A Different….iated
Mathematics Classroom
Adapted from a presentation by:
Dr. Laura Rader
May 14 &15, 2008
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Teachers modify
– Content: the what …..examples?
– Process: the how …..examples?
– Product: the vehicle used to demonstrate
understanding …..examples?
Activity: Create Scaffolded Question set of 15 questions on cards
Activity: Create A Jeopardy game using Jeopardy blank, Internet and resources
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Students vary in
– Readiness: what is my understanding now?
– Interest: why should I want to do this?
– Learning Profile: how do I best learn and
understand?
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Speak their language!
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Readiness
Interest
Growth
Motivation
Judy Rex presentation 2006
Learning Style
Efficiency
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Readiness
How do you get to know your learners?
How do you use this information?
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Are they Ready?
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Readiness
 Know
where you want students to be
 Begin
where the students are
 Continually
 Keep
assess your students
USEFUL records and data
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
“Effective differentiated classrooms include
many times in which whole-class, nondifferentiated fare is the order of the day.
Discuss

Modify a curricular element only when (1)
you see a student need and (2) you are
convinced that modification increases the
likelihood that the learner will understand
important ideas and use important skills more
thoroughly as a result”
The differentiated Classroom, Tomlinson p11
Discuss: Reasonable?
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Ways to incorporate interest

Create interest within a lesson
– Give choice within content
– Give choice for the final product

Use general interests
– Incorporate interests outside of school.
For example: sports, clubs, parents, history, news

Hook student interest through relevance
– Applications, connections with other sections
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Differentiation by Interest
Math
Sequence of Numbers –Real Number System
Choice Board
Write a poem
about the number
groups or
sequence of
numbers
Sing a song/rap
about the groups
or sequence of
numbers
Draw a picture that
represents the
grouping of
numbers
Construct a
number line with
only decimals and
fractions with
different
denominators
Web search and
report- if it’s not a
Real Number, what
is it?...how do we
sequence non Real
numbers
Write a paragraph
about the importance
of understanding the
ordering of numbers
in elation to
Money/Finances and
what number groups
are associated with
money
Explain and
describe the
problem generated
from a geometric
representation of
an irrational
number using the
Pythagorean
Theorem
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Learning Style
What type of learner are you?
How do you know?
To what extent is your learning style
reflected in your teaching style?
Rodney S… Trumpet
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“As we start a new school year, Mr. Smith, I just
want you to know that I’m an Abstract-Sequential learner
and trust that you’ll conduct yourself accordingly!” 13
“Have some respect for my learning style!”
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Learning Style

Conduct surveys to collect data
– Multiple intelligences: musical, verbal/linguistic, logical
interpersonal, intrapersonal, kinesthetic, visual/spatial
– Sternberg: creative, practical, analytical
– Modality: visual, verbal, kinesthetic
– Jung, 4MAT, Array: social interaction and personality

Use data to purposefully group students
– Like grouping
– Unlike grouping
– Whole group
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Resources for learning profiles

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www.e2c2.com/fileupload.asp
MI, Sternberg, modality & array interaction surveys
http://www.learning-styles-online.com/ ACTIVITY Online
MI with graphs
http://www.engr.ncsu.edu/learningstyles/ilsweb.html
global vs sequential
http://www.rrcc-online.com/~psych/LSInventory.html
Sternberg’s survey
http://ttc.coe.uga.edu/surveys/
MI survey & others
http://www.brookhavencollege.edu/learningstyle/modality_test.html
sensory modality
http://www.humanmetrics.com/cgi-win/JTypes1.htm
personality assessment
http://www.cse.fau.edu/~maria/COURSES/CAP5100-UI/LearningStyles.html
4mat personality type – group dynamics
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Multiple Intelligences Product Grid


Categorizes different
products under separate
headings
Many are listed in more than
one column and may look
different due to the
approach taken
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Howard Gardner’s Multiple-Intelligences Theory
Things to Remember
Know your learner; Use the information
 DI does not have to be a project
 You don’t have to use a specific DI tool
 You don’t have to do DI all the time

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Check for Understanding
Thumbs up?
Thumbs down?
Thumbs sideways?
Exit Slips
Homework
Error Analysis
and?
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Begin Slowly – Just Begin!
Low-Prep Differentiation
Choices of books
Homework options
Use of working buddies
Varied journal Prompts
Orbitals
Varied pacing with anchor options
Student-teaching goal setting
Work alone / together
Whole-to-part and part-to-whole explorations
Flexible seating
Varied computer programs
Design-A-Day
Varied Supplementary materials
Options for varied modes of expression
Varying scaffolding
Let’s Make a Deal projects
Computer mentors
Think-Pair-Share by readiness, interest, learning profile
Use of collaboration, independence, and cooperation
Open-ended activities
Mini-workshops to reteach or extend skills
Jigsaw
Negotiated Criteria
Explorations by interests
Games to practice mastery of information
Multiple levels of questions
High-Prep Differentiation
Tiered activities and labs
Tiered products
Independent studies
Multiple texts
Alternative assessments
Learning contracts
4-MAT
Multiple-intelligence options
Compacting
Spelling by readiness
Entry Points
Varying organizers
Lectures coupled with graphic organizers
Community mentorships
Interest groups
Tiered centers
Interest centers
Personal agendas
Literature Circles
Stations
Complex Instruction
Group Investigation
Tape-recorded materials
Teams, Games, and Tournaments
Choice Boards
Think-Tac-Toe
Simulations
Problem-Based Learning
Graduated Rubrics
Flexible reading formats
Student-centered writing formats
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Benefits of DI

Decreases behavior problems

Stretches each student

Engages students for learning

Focuses on student rather than teacher

Creates variety

Offers choice
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Fair Game Dilemma
Tiered Math Assignment
Tier ?
A few students want me to play a game with them. They
will give me a dime for each odd sum I roll with two die. I
have to give them a dime for each even sum they roll with
two die. I think I’m going to get cheated! I noticed that I
can’t roll one of my odd numbers – 1! I only get a choice
of 5 odd numbers (3, 5, 7, 9, 11) but they will get a choice
of 6 even numbers (2, 4, 6, 8, 10, 12). Should I play this
game with the students? Using as much mathematical
language and representation as you can, show me that this
is or is not a fair game.
Data Analysis and Probability Standard for Grades 6-8 (NCTM)
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Tiering Continued…..
Tier ?
A few students want me to play a game with them. They
will give me a dime for each odd sum I roll with two die. I
have to give them a dime for each even sum they roll with
two die. I think I’m going to get cheated! Should I play
this game with the students? Using as much mathematical
language and representation as you can, show me that this
is or is not a fair game.
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Tiering Continued……
Tier ?
A few students want me to play a game with them. They
will give me a dime for each odd sum I roll with two die. I
have to give them a dime for each even sum they roll with
two die. I think I’m going to get cheated! I noticed that I
can’t roll one of my odd numbers – 1! I only get a choice
of 5 odd numbers (3, 5, 7, 9, 11) but they will get a choice
of 6 even numbers (2, 4, 6, 8, 10, 12). List all of the
possible ways of getting each sum using the digits 1-6.
Then determine the probability of getting an even and odd
sum. Use the information to draw a conclusion, is this a
fair game to play with the students?
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Developing a Tiered Activity
1
Select the activity organizer
•concept
Essential to building
•generalization
a framework of
2
• readiness range
• interests
• learning profile
• talents
understanding
3
Create an activity that is
• interesting
• high level
• causes students to use
key skill(s) to understand
a key idea
Think about your students/use assessments
skills
reading
thinking
information
4
Chart the
complexity of
the activity
High skill/
Complexity
Low skill/
complexity
5
Clone the activity along the ladder as
needed to ensure challenge and success
for your students, in
•
materials – basic to advanced
•
•
•
form of expression – from familiar to
unfamiliar
from personal experience to removed
from personal experience
equalizer
6
Match task to student based on
student profile and task
requirements
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Differentiation by Learning Style
Math - Exponential Equations

Global: (Whole to Parts)
–
–
–
–
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Skim chapter to explore exponential equations
Show examples of when exponentials are used
Show connection to linear equations/compound interest
Begin defining parts of linear equations
Sequential: (Parts to Whole)
–
–
–
–
–
Define parts of linear equation
Show possible graphs
Define parts of exponential equation
Show possible graphs
Explain differences and similarities
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Differentiation by Readiness
Math - Algebra Operations - Rainbow
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Differentiated Instruction (DI):
a Definition
“Differentiated instruction is a teaching
philosophy based on the premise that
teachers should adapt instruction to student
differences….Teachers should modify their
instruction to meet students’ varying
readiness levels, learning preferences, and
interests.”
– Carol Ann Tomlinson, Associate Professor
University of Virginia
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