture of engagementProfessional development

The “How to” for Student Engagement

Design for rigorous and relevant learningPersonalize the learning giving choices,

attending to learning styles, and using background knowledge and talents

Use active learning strategiesFocus on literacy in ALL classes Create the ideal classroom environment

physically, visually, and emotionally

Diagnostic Thinking

Assessment-based planning

Formative and summative data design,

collection, and analysis

Selected strategies based on data

Diagnostic dialogue

Student Growth

TTotal Group

AAlone

PPaired

SSmall Groups

•Comprehension•Recall•Modeling other levels of thinking•Checking for level

•Analyze•Synthesize•Adaptive reasoning•Evaluation

•Analytical•Synthesize•Decision making•Evaluation

•Systems thinking•Application•Decision making•Criteria establishment•Comprehension

Meeting Diverse Learner Needs:Assessing YourAssets

Meeting Diverse Learner Needs

DiagnosticThinking

Strategy Toolkit

AlignedCurriculum

andAssessments

Personal Connections

What can You Differentiate?

Time Teaching Strategies Learning Strategies Classroom Assessments Materials and Resources Grouping Expectations

- Tracking

- A New Strategy

- Static

- Teaching to the Middle

- A series of activities

- Lowering the Bar

- Flexible Grouping

- Student Centered

- Rigorous / Relevant

- For all Learners

- Based on academic and personal needs

- Fosters relationshipsand reflection

IS NOT… IS…

Differentiated Instruction

What does it take to differentiate?

Set rigorous and relevant goals Students need to know / be able to do? Where are they on the

learning curve now? Select instructional strategies

that will enhance the learning. Monitor student progress and

adjust instruction if needed.

Natural Differentiation When meeting student needs

is just a part of what you do, how you think, and the results you get with students

Students can begin to differentiate for themselves.

Learning Styles/ Learning Styles/ Personality TypesPersonality Types

Florida and the Islands Comprehensive Florida and the Islands Comprehensive CenterCenter

Brain research confirms Brain research confirms what experienced teachers what experienced teachers have always known:have always known:

• No two children are alikeNo two children are alike• No two children learn in the No two children learn in the

identical wayidentical way• An enriched environment for one An enriched environment for one

student is not necessarily enriched student is not necessarily enriched for anotherfor another

• In the classroom we should teach In the classroom we should teach children to think for themselveschildren to think for themselves

Marian DiamondMarian Diamond

Why should I care aboutWhy should I care about learning styles? learning styles?

• The way a child learns affects The way a child learns affects his/her entire personality and his/her entire personality and development.development.

• Understanding learning styles Understanding learning styles will help teachers and students to will help teachers and students to better communicate.better communicate.

• Understanding learning styles Understanding learning styles will help teachers to differentiate will help teachers to differentiate instruction.instruction.

What is a learning style?What is a learning style?

• A learning style is…A learning style is…– a way to take in and process a way to take in and process

informationinformation– a preference that gets stronger a preference that gets stronger

the more it is usedthe more it is used– the way the mind operatesthe way the mind operates– the way we learn!the way we learn!

SSensing ensing TThinking Learnerhinking Learner(ST)(ST)

• Likes:Likes:– Immediate responses and feedbackImmediate responses and feedback– Details and sequential orderDetails and sequential order– Hands-on activities with a specific, Hands-on activities with a specific,

correct answercorrect answer– Clear, concise, step-by-step directionsClear, concise, step-by-step directions– Knowing exact expectations; why Knowing exact expectations; why

something has to be done, and how something has to be done, and how well it is to be donewell it is to be done

– Drill and practiceDrill and practice

IInntuitive tuitive TThinking Learner hinking Learner (NT)(NT)

• Likes:Likes:– Planning and organizing before Planning and organizing before

workingworking– Working independentlyWorking independently– Analyzing and examining pros and consAnalyzing and examining pros and cons– Arguing and debatingArguing and debating– Thinking about ideas and how they are Thinking about ideas and how they are

relatedrelated– Finding/designing a new way to do Finding/designing a new way to do

somethingsomething– Logical and strategic gamesLogical and strategic games

IInntuitive tuitive FFeeling Learnereeling Learner(NF)(NF)

• Likes:Likes:– Learning without time constraintsLearning without time constraints– Praise for personal ideas and Praise for personal ideas and

insightsinsights– Using creativity and imaginationUsing creativity and imagination– Open-ended activities with many Open-ended activities with many

possibilitiespossibilities– Working on many things at onceWorking on many things at once– Self-expression and self-discoverySelf-expression and self-discovery– Creative and artistic activitiesCreative and artistic activities

SSensing ensing FFeeling Learnereeling Learner(SF)(SF)

• Likes:Likes:– Getting personal attention and praiseGetting personal attention and praise– Sharing feelings and experiencesSharing feelings and experiences– Working in groups/being part of a teamWorking in groups/being part of a team– Having someone show how to do Having someone show how to do

somethingsomething– Role-playing and personal expressionRole-playing and personal expression– Non-competitive games where no one Non-competitive games where no one

losesloses– Interpersonal activities; opportunities to Interpersonal activities; opportunities to

learn about himself/herselflearn about himself/herself

What is your learning style?What is your learning style?

Sensing Thinking (ST)Sensing Thinking (ST)

Intuitive Thinking (NT)Intuitive Thinking (NT)

Intuitive Feeling (NF)Intuitive Feeling (NF)

Sensing Feeling (SF)Sensing Feeling (SF)

Questions:Questions:

• Sensing Thinking (ST): WHAT?Sensing Thinking (ST): WHAT?

• Intuitive Thinking (NT): WHY?Intuitive Thinking (NT): WHY?

• Intuitive Feeling (NF): WHAT IF?Intuitive Feeling (NF): WHAT IF?

• Sensing Feeling (SF): WHAT Sensing Feeling (SF): WHAT DOES IT MEAN TO ME?DOES IT MEAN TO ME?

In A Nutshell…In A Nutshell…

• No one learning style is better than No one learning style is better than another.another.

• We all have characteristics of each We all have characteristics of each learning style; some characteristics are learning style; some characteristics are just stronger than others.just stronger than others.

• Learning about each style will help us Learning about each style will help us to better understand and communicate to better understand and communicate with our students.with our students.

• Knowing about each learning style will Knowing about each learning style will help teachers to better understand help teachers to better understand how students learn and how to how students learn and how to differentiate instruction.differentiate instruction.

- Tracking

- A New Strategy

- Static

- Teaching to the Middle

- A series of activities

- Lowering the Bar

- Flexible Grouping

- Student Centered

- Rigorous / Relevant

- For all Learners

- Based on academic and personal needs

- Fosters relationshipsand reflection

IS NOT… IS…

Differentiated Instruction

Differentiated InstructionContent

Learn how to subtract using two-digit numbers versus larger numbers in the context of word problems

ProcessAccessing the material through centers (stations)

versus the web

ProductDemonstrate understanding of a geometric concept

by solving a problem set versus building a model

Meeting Diverse Learner Needs:Assessing YourAssets

Meeting Diverse Learner Needs

DiagnosticThinking

Strategy Toolkit

AlignedCurriculum

andAssessments

Personal Connections

Vocabulary Strategies

Vocabulary Strategies

English language learners need to develop the language of mathematics.

Pair/Share: How do you teach vocabulary?

Vocabulary is the Gateway to Inferential Thinking

Most of us learned to teach vocabulary by having students:Write the word several timesFind the definitionWrite it in a sentence

Meta-research from William Nagy, Teaching Vocabulary to Improve Comprehension, ERIC, 2000 reports that…

These are the three least effective methods of initially teaching vocabulary!

Larry Bell’s 12 Powerful Words 1. Trace          List in steps 2. Analyze        Break apart 3. Infer             Read between the lines 4. Evaluate       Judge 5. Formulate     Create 6. Describe      Tell all about 7. Support       Back up with details 8. Explain         Tell how 9. Summarize   Give me the short version10. Compare   All the ways they are alike11. Contrast    All the ways they are different12. Predict      What will happen next

Verbal Rehearsal

Connect with prior learning

Association method

Think-Pair-Share

Visual Clueing

Post key words

Color code or place with pictures, clip art

3. Examples and Non-Examples• Most famous strategy is

the “Frayer Method”

• Non-linguistic symbol creation

• What is it, what isn’t it?

• Add to a class Blog

Frayer Method

Examples Non-examples

Non-linguistic Representation

Use or

Application – put in context

Now write your own definition:

Concept

AnalogiesConnect to prior knowledge.Use opposites.Use as prompt, questions for discussion.Use verbal, visual or written analogies.Analogies are one of the pre-requisites for inference.

Pictures and Demonstrations

Use posters for a demonstrationUse pictures on homeworkDemonstrate an idea and use visuals or

PowerPointHave students role play an ideaUse color highlighting in print and

electronicallyText message and add a picture

or require and action

Graphic Organizers

Brain friendly Creates patterns for the brain Supports concept development Multi-purpose Cross content application with little

modification (101 Uses) Motivating to reluctant writers – small

spaces

Array Web

Concept

Parts or Characteristics

T-ChartsDATA or IDEA

T- ChartIDEA T-Chart

Opinion or Proof or

Estimate Evidence

Venn Diagram

Vocabulary Strategies, Writing Strategies and Graphic Organizers

Combine for High Payoff

Add some cooperative grouping and you have instant results based

learning

May Your Moments be Many!

“Educators are addicted to the moment when a student’s eyes light up, when the teaching becomes learning. May your days be filled with such moments.”

Philip Patrick Horenstein

1587 Route 146, Rexford, NY 12148

E-mail - info@LeaderEd.com

www.LeaderEd.com

Phone (518) 399-2776Fax (518) 399-7607

Analogical ReasoningWhat is it?Identifying how one set of concepts has similar

relationships to those found in another set of concepts

Process:1. Identify relationships between the two elements in

the first set.2. Identify which element in the first set is most closely

related to the single element in the second set.3. Identify an element that would make the second set

of elements have the same relationship as the first set.

(Marzano and Arrendando)

Analogical Reasoning: Your Turn

• Fly is to soar like yell is to:– Whisper

– Shout

– Swim

• Tree: penny :: lion:– Horse

– Sky

– Pencil

• Morning: night :: 4 :– 1

– 3

– 6

• Rain: mud :: bud:– Wings

– Flower

– Fertilizer

Nine Analogical Relationships• Synonyms or similar

relationships (pretty-cute)• Antonyms or dissimilar

relationships (hot-cold)• Concepts within the same

class (independent variables and dependent variables)

• Category name and member (cells-plant cells)

• One concept turns into another (tadpole-frog)

• One concept performs a function on another (territory dispute-war)

• Time or sequence relationship (morning-noon)

• Quantity, size, or physical dimension relationship (tall-Empire State Building)

• Part to whole (hero-fantasy)

Why are these important?What are some examples in in

math at your grade level?

6. Combining Clues to Utilize the Definition

• Give clues leading to a definition.

• Develop characteristics or map patterns.

• Develop relationships to prior knowledge - web the features before the center of the web.

• Have students guess the word with clues and give a use.

• Also known as “constructivist vocabulary development”

7. Verbal and Physical Memories

• What does it look like…• What does it feel like…• Verbalize as you perform an

action• Attach a physical movement with

the work• Type a written response that uses

the concept• Act it out, performance-based• Explain as you perform an

experiment

8. Key Word Method• Not all words are equal, so teach

the underlying concepts through bold print, color, webs

• Use feature analysis

• Establish parts to whole relationships

• Create an array with concepts in different degrees

9. Creating Patterns and Graphic Organizers

• Use cause and effect mapping

• Use multiple column note-taking with words

• Use linear or hierarchical arrays to show relationships

Two More Vocabulary Strategies that are Graphical

• The next two strategies include the use of graphic organizers.

• In addition, some content areas and some types of text work with non-prose materials, so what are some graphic organizers that support math, science and the use of visual materials

Sequence or Time Sequence

Adjusted or Triple Venn

INFLUENCE OF MULTIPLES:

Elements

Parts

Causes

Conditions

10. Semantic Feature AnalysisTraditional Semantic Feature Analysis

Comparison of Pets

Big Idea 1:

• Develop an understanding of and fluency with multiplication and division of fractions and decimals.

• MA.6.A.1.1-Explain and justify procedures for multiplying and dividing fractions and decimals