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Differentiation for Gifted Learners


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Title: Differentiation for Gifted Learners

Differentiation for Gifted Learners
  • Lori Comallie-Caplan
  • Professional Development Day
  • 10/24/2008

(No Transcript)
Session Objectives
  • Session participants will
  • Articulate and discuss how the AES model
    incorporates Coaching for Differentiation
  • Define 8 general strategies of differentiation
    and their application to the general education
  • Define 3 new strategies using critical thinking
    to differentiate instruction in the general
    education classroom.
  • Define 3 new strategies using creativity to
    differentiate instruction in the general
    education classroom
  • Be able to utilize the COS-R in coaching for
    differentiation in the general education

The AES Model
The AES Model
The AES Model
The AES Model
What is Differentiated Curriculum for the Gifted
in the Context of Curriculum Standards for all?
  • Features
  • Acceleration
  • Complexity
  • Depth
  • Challenge
  • Creativity

Differentiation Feature Acceleration
  • Fewer tasks assigned to master standard
  • Assessed earlier or prior to teaching
  • Clustered by higher order thinking skills

Center for Gifted Education School of Education
The College of William and Mary
Differentiation Feature Complexity
  • Used multiple higher level skills
  • Added more variables to study
  • Required multiple resources

Center for Gifted Education School of Education
The College of William and Mary
Differentiation FeatureDepth
  • Studied a concept in multiple applications
  • Conducted original research
  • Developed a product

Center for Gifted Education School of Education
The College of William and Mary
Differentiation Feature Challenge
  • Advanced resources employed
  • Sophisticated content stimuli used
  • Cross-disciplinary applications made
  • Reasoning made explicit

Center for Gifted Education School of Education
The College of William and Mary
Differentiation Feature Creativity
  • Designed/constructed a model based on principles
    or criteria
  • Provided alternatives for tasks, products, and
  • Emphasized oral and written communication to a
    real-world audience

Center for Gifted Education School of Education
The College of William and Mary
A Review of the Strategies
  • Anchor
  • Choice
  • Six Hats
  • Cubing
  • Structured
  • Academic
  • Controversy
  • The Profiler
  • Tri - Minder
  • Rafts

  • Describe
  • Strengths
  • Weaknesses
  • Application

  • Describe
  • Strengths
  • Weaknesses
  • Application

Six Hats
  • Describe
  • Strengths
  • Weaknesses
  • Application

  • Describe
  • Strengths
  • Weaknesses
  • Application

Structured Academic Controvery
  • Describe
  • Strengths
  • Weaknesses
  • Application

The profiler
  • Describe
  • Strengths
  • Weaknesses
  • Application

  • Describe
  • Strengths
  • Weaknesses
  • Application

  • Describe
  • Strengths
  • Weaknesses
  • Application

Using Classroom Observation Scales for
Instructional Improvement
Assessing Classroom PracticeGeneral Purposes
  • Conduct classroom observations in multiple
    instructional contexts.
  • Examine differences in instructional behaviors in
    different organizational patterns, different
    teacher groups, and different subject areas.
  • Provide evidence of need for professional

Assessing Classroom PracticeLiterature Review
  • No documented differentiation practices for
    gifted in heterogeneous classrooms (84)
    (Westberg, Archambault, Dobyns, Salvin,1993)
  • Ineffective teachers over 3 years resulting in
    depressed effects on student achievement in math
    regardless of ability level (Sanders Rivers,
  • Positive effects of employing key practices (e.g.
    critical thinking or metacognition) on student
    learning in math science for elementary and
    middle school levels (Wenglinsky, 2000)

Assessing Classroom PracticeLiterature Review
  • Higher-level reform behavior takes a minimum of
    two years of intensive training to demonstrate
    results (Borko, 1993)
  • Content-based curriculum intervention for gifted
    coupled with staff development results in
    significant important growth gains (Little,
    Feng, VanTassel-Baska, Rogers, Avery, 2003
    VanTassel-Baska, Zuo, Avery Little, 2002
    VanTassel-Baska, Bass, Ries, Poland Avery, 1998)

Assessing Classroom PracticeInstrument
Construction (COS-R)
  • Categories are consonant with research on
    effective teaching practices, teacher reform
    literature, and teaching high-ability learners
  • Curriculum Planning and Delivery
  • Accommodations for Individual Differences
  • Problem Solving
  • Critical Thinking Strategies
  • Creative Thinking Strategies
  • Research Strategies

Assessing Classroom PracticeTechnical Adequacy
of COS-R
  • Content validity (.97)
  • Reliability (.91- .93)
  • Inter-rater reliability (.87 - .89)
  • Two study replications of scale use produce
    similar results

Critical Thinking Strategies
  • encouraged students to judge or evaluate
    situations, problems, or issues
  • engaged students in comparing and contrasting
    ideas (e.g., analyze generated ideas)
  • provided opportunities for students to generalize
    from concrete data or information to the
  • encouraged student synthesis or summary of
    information within or across disciplines.

Creative Thinking Strategies
  • solicited many diverse thoughts about issues or
  • engaged students in the exploration of diverse
    points of view to reframe ideas
  • encouraged students to demonstrate
    open-mindedness and tolerance of imaginative,
    sometimes playful solutions to problems
  • provided opportunities for students to develop
    and elaborate on their ideas.

Differentiating Using Critical Thinking
  • Models Used by the College of William and Mary

Pauls Model of Reasoning
Got a Problem
  • What is the problem?
  • Why are we reasoning about it?
  • What are the points of view?
  • What are the assumptions people make?
  • What are the important concepts?
  • What evidence supports the point of view?
  • What inferences can we make?
  • What would be the consequences of different
  • --based on Paul (1992)
  • Center for Gifted EducationThe College of
    William and Mary

Elements of Reasoning
-- Paul, 1992
Question Tree based on Reasoning Model
  • What is the question or issue of interest?
  • What is the purpose of _____________?
  • What points of view or perspectives are important
  • understanding __________________?
  • What assumptions underlie each perspective on
  • What data/evidence support a given perspective on
  • What inference can be made about ______________,
    based on the evidence?
  • What are the implications and consequences of

Standards of Reasoning
  • Are there enough reasons to make a convincing
  • Is the evidence correct or right?
  • Are the reasons clear?
  • Are specific reasons or examples included rather
    than vague generalizations?
  • Are the arguments and reasons strong and
  • Is the thinking logical?

Pauls Model of ReasoningThe Crucible
  • What is the central problem of the play?
  • What was Millers purpose in writing it, do you
  • How do the following concepts apply to The
    Crucible loyalty, truth, revenge, and absolute
  • What assumptions are made by the Salem citizenry
    about guilt and innocence?
  • Which point of view is the most crucial to the
    play Abigails, Elizabeths, or Johns? What
    role does each perspective play in plot

Pauls Model of ReasoningThe Crucible
  • What data or evidence from the play would suggest
    that witchcraft is not at work?
  • What inferences do you draw from the following
    statement by John Proctor for now, I do think
    I see some shred of goodness in John Proctor.
    Not enough to wave a banner with, but white
    enough to keep it from such dogs.
  • What are the consequences for individuals and
    society of seeing the world in black and white
    terms (e.g. good and evil)?

The Logic of History
Be aware Much human thinking is historical. We
use our beliefs (formed in the past) to make
thousands of decisions in the present and plans
for the future. much of this historical thinking
is deeply flawed.
Elder, L. Paul, R. (2003). The foundations of
analytic thinking. The Foundation for Critical
Reasoning about a Situation or Event
  • Based on the elements and premise of the Paul
    model, this reasoning model should be used when
    analyzing a specific event where two or more
    people or groups of people conflict with one
    another and have a vested interest in the outcome
    of the event.

Reasoning about a Situation or Event
What is the situation?
Who are the stakeholders?
What is the point of view for each stakeholder?
What are the assumptions of each group?
What are the implications of these views?
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The Literature Web
  • The Literature Web is a model designed to guide
    interpretation of a literature selection by
    encouraging a reader to connect personal response
    with particular elements of the text. The web may
    be completed independently and/or as a tool for
    discussion. Recommended use is to have students
    complete the web independently and then share
    ideas in a small group, followed by a
    teacher-facilitated debriefing.

Literature Web
  • The web has five components
  • Key Words interesting, unfamiliar, striking, or
    particularly important words and phrases
    contained within the text
  • Feelings the readers feelings, with discussion
    of specific text details inspiring them the
    characters feelings and the feelings the reader
    infers the author intended to inspire
  • Ideas major themes and main ideas of the text
    key concepts
  • Images and Symbols notable sensory images in the
    text, pictures in they readers mind and the
    text that inspired them, symbols for abstract
  • Structure the form and structure of the writing
    and how they contribute to meaning may identify
    such features as use of unusual time sequence in
    narrative, such as flashbacks, use of voice, use
    of figurative language, etc. style of writing

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Hamburger Model for Persuasive Writing
Hamburger Model continued
  • The Hamburger Model uses the familiar metaphor of
    a sandwich to help students construct a paragraph
    or essay. Students begin by stating their point
    of view on the issue in question (the top bun).
    They then provide reasons, or evidence, to
    support their claim they should try to
    incorporate at least three supportive reasons
    (the patties). Elaboration on the reasons
    provides additional detail (the fixings). A
    concluding sentence or paragraph wraps up the
    sandwich (the bottom bun).

Dagwood Model
Dagwood Model Continued
  • The Dagwood Model is an extended version of the
    sandwich metaphor (i.e. the famous sandwich of
    the cartoon character). This model is designed to
    help students construct a persuasive essay which
    also addresses the arguments of the contrasting
    viewpoint. Thus, the sandwich contains multiple
    layers of "patties" or reasons and their
    contrasting viewpoints, as well as many "fixings"
    or elaborations.

The Vocabulary Web
  • The Vocabulary Web is a tool for exploring words
    in depth. It asks students to investigate a
    single word in detail, finding its definition,
    synonyms and antonyms, and etymological
    information. With this information, students then
    identify word families, or other words using
    the same meaning-based stems as the original
    word and they provide an example of the word,
    which may be a sentence or analogy using the
    word, a visual or dramatic representation, or
    another creative form.

Vocabulary Web
Analyzing Primary Resources
  • The Analyzing Primary Sources model has been
    developed as a means for teaching students how to
    confront a historical document, the questions to
    ask of it, and how to critically examine
    information they receive. The chart guides
    students from establishing a context and purpose
    for the source to evaluating and interpreting the
    source, including its authenticity/reliability
    and consequences/outcomes.

Analyzing Primary Sources
Establishing a context and intent for the source
Understanding the Source
Analyzing Primary Resources
Evaluating/Interpreting the source
The Research Model
  • The Research Model provides students with a way
    to approach an issue of significance and explore
    it individually and in small groups. Its
    organization follows major elements of reasoning.
    Teachers are encouraged to model each stage of
    this process in class.

Research Model
1. Identify your issue or problem. What is the
issue or problem? Who are the stakeholders and
what are their positions? What is my position on
this issue?
2. Read about your issue and identify points of
view or arguments through information
sources. What are my print sources? What are my
media sources? What are my people sources? What
primary and secondary source documents might I
use? What are my preliminary findings based on a
review of existing sources?
Center for Gifted Education School of Education
The College of William and Mary
3. Form a set of questions that can be answered
by a specific set of data 1) What would be the
results of _____________? 2) Who would benefit
and by how much? 3) Who would be harmed and by
how much? My research questions
4. Gather evidence through research techniques
such as surveys, interviews, or analysis of
primary and secondary source documents. What
survey questions should I ask? What interview
questions should I ask? What generalizations do
secondary sources give? What data and evidence
can I find in primary sources to support
different sides of the issue?
5. Manipulate and transform data so that they can
be interpreted. How can I summarize what I found
out? Should I develop charts, diagrams, or graphs
to represent my data?
Center for Gifted Education School of Education
The College of William and Mary
6. Draw conclusions and make inferences. What do
the data mean? How can I interpret what I found
out? How do the data support my original point of
view? How do they support other points of
view? What conclusions can I make about the issue?
7. Determine implications and consequences. What
are the consequences of following the point of
view that I support? Do I know enough or are
there now new questions to be answered?
8. Communicate your findings. (Prepare an oral
presentation for classmates based on note cards
and written report.) What are my purpose,
issue, and point of view, and how will I explain
them? What data will I use to support my point of
view? How will I conclude my presentation?
Center for Gifted Education School of Education
The College of William and Mary
Research Example Science Math
  • Ask students to design an experiment to test a
    question of interest to them
  • Examples
  • Do people prefer Product X over Product Y?
  • Are ants attracted to sugar?
  • Are girls more addicted to computers than boys?
  • A research report must be prepared and presented,
    using technology applications. Be sure to address
    hypothesis, data collection techniques,
    appropriate data tables, conclusions, and
    implications of the findings based on the
    original question.

Research Example - Language Arts
  • Over the years there have been many ways to
    preserve memories, or to keep important things
    from being forgotten. Brainstorm some of the
    ways people preserve memories. How many can you
    think of? Which of these ways require technology
    such as electricity? Divide your list into two
    groups traditional methods that do not depend
    on technology and modern methods that use
    technology. What are the advantages and
    disadvantages of each type?
  • Choose a point of view about the best ways to
    preserve memories. Do some research to support
    your point of view. Your research might include
    library materials, interviews, or a poll.
  • Later in this unit you will write a short paper
    (1-2 pages) and give a two-minute presentation on
    your point of view, supported by your findings.
  • Journeys and Destinations, Grades 2-3

Research Example - Social Studies
  • You will sign up for a person or event from the
    1920s to explore in your project. From your
    research you will create a learning booth or
    mini-museum that your classmates will visit, so
    you should make it as entertaining and
    interesting as possible.
  • You will need to include the following
  • Pictures or other visual aides (audio if
  • Timeline placing the person or event
  • Description of your person/issue
  • An explanation of the person/issues significance
    in the 1920s and today
  • A handout (or brochure) that includes basic
    information on the contents of your museum and
    entices people to come and see the exhibit.
  • Visitors should be able to determine who/what was
    the main focus of your museum, how the person and
    related issue/event fit on a timeline of the
    1920s, and the significance of the person and
    related issue/event(s) to life in the 1920s and
    to life today.
  • The 1920s in America A Decade of Tensions,
    Grades 6-7

Create a research task demand in your area of
learning for gifted learners.Use the examples
as prototypical models.
  • Mega Math
  • http//www.c3.lanl.gov/mega-math/
  • Connected Math
  • http//connectedmath.msu.edu/teaching/gifted.shtml
  • National Library of Visual Manipulatives
  • http//nlvm.usu.edu/en/nav/vLibrary.html
  • WebMath
  • http//www.webmath.com/
  • Descartes Cove
  • http//www.cty.jhu.edu/cde/cove
  • K-12 Resources for Mathematics Education
  • archives.math.utk.edu/k12.html
  • Linda Sheffields Web Pages
  • Resources for Teachers - www.nku.edu/mathed/tr.ht
  • Resources for PreK-grade 12 students -

Math Competitions
  • American Mathematics Competitions (AMC) -
    www.unl.edu/amc The purpose of the AMC is to
    increase interest in mathematics and to develop
    problem solving ability through a friendly
    competition. MATHCOUNTS - mathcounts.org/
  • MATHCOUNTS is a national program for competition
    in mathematics for 7th and 8th graders. School
    teams use materials provided by MATHCOUNTS to
    practice throughout the fall.
  • Mathematics Olympiads for Elementary and Middle
    Schools - www.moems.org/These are contest
    problems that are administered 5 times during the
    school year within the school. The top few scores
    are sent as the "team score" as part of the
    competition. The problems are challenging and

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  • To use Q Matrix
  • 1. Identify the level of thinking you wish your
    question to elicit and select word pairs to match
    your instructional focus
  • knowledge word pairs upper left portion of
  • evaluation word pairs lower right
  • As you move in any direction from the What is?
    you are moving toward questions which require
    more in-depth thinking

  • To use Q Matrix
  • 1. Identify the level of thinking you wish your
    question to elicit and select word pairs to match
    your instructional focus
  • knowledge word pairs upper left portion of
  • evaluation word pairs lower right
  • As you move in any direction from the What is?
    you are moving toward questions which require
    more in-depth thinking

  • 2. Choose any word pair
  • -use this word pair as the first two words in
  • your question followed by the appropriate
  • Example Which might
  • Which might be the best way to solve this
  • OR
  • -embed the words in your question
  • Example Of all the solutions weve
    discussed, which do you do feel might provide the
    best solution to this problem?

  • 3. The horizontal items represent the subject of
    the question (event, situation, choice, person,
    reason, means)
  • 4. The vertical items represent the process
    (present, past, possibility, probability,
    prediction, imagination)

  • Quadrants
  • I Asks for facts
  • II Asks for comparisons, explanations,
  • III Asks for predictions and possibilities
  • IV Asks for speculations, probabilities and

Argument Mapping Tool
  • Tutorial 1 - Simple Arguments Introduces simple
    arguments, the most basic units of reasoning.
    Discusses various kinds, their parts, and how to
    map them.
  • Tutorial 2 - Simple Argument Structure
  • Looks in more detail at the internal structure of
    simple arguments. Gives simple guidelines for
    identifying assumptions and ensuring that the
    whole thing hangs together properly.
  • Tutorial 3 - Multi-Reason Arguments
  • Studies arguments in which more than one reason
    or objection bear upon a single claim.  Discusses
    some common mistakes in mapping such arguments.
  • Tutorial 4 - Multi-Layer Arguments
  • In multi-layer arguments, reasons or objections
    are themselves supported or opposed by further
    arguments.  This tutorial covers the main kinds
    of multi-layer arguments, how to map them, and
    how to avoid some common errors.
  • Tutorial 5 - Inference Objections
  • Inference objections are a kind of multi-layer
    argument, and mapping them is particularly
    challenging.  This tutorial shows how to map
    inference objections as objections to hidden
  • Tutorial 6 - Macrostructure
  • The "macrostructure" is the structure of complex
    arguments on a large scale.  This tutorial covers
    some fundamental principles for producing maps of
    well-structured complex arguments.
  • By the end of these tutorials, if you have done
    the exercises properly, you should have acquired
    basic skills of argument mapping, and have a
    deeper understanding of the nature of reasoning
    and argumentation.
  • http//austhink.com/reason/tutorialhttp//austhink

Explora Tree
  • http//www.exploratree.org.uk/
  • Free online library of thinking guides
  • Print them out or fill in and complete your
    project on the exploratree website
  • Build up a personal portfolio of useful thinking
  • Change or customise them using images, text and

Differentiation through Creativity
According to Torrance,
  • When a person has no learned or practiced
    solution to a problem, some degree of creativity
    is required


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1. Use Humor
  • Go to http//www.cagle.com
  • Cartoons are changed frequently

  • Another tack is to have participants draw
    cartoons to represent current or historical
    events, OR

  • Or, create a cartoon to represent the other side
    of the issue. Here, participants could discuss
    the issues on both sides of a controversy, such
    as the Patriot Act, and draw an editorial cartoon
    in answer to this one.

  • Cartoons can be used to teach science, art,
    journalism, English, and research, too.

2. Use an encounter experience
  • EXAMPLE Introducing a Lesson on Native Americans
  • What kind of Native American are you?
  • What do you see? Hear? Smell? Taste? Feel?
  • You are away from the rest of your people. Why?
  • You hear voices of the enemy near. Who are they?
    What are they doing?
  • What have you learned about? What would you like
    to know?
  • Question of
  • Identity
  • Awareness
  • Isolation
  • Risk or danger
  • Wisdom

3. Inkblot
  • Groups of 4 with inkblot or paint blot on paper
  • Fold the paper in half horizontally and
  • 2. Then put a few drops of paint, refold paper
    and press to smear.
  • 3. Number the 4 sides and brainstorm for 2-3
    minutes on each side what the blob could be.

Inkblot Applications
  • Creativity--discuss who had the most
  • Responses (fluency),
  • Unusual response (originality),
  • Detailed response (elaboration),
  • Categories of responses (flexibility)
  • Recognize other attributes of creativity such as
    humor, emotion, fantasy, etc.
  • Geometry--Use graph paper make a polygon out of
    the figure figure (or estimate) the area
  • Art--Have students choose to draw or paint
    details to complete the picture
  • Language Arts/English/Foreign Language--Have
    students write stories about the picture

4. Movement
  • Familiarize students with Rube Goldberg machines
    like the one below.

  • Machine
  • A volunteer makes a repeated machine-like
  • one by one others add a motion to the machine.
  • remaining students are asked to brainstorm what
    the machine is and how the various movements work
  • Gives students an opportunity to express
    creativity through movement.

5.Brainstorming and Just Suppose
  • Principles
  • 1. Deferment of judgment.
  • 2. Quantity breeds quality.
  • Rules
  • 1. Criticism is ruled out.
  • 2. Free wheeling is welcomed.
  • 3. Quantity is wanted.
  • 4. Combination and improvement are
  • Economics Example Just suppose you won the
    lottery, what would you do with the money? What
    might some effects be?
  • Science/Social Studies Just suppose we could
    cure all diseases. What would be the effect?
  • Mathematics Just suppose you could invent your
    own symbol system for mathematics. What might be
    some symbols you would create, and what would
    they mean?

6. Scamper (Eberle, 1971)
  • Substitute
  • Combine
  • Adapt
  • Magnify or minify
  • Put to other uses
  • Eliminate
  • Reverse or rearrange

What are some ways that we could make zoos
better for animals?
  • Substitute--group animals and vegetation together
    as in the wild and let them hunt or forage for
    their own food
  • Combine--have the birds from the aviary in the
    same place with the monkeys
  • Adapt--use climate control domes and vegetation
    to simulate their natural environment
  • Magnify or minify--make zoos larger with more
    space breed smaller versions of animals so that
    the space seems larger

What are some ways that we could make zoos
better for animals? (Contd)
  • Put to other uses--give the animals activities to
    occupy them
  • Eliminate--remove as many unnatural sensations as
    possible--sights, sounds, smells, foods,
    textures, etc.
  • Reverse or rearrange-- put the people in
    enclosures and let the animals run free

  • Language Arts How might you use the SCAMPER
    techniques to change a familiar story?
  • Social Studies How might you apply the ideas of
    SCAMPER to create a new society?
  • Mathematics Can you write word problems using
    the ideas of SCAMPER?
  • Science How can you design a new experiment
    using the principles of SCAMPER.

7. Metaphorical Thinking
  • Life is like...
  • ...a jigsaw puzzle but you don't have the
    picture on the front of the box to know what it's
    supposed to look like. Sometimes you're not even
    sure you have all the pieces.
  • ...riding an elevator. It has a lot of ups and
    downs and someone is always pushing your buttons.
    Sometimes you get the shaft, but what really
    bothers you are the jerks."
  • What do you think life is like?

8. Forced Fit
  • If you cant think of a comparison, try choosing
    anything and figuring out how they are alike.
  • Life is like a book. How?
  • What is a garden like? How?
  • How are schools like businesses? prisons?
    gardens? Zoos?
  • Play a game with two teams each must think of a
    problem and an unlikely object with which to
    solve it. If the solvers can think of a
    reasonable solution using the object, they get a
    point. Otherwise those presenting the problem get
    the point. Take turns.
  • Example How could you use a spoon to get
    children to clean their rooms?
  • (If anyone can help solve this problem, with or
    without a spoon, all of us parents will be
    eternally grateful!

The Parable of the Sad Bear
An Allegory On The School Experience of A
Creative Child
  • Once upon a time there was a very sad bear who
    was kept in a very small cage at the town zoo.
    When he wasnt eating or sleeping, he spent his
    time pacing--8 paces forward and 8 paces back.
    Again and again he paced the cage.

  • One day the zoo keeper said, Its sad to see
    this bear pacing back and forth. I shall build
    him a great, open space where he can run and
    play. So he did.

As the space was completed, great waves of
anticipation charged through the town.
Finally the magic day came to move the bear to
his headquarters. The mayor gave a speech as the
children screamed with excitement.
The town band played loudly as the great beast
was moved to his new large space. Everyone
watched as the bear looked to his left, then to
his right and began to move
1 step, 2, 5, 8 paces forward, and 8 back again.
To the shocked amazement of the crowd, he paced
the parameters of his old, very small cage.
Minds, like bears, grow accustomed to narrow
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