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Differentiation - What Works?. Jim Miles International Center for Leadership in Education. Welcome to the Middle School Mathematics Initiative!. It’s All About Math!. Institute Theme: Closing the Achievement Gap – Strategies to Support Struggling Learners. It’s All About Math!.

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differentiation what works

Differentiation - What Works?

Jim MilesInternational Center for Leadership in Education

Welcome to the Middle School Mathematics Initiative!

It’s All About Math!

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


Florida Council of Teachers of Mathematics



It’s All About Math!


  • 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:
  • What is the name of the lesson you reviewed?
  • 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 Solving
    • Reasoning and Proof
    • Communication
    • Connections
    • Representations
  • 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
  • Differentiated Instruction
  • Differentiation Math Strategies
  • Learning Styles
  • Vocabulary Strategies
critical questions
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
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
why differentiation does not succeed in schools
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

Differentiating a 6th Grade math Classroom

Problem Solving

  • Problem representation
    • Pictorial versus Schematic representation
    • Goal: develop schematic representations: relationship among the problem parts
  • Problem execution
  • Stations
    • Same concepts taught differently: algebra
differentiated instruction
Differentiated Instruction
  • Content
    • Learn how to subtract using two-digit numbers versus larger numbers in the context of word problems
  • Process
    • Accessing the material through centers (stations) versus the web
  • Product
    • Demonstrate understanding of a geometric concept by solving a problem set versus building a model
differentiated instruction17
Differentiated Instruction
  • 30 different ways to teach the same lesson
  • Linking student readiness to differentiation
    • Through relevance
    • Student learning mode
our math students
Our Math Students
  • English Language Learners
  • Gifted students
  • Struggling students
english language learners
English Language Learners
  • Helping 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 done
    • Accelerate learning that is grade-level appropriate.
    • Give students challenging work with the support they need to be successful.
collaborative groups
Collaborative Groups

Create 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
Differentiation in the Classroom

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

supporting structures for natural differentiation
Supporting Structures For Natural Differentiation
  • Aligned Curriculum and Assessments
  • Strategy Toolkit
  • Personal Connections
  • Diagnostic Thinking
aligned curriculum and assessments
Rigor / Relevance

Aligned Formative and Summative Assessments



Critical questions

Powerful standards

Aligned Curriculum and Assessments
strategy toolkit
Strategy Toolkit
  • Literacy: Thinking and communicating
  • DTQ Literacy
  • Critical thinking
  • Brain friendly
  • Multiple intelligencesor learning styles
  • Research-based
  • Subgroup specific

Quick Write

selection of strategies
Data Collection:

Areas for Focus and Support


Process, product or performance


Relationship and Reflection


Standards Basis:

Areas for Focus and Support





Readiness for next level

Selection of Strategies

Researched-based Best Practices

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


personal connections
Personal Connections

For students and staff

  • Relationships
  • Reflection
  • Trust
  • Coachingand 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

In a Culture of Learning, Students
student engagement
Student Engagement
  • Cultivate one-on-one relationships
  • Learn and use new skills and habits
  • Use effective instructional strategies
  • Engage ALL students in activities/discussions
  • Promote School wide culture of engagement
  • Professional development
the how to for student engagement
The “How to” for Student Engagement
  • Design for rigorous and relevant learning
  • Personalize the learning giving choices, attending to learning styles, and using background knowledge and talents
  • Use active learning strategies
  • Focus on literacy in ALL classes
  • Create the ideal classroom environment physically, visually, and emotionally
diagnostic thinking
Diagnostic Thinking
  • Assessment-based planning
  • Formative and summative data design, collection, and analysis
  • Selected strategies based on data
  • Diagnostic dialogue
  • Student Growth


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

Total Group





  • Analyze
  • Synthesize
  • Adaptive reasoning
  • Evaluation
  • Analytical
  • Synthesize
  • Decision making
  • Evaluation
  • Systems thinking
  • Application
  • Decision making
  • Criteria establishment
  • Comprehension















Meeting Diverse Learner Needs:Assessing YourAssets


What can You Differentiate?

  • Time
  • Teaching Strategies
  • Learning Strategies
  • Classroom Assessments
  • Materials and Resources
  • Grouping
  • Expectations
differentiated instruction36
Differentiated 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

what does it take to differentiate
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 strategiesthat will enhance the learning.
  • Monitor student progress andadjust 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 personality types

Learning Styles/ Personality Types

Florida and the Islands Comprehensive Center

brain research confirms what experienced teachers have always known
Brain research confirms what experienced teachers have always known:
  • No two children are alike
  • No two children learn in the identical way
  • An enriched environment for one student is not necessarily enriched for another
  • In the classroom we should teach children to think for themselves

Marian Diamond

why should i care about learning styles
Why should I care about learning styles?
  • The way a child learns affects his/her entire personality and development.
  • Understanding learning styles will help teachers and students to better communicate.
  • Understanding learning styles will help teachers to differentiate instruction.
what is a learning style
What is a learning style?
  • A learning style is…
    • a way to take in and process information
    • a preference that gets stronger the more it is used
    • the way the mind operates
    • the way we learn!
s ensing t hinking learner st
Sensing Thinking Learner(ST)
  • Likes:
    • Immediate responses and feedback
    • Details and sequential order
    • Hands-on activities with a specific, correct answer
    • Clear, concise, step-by-step directions
    • Knowing exact expectations; why something has to be done, and how well it is to be done
    • Drill and practice
i n tuitive t hinking learner nt
Intuitive Thinking Learner (NT)
  • Likes:
    • Planning and organizing before working
    • Working independently
    • Analyzing and examining pros and cons
    • Arguing and debating
    • Thinking about ideas and how they are related
    • Finding/designing a new way to do something
    • Logical and strategic games
i n tuitive f eeling learner nf
Intuitive Feeling Learner(NF)
  • Likes:
    • Learning without time constraints
    • Praise for personal ideas and insights
    • Using creativity and imagination
    • Open-ended activities with many possibilities
    • Working on many things at once
    • Self-expression and self-discovery
    • Creative and artistic activities
s ensing f eeling learner sf
Sensing Feeling Learner(SF)
  • Likes:
    • Getting personal attention and praise
    • Sharing feelings and experiences
    • Working in groups/being part of a team
    • Having someone show how to do something
    • Role-playing and personal expression
    • Non-competitive games where no one loses
    • Interpersonal activities; opportunities to learn about himself/herself
what is your learning style
What is your learning style?

Sensing Thinking (ST)

Intuitive Thinking (NT)

Intuitive Feeling (NF)

Sensing Feeling (SF)

  • Sensing Thinking (ST): WHAT?
  • Intuitive Thinking (NT): WHY?
  • Intuitive Feeling (NF): WHAT IF?
  • Sensing Feeling (SF): WHAT DOES IT MEAN TO ME?
in a nutshell
In A Nutshell…
  • No one learning style is better than another.
  • We all have characteristics of each learning style; some characteristics are just stronger than others.
  • Learning about each style will help us to better understand and communicate with our students.
  • Knowing about each learning style will help teachers to better understand how students learn and how to differentiate instruction.
differentiated instruction54
Differentiated 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

differentiated instruction55
Differentiated Instruction
  • Content
    • Learn how to subtract using two-digit numbers versus larger numbers in the context of word problems
  • Process
    • Accessing the material through centers (stations) versus the web
  • Product
    • Demonstrate understanding of a geometric concept by solving a problem set versus building a model















Meeting Diverse Learner Needs:Assessing YourAssets

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 times
  • Find the definition
  • Write 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 version

10. Compare   All the ways they are alike

11. Contrast    All the ways they are different

12. Predict      What will happen next

verbal rehearsal
Verbal Rehearsal
  • Connect with prior learning
  • Association method
  • Think-Pair-Share
visual clueing
Visual Clueing
  • Post key words
  • Color code or place with pictures, clip art
3 examples and non examples
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
  • Connect 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
Pictures and Demonstrations
  • Use posters for a demonstration
  • Use pictures on homework
  • Demonstrate an idea and use visuals or PowerPoint
  • Have students role play an idea
  • Use color highlighting in print and electronically
  • Text message and add a picture or require and action
graphic organizers
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
Array Web

Parts or



t charts


T- Chart

IDEA T-Chart

Opinion or Proof or

Estimate Evidence

vocabulary strategies writing strategies and graphic organizers combine for high payoff

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
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


Phone (518) 399-2776

Fax (518) 399-7607

analogical reasoning
Analogical Reasoning

What is it?

Identifying how one set of concepts has similar relationships to those found in another set of concepts


  • Identify relationships between the two elements in the first set.
  • Identify which element in the first set is most closely related to the single element in the second set.
  • 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:




Tree: penny :: lion:




Morning: night :: 4 :




Rain: mud :: bud:




Analogical Reasoning: Your Turn
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?

Nine Analogical Relationships
6 combining clues to utilize the definition
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
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
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
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
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
adjusted or triple venn
Adjusted or Triple Venn






big idea 1
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