Reach Every Student Through Differentiation
http://www.diffcentral.com/Video_Clips.html
Corners Differentiated
Activity
 G O TO T H E C O R N E R T H AT B E S T D E S C R I B E S
YO U R L E A R N I N G S T Y L E A N D S H A R E W I T H
T H E PA RT I C I PA N T S I N YO U R C O R N E R :
 Prior
experience with Differentiated
Instruction
 An example of how your learner
preferences affect your learning
and teaching
What is your Mathematical Learning Style?
• The Mastery Style: People in this category tend to
work step–by–step.
• The Understanding Style: People in this category
tend to search for patterns, categories, and reasons.
• The Interpersonal Style: People in this category tend
to learn through conversation and personal
relationship and association.
• The Self-Expressive Style: People in this category
tend to visualize and create images and pursue
multiple strategies.
Mathematical Learning
 Students who favor the Mastery style learn most easily
from teaching approaches that emphasize step-by-step
demonstrations and repetitive practices. They struggle with
abstractions, explanations, and non-routine problem
solving.
 Students who favor the Understanding style learn most
easily from teaching approaches that emphasize concepts
and the reasoning behind mathematical operations. These
students struggle with work that emphasizes collaboration,
application, and routine drill and practice.
Mathematical Learning
 Students who favor the Interpersonal style learn most
easily from teaching approaches that emphasize
cooperative learning, real-life contexts, and connections to
everyday life. This group struggles with independent
seatwork, abstraction, and out-of-context, non-routine
problem solving.
 Students who favor the Self-Expressive style learn most
easily from teaching approaches that emphasize
visualization and exploration. These students struggle with
step-by-step computation and routine drill and practice.
What is Differentiation?
 “At its most basic level, differentiating instruction means
“shaking up” what goes on in the classroom so that students
have multiple options for taking in information, making
sense of ideas and expressing what they learn… a
differentiated classroom provides different avenues to
acquiring content, to processing and making sense of
ideas, and to developing products so that each student
can learn effectively.” (Carol Tomlinson, 1999, p.1)
Today’s Student
Diverse
Students
Reasons for DI
 Gap in achievement levels
 Focused and coherent curriculum
 Increased student expectations
 Higher demand for mathematical skills
Teachers differentiate by:
 WHAT we want students to learn
and HOW we give them access
to it.
 HOW a student makes sense of
the learning.
 WHAT a student makes or does that
SHOWS he/she has the knowledge,
understanding, and skills that were
taught.
Know your Students
Learner Profiles
Interests
Readiness
• Student
learning styles
• Interviews
• Questionnaires
• Formal/informal
assessments
• Anecdotal
records
Create a Responsive Learning Environment
 Know your learners
 More than desk alignment
 Provide a safe place to make mistakes and learn from
them
 Meet your learners “where they are”
 Think about how you can Make Math Irresistible!
Learning Goals
DIFFERENTIATION…
is the proactive acceptance of and planning for student differences,
including their
readiness
interests
learning profiles
Teachers can respond to student differences by differentiating
content
process
products
environment
while always keeping in mind the guiding principles of
respectful tasks ongoing assessment & adjustment
flexible groups
Differentiating Instruction
C - R- A
“ … ALLOWS ALL STUDENTS TO ACCESS THE SAME
C L A S S R O O M C U R R I C U L U M B Y P R O V I D I N G E N T RY P O I N T S ,
L E A R N I N G TA S K S , A N D O U T C O M E S T H AT A R E TA I L O R E D
TO THE STUDENTS’ NEEDS.”
(HALL, STRANGMAN, & MEYER, 2003)
Concrete
Representational
Abstract
“I actually think
that the most
important thing
that teachers
should be
thinking about
is not the
activity that
they choose,
it’s the questions
they ask.”
“Love Learning with Dr. Marian Small”
video 5:51 minutes
http://www.3plearning.com/dr-marian-small-explainsimportance-thinking-math/
Developing Mathematical Thinking
with Effective Questions
 To help students build confidence
and rely on their own
understanding, ask…
 To help students learn to reason
mathematically, ask…
• To check student progress,
ask…
• To help students collectively
make sense of mathematics,
ask…
• To encourage conjecturing,
ask…
 To promote problem solving,
ask…
 To help when students get stuck,
ask…
 To make connections among ideas
and applications, ask…
 To encourage reflection, ask…
“Beyond One Right Answer”
Dr. Marian Small
“DIFFERENTIATING
INSTRUCTION IS A GREAT WAY
TO MAKE MATH MEANINGFUL
FOR ALL. IT'S JUST A
QUESTION OF THE QUESTIONS
TEACHERS POSE.”
Consider the following two scenarios.
Do they sound familiar?
Scenario 1:
Scenario 2:
 A teacher decides that she wants a
 A teacher is working on teaching
math lesson to focus on two-digit
by two-digit multiplication.
 She finds an appropriate problem
for the students to work on.
Although she knows that six or
seven students still struggle with the
concepts involved in multiplying by
even a single-digit number, she
presents the problem to all
students, making sure that the
struggling students receive help
from herself or other students.
fact families.
 He asks students to describe the
fact family for 3 + 4. One student
offers a response:
3 + 4, 4 + 3, 7 - 4, 7 - 3.
The teacher records this on the
board and checks that other
students concur. The whole episode
takes less than five minutes, only
one student responded, and now
the teacher needs to set up another
activity.
Two Beliefs That Need to Change
 …all students should work
on the same problem at the
same time (Scenario 1)
 each math question should
have a single answer
(Scenario 2)
Both scenarios
reflect common practice among many hardworking and capable teachers.
But what else can teachers really do?
An Idea Takes Root
BackgroundTwo “universes collided” whenever the research of one of
Dr. Small’s graduate students (the kinds of questions that math teachers
ask during instruction) and what she was working on at that time
(researching the various phases of student development in each strand of
mathematics). Dr. Small noticed that there was potential in using
questioning as a way to differentiate instruction in a classroom with
groups of students at different levels.
What emerged was the delineation of two core
techniques for differentiating instruction in
mathematics in a meaningful, but manageable way.
Open-Ended
Questions
Teachers create open
questions by
allowing for a certain
level of ambiguity.
Students may initially
be a little
uncomfortable with
ambiguity, but they
almost always
‘warm up to’ and
appreciate the
latitude that the
ambiguity allows.
Parallel Tasks
Focusing on the same “big ideas”, but different levels of difficulty
Strategy 1:
Strategy 2:
• Teacher may let students
• Pose common questions for all
choose between two
problems which have been
written with different levels
of difficulty.
students to answer. The
teacher could ask questions,
no matter which task the
student(s) completed.
• The questions focus on
common elements; however,
asking students to describe
their specific strategies gives
opportunities to differentiate.
Louisiana Believes
Department of Education Video Library
7th Grade
Summary:
High School
Summary:
In this 7th grade Math
lesson, students categorize
expressions, equations, and
inequalities and discuss
how they know how to
categorize them.
(video 5:30 min.)
By the end of the class, to
be able to simplify
rational expressions.
Video Notes/Reflection
(video 9:28 min.)
Video Notes/Reflection
Differentiation using Tiered Lessons
“TIERED ACTIVITIES ARE REALLY
QUITE ESSENTIAL. THEY ARE
ALMOST THE MEAT AND POTATOES
OF DIFFERENTIATION.” ( T O M L I N S O N )
What is Tiered Instruction?
Teachers use tiered
activities so that all
students focus on
essential understandings
and skills but at different
levels of complexity,
abstractness, and openendedness.
By keeping the focus of the
activity the same, but
providing routes of access at
varying degrees of difficulty,
the teacher maximizes the
likelihood that:
1) each student comes away
with pivotal skills &
understandings
2) each student is appropriately
challenged.
When Tiering Instruction:
Adjust the…
o Level of Complexity
o Amount of Structure
o Materials
o Time/Place
o Number of Steps
o Form of Expression
o Level of Dependence
Example of a tiered lesson K-2
Open-Ended Probes
 How do you describe a cube to someone who has never seen one?
 The answer is 87. What could the question be?
 How is measurement used in your home?
 How might we write numbers if we didn’t have zeroes?
 Imagine you are trying to help someone understand what three-
tenths means.
What pictures could you draw to be helpful?
How many different pictures can you make?
Strategies for
Subject: Mathematics - Statistics
Grade: Twelfth
Standard: Data Analysis and Probability from the National Council of Teachers of Mathematics Principles and
Standards for School Mathematics
Key Concept:
Key Concept: Students are knowledgeable, analytical, thoughtful consumers of data.
Generalization: Students formulate a question that can be addressed with data and collect, organize, and display the data.
Background:
This lesson would be an end-of-course culminating activity and should be completed in groups consisting of two to four
students.
Students choose a tier according to interest in a question and decide to use a survey, observational study, or experiment to
answer the question.
Directions for all the tiers are the same. Students determine a question they would like to answer, decide on a appropriate
means for data collection, and prepare a presentation of the information to share with the class. The presentation should
include a complete analysis of the data and the answer to the question of interest. However, a variety of presentation
methods would be appropriate, e.g., a poster, a PowerPoint display, a written report, or a radio/TV show interview.
This lesson will take a number of days to complete as students will need time to decide on a question, collect the data,
analyze the data, and prepare the presentation. You will also need 1-2 days for students to make their presentations.
This lesson is tiered in process and product according to interest.
The tiers could be based on the questions or the products. Those listed here represent the products produced.
Tier 1: Poster
Tier II: Power Point
Tier III: Written report
Tier IV: Radio/TV
Assessment: Assessment:
A rubric for each product should be based primarily on neatness, organization, accuracy of the information, and accuracy
of the statistical analysis. The rubrics should be given to the students at the beginning the lesson since the decision on
which product will be made after selecting a question.
Sample Model Lesson Framework
Whole
Math Message/Warm – Up
Whole
Lesson
Part
Student Activity
Group 1
Group 2
Group 3
Whole
• Share Time
Misunderstandings vs. Reality
Misunderstandings
 Differentiation is a set of
instructional strategies.
 It’s adequate for a district or
school leader to tell or show
teachers how to differentiate
effectively.
 Differentiation is something a
teacher does or doesn’t do.
 Differentiation is just about
instruction.
Reality
 Differentiation is a philosophy – a way
of thinking about teaching & learning –
it is a set of principles.
 Learning to differentiate requires
rethinking of one’s classroom practice
through assessment and adjustment.
 Most teachers in a classroom for one
day DO pay attention to student
variations, put very few proactively plan
to address all student differences.
 Differentiation is inseparable from a
positive learning environment,
curriculum, and flexible management.
It’s well to remember that:
THINGS TAKE TIME