1

Fold the gray piece of cardstock in half.

2

•Write your name in all capital letters if you were a strong math student in school.•Write your name in all lowercase letters if you struggled with math in school.

3

If you had to choose 10 math problems to complete, would you choose computation problems or word problems?•Computation Create a border around your name using numbers.•Word ProblemsCreate a border around your name using letters.

4

On the other side of your name tent list math strategies that you were taught to use when you were in school.

Name Tent ActivityName Tent Activity

Taking The Puzzle Out Of Problem Solving

Taking The Puzzle Out Of Problem Solving

Word Problem Strategies & Universal Design For Learning

Word Problem Strategies & Universal Design For Learning

Universal Design for Learning (UDL)Universal Design for Learning (UDL)

• A theory of learning and teaching based on brain research techniques

• Resists a one-size-fits-all approach to education

• Teachers, educators, and materials should effectively respond to the individual differences inherent within a learning environment.

http://en.wikipedia.org/w/index.php?title=Special:Cite&page=Universal_Design_for_Learning&id=193068846

A Matter Of Equal AccessA Matter Of Equal Access

• “A UDL curriculum takes on the burden of adaptation so that the student doesn’t have to, minimizing barriers and maximizing access to both information and learning.” (Stangman, Hall, Meyer 2003)

http://www.k8accesscenter.org/training_resources/udl/GraphicOrganizersHTML.asp

a blueprint for creating flexible goals, methods, materials, and

assessments that accommodate learner

differences

Multiple means of

representation

Multiple means of engagement

Multiple means of action and expression

Three Basic Principles

http://www.cast.org/research/udl/index.htmlUniversal Design For LearningUniversal Design For Learning

Brain Networks&

Learning

Recognition(What?)

•Identifying•Categorizing

Affective(Why?)

•Engaging•Motivating•Challenging•Interesting

Strategic(How?)

•Planning•Performing•Organizing•Expressing

http://www.cast.org/research/udl/index.html

Strategic

Representation

Give learners a variety of ways to gather facts and information.

Give learners a variety of ways to demonstrate their knowledge and skills.

Give learners a variety of ways to connect to learning so that individual learning styles are honored.

Action &Expression

Engagement

Recognition

Affective

UDL

Principles

Brain

Networks

http://www.cast.org/research/udl/index.html

Graphic OrganizersGraphic Organizers

• “A graphic organizer is a visual and graphic display that depicts the relationships between facts, terms, and or ideas within a learning task. “ (Stangman, Hall, Meyer 2003)

http://www.k8accesscenter.org/training_resources/udl/GraphicOrganizersHTML.asp

Depict RelationshipsDepict Relationships Categorize &

Organize Information

Categorize &Organize Information

Visual & Graphic DisplaysVisual & Graphic Displays

TitleTitleGraphic

Organizers

FlexibleFlexible

Learning TaskLearning Task

http://www.k8accesscenter.org/training_resources/udl/GraphicOrganizersHTML.asp

Improvement Researchers

Stanford Diagnostic

Reading Test (Boyle & Weishaar, 1997)

Comprehension

questions

(Boyle & Weishaar, 1997; Darch et al., 1986; Gardill & Jitendra, 1999; Idol & Croll, 1987;Sinatra et al. 1984)

Concept

acquisition test (Bulgren et al., 1988)

Teacher-made

tests (Bulgren et al., 1988; Willerman & Mac Harg, 1991)

Written

summaries (Gallego, Duran & Scanlon,

1989)

Student Performance Results Following Graphic Student Performance Results Following Graphic Organizer ImplementationOrganizer Implementation

http://www.k8accesscenter.org/training_resources/udl/GraphicOrganizersHTML.asp

Flexible Flexible Methods of Methods of ExpressionExpression

Graphic Organizers & UDLGraphic Organizers & UDLhttp://www.k8accesscenter.org/training_resources/udl/GraphicOrganizersHTML.asp

Flexible Flexible Methods of Methods of

PresentationPresentation

Flexible Flexible Methods of Methods of

EngagementEngagement

Part To Whole

Relations

VarietyOf

Formats

VisualizePatterns

SupportsPrior

Knowledge

AlternativeTo Linear

Text

SupportedPractice

ChoiceOf

Tools

DifferentMedia

VaryingLevels OfChallenge

10 Minute Break

During the break think about your current use of graphic organizers.

Do you use them for math instruction?

Do you think they could be used to improve student outcomes with math word problems?

20

50

20

50

10

40

030

0

20

40

60

80

100

1 2 3 4

Graphic Organizer Impact On 4 Special Education Students'

Math Scores

Increase

PreTest

(Coleman 2006)

Text 2

Text 3

Representing& Solving Math

Problems

Students With Disabilities Students With Disabilities Struggle WithStruggle With

Representing & Solving

Math Problems

IdentifyingKey

Information

ConnectingRelationships

StrategicallyApproaching

MathProblems

MathProcedures

&Fluency

How Can Graphic Organizers Help?How Can Graphic Organizers Help?(Maccini & Gagnon, 2005)

Good Good Problem Problem SolversSolvers

Estimate

Hypothesize

Text 1 Read For Understanding

Compute&Check

Paraphrase

Visualize

What’s Really Involved?What’s Really Involved?(Montague, 2004)

Common Types Of Math Graphic

Organizers

Hierarchical

Sequence Chart

SequenceCompare &

Contrast(Venn

Diagram)

What are we already using?

1

2

3

http://www.k8accesscenter.org/training_resources/mathgraphicorganizers.asp

Change Set

Group Set

Compare Set

Teaching Teaching students to students to classify word classify word problems as problems as one of 3 one of 3 types can types can help them help them comprehend comprehend and plan.and plan.

Is there a better way?(Jitendra, 2002)

Change Set

•A A beginning beginning set is set is identified.identified.•A change A change occursoccurs•The ending The ending set is what set is what exists after exists after the change.the change.

Is there a better way?(Jitendra, 2002)

Your Text here

The Beginning Set

Caroline is8 years old

2(Brittany’s

Age ¼ Caroline’s

Age)

The Ending Set

The Change Set

Brittany is ¼ Caroline’s age. If Brittany is 2 years old, what is Caroline’s age? VDOE 7th Grade

Released Test 2006

What has to happen to

Brittany’s age to change it to

Caroline’s age?

X 4Caroline’s age is 4 times Brittany’s

age?

Change Set ActivityChange Set Activity

• Regroup by the symbols on the sticker on the back of your folder.– Concrete Group

• Use manipulatives to illustrate the problem on the change set work mat.

– Representational / Semi-Concrete Group• Illustrate the problem with drawings on the

change set work mat.– Abstract Group

• Use number symbols to illustrate the problem on the change set work mat.

Change Set ActivityChange Set Activity VDOE 7th Grade Released Test 2006

Change Set ActivityChange Set Activity VDOE 7th Grade Released Test 2006

Group Set

•Group set Group set problems problems involve involve understanding understanding the part to the part to whole whole relationship.relationship.•The whole is The whole is equal to the equal to the sum of its parts.sum of its parts.

Is there a better way?(Jitendra, 2002)

A farmer has 6 cartons of specialty eggs for sale. Each carton contains12 eggs. If 2/3 of the eggs are brown eggs, what is the total number of brown eggs he has for sale?

Smaller Sets

Larger Set

6 Cartons Of 12 Eggs

Brown Eggs

Other Eggs

VDOE 6th Grade Released Test 2007

1/3 of 72

Or24

2/3 of 72

Or48

Or

72 Eggs

Is the information about other eggs nice to know or

necessary?

The Concrete The Concrete Group Rotates To Group Rotates To

The The RepresentationalRepresentational

StationStation

Group Set Activity

The Abstract The Abstract Group Rotates To Group Rotates To

The Concrete The Concrete StationStation

The The Representational Representational Group Rotates To Group Rotates To

The Abstract The Abstract StationStation

Group Set Activity VDOE 6th Grade Released Test 2007

Group Set Activity VDOE 6th Grade Released Test 2007

10 Minute Break

During the break think about the possible ways to differentiate math instruction using graphic organizers.

Do all students need to use math graphic organizers in the same way?

Compare Set

•Focus on 2 Focus on 2 setssets•Each has Each has smaller or smaller or larger valuelarger value•Each has Each has the same unit the same unit of measureof measure

Is there a better way?(Jitendra, 2002)

1/8 inch = 1 foot

Actual Patio LengthActual Patio Length

ComparedSet

DifferenceSet

ReferentSet

The scale blueprint of a rectangular patio is drawn 1/8 inch to 1 The scale blueprint of a rectangular patio is drawn 1/8 inch to 1 foot. If the patio is 14 feet long, what is the measure of the patio’s foot. If the patio is 14 feet long, what is the measure of the patio’s length on the blueprint?length on the blueprint?

VDOE 8th Grade Released Test 2007

BlueprintPatio Length

BlueprintPatio Length

14 feet

ScaleScale

1 3/4 inches

What do you have to do with the actual patio length and scale

to get the blueprint length?

The Concrete The Concrete Group Rotates To Group Rotates To

The AbstractThe AbstractStationStation

Compare Set Activity

The Abstract The Abstract Group Rotates To Group Rotates To

The The RepresentationalRepresentational

StationStation

The The Representational Representational Group Rotates To Group Rotates To

The Concrete The Concrete StationStation

Compare Set ActivityVDOE 8th Grade Released Test 2007

Compare Set ActivityVDOE 8th Grade Released Test 2007