Transcript Differentiation & Mathematics

Differentiated
Instruction
Rob Irwin
Purpose
• Develop shared and practical
understandings of differentiation as related
to the effective teaching of Mathematics
• Tiering as a differentiation strategy
• Tiering Math Games & Trailblazers
lessons
Processes/Payoff
• Processes:
Question Car Park; Think, Pair, Share;
Paired/ Quad Brainstorm; Games
Rotations; Discussion; Gallery Walk;
Group Planning
• Payoff: Leave the workshop with practical
ideas for differentiating instruction through
the strategy of tiering
Protocols for working as a
professional learning community
• Adopt a sense of responsibility for the group as a
community of learners
• One person at a time talking so as to keep the meaning
• Attend to and listen to others
• Accept where others are at
• Suspend judgement
• Allow and give no putdowns
• Common signal for gaining
everyone’s attention
“Question Car Park”
• Write down your
questions and issues on
the post-it notes provided
throughout the sessions
and “park” them in the
“Question Car Park”
charts on the walls of the
room.
• I will work at answering
them at the beginning of
the next two sessions.
Treasure Hunt for Diversity
Using the
Treasure Hunt
grid, complete
each section
by finding
colleagues who
match the
description.
Challenges of today’s students
• As a group, brainstorm (and jot down in
your reflective journals) all the needs of
students you have worked with in your
classrooms this year or in the past.
Challenges of today’s students
The diversity of students in
your classroom:
• “Learning styles (visual,
spatial, auditory, tactile,
kinaesthetic)
• Interests
• Strengths/ Weaknesses
• Cognitive abilities
• ELL’s
• Attitudes/ Motivation/
Persistence/ Confidence
• Readiness
• Socio-Economic and
Family Factors
• Learning Pace
• Gender Influences
• Cultural/Ethnic
influences
Challenges of Today’s Students
“Normal is only a setting on the washing
machine”
Schmidt, M (2006). Losing Sight of the Shore: Differentiating Curriculum and Instruction.
A Once Upon A Time Story
About A Blonde Student
Once upon a time there was a lovely, young
student named Goldilocks. She was an
adventurous sort, so one day she went walking
through the forest in search of a teacher.
As Goldilocks rounded a bend in the path, she
came into a bright clearing in the forest. She was
very excited to find a teacher presenting a
lesson that at first captured her attention.
Goldilocks tried to stay engaged and learn, but
she became frustrated as it was just too difficult.
The story continues…..
She sighed, waved goodbye to the first teacher,
and continued on her way.
Goldilocks walked a bit longer and ambled up a hill
where she found herself in a wide, flower-filled
pasture. There a second teacher sat, seemingly
waiting just for her.
This teacher began her lesson, but Goldilocks
soon became bored because it was just too
easy. She waved goodbye to the second
teacher, and once again went on her way.
The story continues…..again!
• Trudging through the forest more slowly
now and less joyfully, she came across a
magnificent meadow that was not only
amazingly colorful but fragrant as well.
There stood another teacher. The teacher
began the lesson, and Goldilocks was
enthralled! This lesson wasn’t too hard! It
wasn’t too easy! It was just right!
What is Differentiation?
Think, Pair, Share:
• Individually, jot down
your own thoughts as
to what you think
differentiation is.
• Share with partner.
• Share with group of 4.
What is Differentiation?
• At its most basic level, differentiating instruction
means “shaking up” what goes on in the
classrooms 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)
How Is It Implemented?
• Use diagnostic assessments to determine
student readiness. These assessments
can be formal or informal. Teachers can
give pre-tests, question students about
their background knowledge, or use KWL
charts (charts that ask students to identify
what they already Know, what they Want
to know, and what they have Learned
about a topic).
How is it implemented?
• Determine student interest. This can be
done by using interest inventories and/or
including students in the planning process.
Teachers can ask students to tell them
what specific interests they have in a
particular topic, and then teachers can try
to incorporate these interests into their
lessons.
How Is It Implemented?
• Identify student learning styles and
environmental preferences. Teachers can get
information about student learning styles by
asking students how they learn best and by
observing student activities. Identifying
environmental preferences includes determining
whether students work best in large or small
groups and what environmental factors might
contribute to or inhibit student learning. For
example, a student might need to be free from
distraction. PLUS you need a good understanding of M.C.
What Does it Look Like for Math?
Math instruction can be differentiated to
allow students to work on skills appropriate
to their readiness level and to explore
mathematics applications through -
• Math games are a very good and easy
way to differentiate learning. Played
correctly students can experience fun
activities while playing different levels of a
game.
• Tiering is another way. Tier the group or
individual activities after the mini lesson.
Differentiated Instruction
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
What is reality now and Where
you want to be: Self-Assessment
Traditional Classroom
Vs Differentiated
Classroom
Using the handout, place
an X on each continuum
where you believe your
teaching is now and a Y
where you’d like to be.
Discuss with your group.
Tiering
as a
Differentiation Strategy:
What is it?
“Tiered activities are really
quite essential. They are
almost the meat and potatoes of
differentiation.”
(Tomlinson)
Differentiating by
Readiness/Tiered Lessons
• Involves having students work on the
same concept at different levels of
complexity and with different levels of
support or open-endedness.
• Not more work or less work, just different
work.
Planning Tiered Assignments
Concept to be Understood
OR
Skill to be Mastered
Create on-level task first then adjust up and down.
Below-Level
Task
On-Level
Task
“Adjusting the
Task”
Above-Level
Task
When Tiering:
Adjust--•
•
•
•
•
•
•
Level of Complexity
Amount of Structure
Materials
Time/Pace
Number of Steps
Form of Expression
Level of Dependence
The “Equalizer”
1. Foundational
Transformational
2. Concrete
Abstract
3. Simple
Complex
4. Fewer Facets
* Low Readability
Multi-Facets
*High Readability
5. Smaller Leap
Greater Leap
6. More Structured
More Open
7. Clearly Defined Problems
8. Less Independence
9. Slower
Fuzzy Problems
Greater Independence
Quicker
Using “the Equalizer: A Tool for
Planning Differentiated Lessons”
(Tomlinson, 2000)
•
“Similar to using the equalizer buttons on a
CD player/stereo, you can slide the buttons
across several different continuums to get the
best combination of sounds for a musical piece.
•
In a differentiated classroom, adjusting the
buttons appropriately for various students’ needs
equalizes their chances of being appropriately
challenged by materials, activities, products in
your classroom”
(Tomlinson, 2000).
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.
Use of State Standards
Use the standards (current state standards
or Common Core standards) to inform the
tiering by seeing the sequence of
development of the concept
Tiering
Let’s look at how to tier a game
Importance of teachers knowing content &
Standards
Let’s look at and then later play…
Flash
HANDOUT IN FOLDER
Now consider this….
Tier 1: One group of students in the class are
very unsure of the basic Count-On (count
on 1,2,3,0) facts
Tier 2: One group of students in the class
may need to practice doubles
Tier 3: One group of students in the class
have automaticity with addition facts to 12,
including Make Ten strategy
WHAT TO DO?
Differentiate the Game using the Equalizer: Addition Flash
Tier 1:
John, Robyn, Liz, Rob,
Karen
Unsure of very basic
count-on facts
Count-on 1,2,3,0
•Foundational
•Less
independence
•Simple
•Observation notes
•Exit slips
Play game with
doubles dominoes
•Concrete
•Game recording
slips
•Observation notes
•Journal
* Play game with
different numbers
(2x6 sided dice;
cards 0-12)
* Missing addend
game
* 3 addend game
•Transformational
•Game recording
slips
•Observation notes
•Journal
Choose specific cards/
specific dice (e.g. +1,
+2,+3,+0 – singly or
combinations of count-on
facts based on students’
needs)
Use of visuals (number line)
Play game Count-On 1,
2, 3, 0
Tier 2: Judith, Barry,
Kate, Jessica, Richie
Need to develop
strategy of doubles
facts
Tier 3:
Dan, Angie, Peter,
Jacinta, Mia
•Multiple facets
•Complex
Tiered Games:
Let’s Experience It
Flash Activity
Cont.
Work with a partner
# 1 Sequence the games in order of
development
# 2 Find as many activities that you could
differentiate into 3 tiers
Let’s Experience It
•
You are going to participate in several games
that have been tiered at three different levels.
1. Your group needs to play each tier of each
game. Compare the three tiers. What is the big
math idea?
2. Complete the template, match each tiered set
of games to the Standards and the Equalizer
3. What are the implications for your own
classroom?
Carousel the Games Around the
Groups/Tables
We’ll move the games
on a given signal
clock-wise
Table 1:
Table 2:
Table 3:
Table 4:
Table 5:
Table 6:
Tiered Games
Group Report
• What did you notice?
Differentiate the Games using
the Equalizer- It’s your turn!
• Each group will find a
Math game, planning
template and butcher’s
paper on their table.
• As a group and using the
‘Equalizer’ and the
Standards in your
handout, adapt the game
and plan for a variety of
students’ needs- tier for
three groups of children
• Tape your group’s poster
up for the gallery walk
Gallery Walk
• One member from each
group stays with the
tiered games poster.
• All groups rotate and the
poster leader describes
the tiering.
• Ask questions
• Get ideas
• Complete template
• Rotate on given signal
Tiering a Daily Math Lesson
in the Workshop Model
Tiering the Student Activity Portion
of the Workshop Model Lesson
Whole
Math Message/Warm-Up
Whole
* Mini-Lesson
Part
Whole
Student ActivityGroup 1
Group 2
Group 3
* Share Time
Tiering a Trailblazer Lesson
Your Turn…
Using the template in your packet, choose
some lessons from the program (eg. first
weeks of school in September) and,
consulting the standards,
tier the student activity portion of each
lesson
How do I begin to differentiate?
• Consider Low Prep/High Prep
differentiation
• See handout on “Hints to Begin”
Let’s Recap
Explicit Visuals of ExpectationsY Chart - Kindergarten
Establishing a Co-operative FrameworkDeveloping a Y Chart for Group Work
Flexible GroupsDifferentiated Games
Using Assessment to Inform the
Differentiation within each Game
Varying Content of Games to
Meet Students’ Needs
Rubric for Differentiation
(developed by Julie Howie A.U.S.S.I.E. Math Consultant)
• Use for reflecting on your practice
Things Take Time
Put up in a place where
it’s easy to see,
The cryptic
admonishment,
T.T.T.
When you feel how
depressingly slow you
climb
It’s well to remember that
THINGS TAKE TIME.
From Tomlinson, C.
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HAVE A GREAT NEW
SCHOOL YEAR!