1. Differentiation - What Works?
Jim Miles International Center for Leadership in Education

2. Welcome to the Middle School Mathematics Initiative!
It’s All About Math!
Welcome to the Middle School Mathematics Initiative!
Institute Theme:
Closing the Achievement Gap – Strategies to Support Struggling Learners

3. Sponsored by: Florida Department of Education
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

4. Objectives: Identify and define struggling learners
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

5. Agenda at a Glance: Day 1 Registration, Continental Breakfast
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

6. Agenda at a Glance: Day 2 Continental Breakfast – Large Room
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

7. Model Lessons - Peer Review
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?

8. Model Lessons - Peer Review
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

9. AGENDA Differentiated Instruction Differentiation Math Strategies
Learning Styles
Vocabulary Strategies

10. Critical Questions What is differentiation?
What does and does not work in differentiation initiatives?

11. 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

12. 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

13. All Students

14. 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

15. 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

16. 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

17. Differentiated Instruction
30 different ways to teach the same lesson
Linking student readiness to differentiation
Through relevance
Student learning mode

18. Our Math Students English Language Learners Gifted students
Struggling students

19. 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.

20. 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

21. Differentiation in the Classroom
There are four supporting systems that interact to make differentiation a natural next step.

22. Supporting Structures For Natural Differentiation
Aligned Curriculum and Assessments
Strategy Toolkit
Personal Connections
Diagnostic Thinking

23. Aligned Curriculum and Assessments
Rigor / Relevance
Aligned Formative and Summative Assessments
Performance-based
Concept-based
Critical questions
Powerful standards

25. Rigor/ Relevance Handbook

26. Instructional Strategies: How to Teach for Rigor and Relevance

27. Strategy Toolkit Literacy: Thinking and communicating DTQ Literacy
Critical thinking
Brain friendly
Multiple intelligences or learning styles
Research-based
Subgroup specific
Quick Write

28. 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
Rigorous
Relevant
Leverage
Endurance
Readiness for next level

29. 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
Setting objectives and providing feedback 23
Generating and testing hypotheses
Questions, cues, and advance organizers 22
Marzano, R., Pickering, D., & Pollack, J., Classroom Instruction That Works, 2001 42

30. Personal Connections For students and staff Relationships Reflection
Trust
Coaching and mentoring
Involvement
Learning communities

31. 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

32. 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

33. 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

34. Diagnostic Thinking Assessment-based planning
Formative and summative data design, collection, and analysis
Selected strategies based on data
Diagnostic dialogue
Student Growth

35. Total Group Alone Paired Small Groups Comprehension Recall
Modeling other levels of thinking
Checking for level
Total Group
Alone
Paired
Small
Groups
Analyze
Synthesize
Adaptive reasoning
Evaluation
Analytical
Synthesize
Decision making
Evaluation
Systems thinking
Application
Decision making
Criteria establishment
Comprehension

36. Meeting Diverse Learner Needs: Assessing Your Assets
Diagnostic
Thinking
Strategy
Toolkit
Aligned
Curriculum
and
Assessments
Personal
Connections

37. What can You Differentiate?
Time
Teaching Strategies
Learning Strategies
Classroom Assessments
Materials and Resources
Grouping
Expectations

38. Differentiated Instruction
IS NOT…
IS…
- 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 relationships and reflection

39. 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.

40. 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.

41. Learning Styles/ Personality Types
Florida and the Islands Comprehensive Center
Learning Styles is one strategy to use for differentiated instruction. This presentation is based on the work of Myers-Briggs, Keirsey-Bates, and Carl Jung.

42. 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

43. 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.

44. 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!
After reviewing this slide, ask participants to view the next four pictures and as they are looking at them, to think of the characteristics of each. Tell them that after they have viewed all four pictures, they will be asked to “choose” one picture that they seemed to identify with, based upon the characteristics they associated with each picture.

45. Show for about 15 seconds and move to next picture.

46. Show for about 15 seconds and move to next picture.

47. Show for about 15 seconds and move to next picture.

48. Show for about 15 seconds. Ask participants to think about all four pictures and then choose the one they “identified” with. If they didn’t identify with any, ask them to choose which one they like the best.
Next, ask participants to go to the chart paper (hung on the wall) that displays the picture they chose. Once in groups, participants will chart the answers to these questions: What makes you feel in-esteem or high? What makes you feel out of esteem or low? Give participants about five minutes to discuss and chart their answers. Ask that they try to come to a consensus in the group. When they are done charting, each group will chose someone to share out the group’s chart, and the rest of the group will return to their seats. Each group will share out. The goal will be for everyone to see the characteristics and commonalities among the people in each group, and the differences in characteristics and commonalities among the different picture groups. In most cases, the picture that a person chooses ends up representing that person’s learning style. After all groups have shared out and discussion is over, continue on with the next slide.

49. 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

50. 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

51. 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

52. 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

53. What is your learning style?
Sensing Thinking (ST)
Intuitive Thinking (NT)
Intuitive Feeling (NF)
Sensing Feeling (SF)
Refer to handout “Identify Type Preference”. Ask participants to review it and check off the characteristics they feel address them. The quadrant with the most checks is most likely their learning style.

54. Questions: Sensing Thinking (ST): WHAT? Intuitive Thinking (NT): WHY?
Intuitive Feeling (NF): WHAT IF?
Sensing Feeling (SF): WHAT DOES IT MEAN TO ME?
Example questions:
ST: WHAT is the correct way to do this?
NT: WHY does is have to be done this way?
NF: WHAT IF we tried doing it this way?
SF: WHAT DOES IT MEAN TO ME to do this?

55. 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.

56. Differentiated Instruction
IS NOT…
IS…
- 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 relationships and reflection

57. 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

58. Meeting Diverse Learner Needs: Assessing Your Assets
Diagnostic
Thinking
Strategy
Toolkit
Aligned
Curriculum
and
Assessments
Personal
Connections

59. Vocabulary Strategies

60. Vocabulary Strategies
English language learners need to develop the language of mathematics.
Vocabulary Strategies
Pair/Share: How do you teach vocabulary?

61. 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!

62. 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

63. Verbal Rehearsal Connect with prior learning Association method
Think-Pair-Share

64. Visual Clueing Post key words
Color code or place with pictures, clip art

65. 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

66. Frayer Method Examples Non-examples Non-linguistic Representation
Use or
Application – put in context
Now write your own definition:
Concept

67. 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.

68. 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

69. 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

70. Array Web
Parts or
Characteristics
Concept

71. T-Charts DATA or IDEA T- Chart IDEA T-Chart Opinion or Proof or
Estimate Evidence

72. Venn Diagram

74. Vocabulary Strategies, Writing Strategies and Graphic Organizers Combine for High Payoff
Add some cooperative grouping and you have instant results based learning

75. 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

76. 1587 Route 146, Rexford, NY -
Phone (518)
Fax (518)

77. Analogical Reasoning What is it?
Identifying how one set of concepts has similar relationships to those found in another set of concepts
Process:
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)

78. 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

79. Nine Analogical Relationships
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?
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)

80. 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”

81. 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

82. 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

83. 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

84. 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

85. Sequence or Time Sequence

86. Adjusted or Triple Venn
INFLUENCE OF MULTIPLES:
Elements
Parts
Causes
Conditions

87. 10. Semantic Feature Analysis Traditional Semantic Feature Analysis
Comparison of Pets

88. 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