```Differentiation - What Works?
Jim Miles
International 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 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
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
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
 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 Instruction
 30 different ways to teach the same lesson
 Linking student readiness to differentiation
 Through relevance
 Student learning mode
Our Math Students
 English Language Learners
 Gifted students
 Struggling students
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
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
There are four
supporting systems
that interact to
make differentiation
a natural next step.
Supporting
Structures
For Natural
Differentiation
1.
2.
3.
4.
Aligned Curriculum and Assessments
Strategy Toolkit
Personal Connections
Diagnostic Thinking
Aligned Curriculum and Assessments
 Rigor / Relevance
 Aligned Formative
and Summative
Assessments
 Performance-based
 Concept-based
 Critical questions
 Powerful standards
Strategy Toolkit
 Literacy: Thinking and communicating
 DTQ Literacy
 Critical thinking
 Brain friendly
 Multiple intelligences
or learning styles
 Research-based
 Subgroup specific
Quick Write
Selection of Strategies
Data Collection:
Standards Basis:
Areas for Focus and Support
Areas for Focus and Support
 Thinking
 Rigorous
 Process, product or
performance
 Content
 Relationship and
Reflection
 Independence
 Relevant
 Leverage
 Endurance
 Readiness for next level
Researched-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 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
 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
 Assessment-based planning
 Formative and summative data design,
collection, and analysis
 Selected strategies based on data
 Diagnostic dialogue
 Student Growth
Total Group
Alone
Paired
Small
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 Your
Assets
Diagnostic
Thinking
Aligned
Curriculum
and
Assessments
Meeting
Diverse
Learner
Needs
Personal
Connections
Strategy
Toolkit
What can You Differentiate?
 Time
 Teaching Strategies
 Learning Strategies
 Classroom Assessments
 Materials and Resources
 Grouping
 Expectations
Differentiated Instruction
IS NOT…
- Tracking
- A New Strategy
- Static
- Teaching to the
Middle
- A series of activities
- Lowering the Bar
IS…
- Flexible Grouping
- Student Centered
- Rigorous / Relevant
- For all Learners
- Based on academic
and personal needs
- Fosters relationships
and reflection
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/
Personality Types
Florida and the Islands Comprehensive Center
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?
• 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?
• 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!
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
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
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
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?
Sensing Thinking (ST)
Intuitive Thinking (NT)
Intuitive Feeling (NF)
Sensing Feeling (SF)
Questions:
• 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…
• 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 Instruction
IS NOT…
- Tracking
- A New Strategy
- Static
- Teaching to the
Middle
- A series of activities
- Lowering the Bar
IS…
- Flexible Grouping
- Student Centered
- Rigorous / Relevant
- For all Learners
- Based on academic
and personal needs
- Fosters relationships
and reflection
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 Your
Assets
Diagnostic
Thinking
Aligned
Curriculum
and
Assessments
Meeting
Diverse
Learner
Needs
Personal
Connections
Strategy
Toolkit
Vocabulary Strategies
English language learners need to
develop the language of mathematics.
Vocabulary Strategies
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.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Trace
Analyze
Infer
Evaluate
Formulate
Describe
Support
Explain
Summarize
Compare
Contrast
Predict
List in steps
Break apart
Read between the lines
Judge
Create
Tell all about
Back up with details
Tell how
Give me the short version
All the ways they are alike
All the ways they are different
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-linguistic
Representation
Non-examples
Concept
Now write your own definition:
Use or
Application – put in
context
Analogies
 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
 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
 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
Parts or
Characteristics
Concept
T-Charts
DATA or IDEA
T- Chart
IDEA 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) 399-2776
Fax
(518) 399-7607
Analogical Reasoning
What 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
One concept performs a
• 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)
function on another (territory
dispute-war)
• Time or sequence relationship
(morning-noon)
• Quantity, size, or physical
dimension relationship (tallEmpire 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 Analysis
Traditional 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
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