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Transcript of 1 Fold the gray piece of cardstock in half. 2 Write your name in all capital letters if you were a...
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Fold the gray piece of cardstock in half.
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•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.
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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.
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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