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 Problems Create 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 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) 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.

A 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.” (National Center on Accessing The General Curriculum, 2003)

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 Universal Design For Learning (What Is Universal Design for Learning, 2007)

Brain Networks & Learning Recognition (What?) Identifying Categorizing Affective (Why?) Engaging Motivating Challenging Interesting Strategic (How?) Planning Performing Organizing Expressing (What Is Universal Design for Learning, 2007)

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 (What Is Universal Design for Learning, 2007)

Graphic 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)

Depict Relationships Categorize & Organize Information Visual & Graphic Displays Title Graphic Organizers Flexible Learning Task

ImprovementResearchers 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 Organizer Implementation

Flexible Methods of Expression Graphic Organizers & UDL Flexible Methods of Presentation Flexible Methods of Engagement Part To Whole Relations Variety Of Formats Visualize Patterns Supports Prior Knowledge Alternative To Linear Text Supported Practice Choice Of Tools Different Media Varying Levels Of Challenge

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?

(Coleman 2006)

Text 2 Text 3 Representing & Solving Math Problems Students With Disabilities Struggle With Representing & Solving Math Problems Identifying Key Information Connecting Relationships Strategically Approaching Math Problems Math Procedures & Fluency How Can Graphic Organizers Help? (Maccini & Gagnon, 2005)

Good Problem Solvers Estimate Hypothesize Text 1 Read For Understanding Compute & Check Paraphrase Visualize What’s Really Involved? (Montague, 2004)

Common Types Of Math Graphic Organizers Hierarchical Sequence Chart Sequence Compare & Contrast (Venn Diagram) What are we already using? (Maccini & Gagnon, 2005)

Change Problem Group Problem Compare Problem Teaching students to classify word problems as one of 3 types can help them comprehend and plan. Is there a better way? (Jitendra, 2002)

Change Problem A beginning set is identified.A beginning set is identified. A change occursA change occurs The ending set is what exists after the change.The ending set is what exists after the change. Is there a better way? (Jitendra, 2002)

Your Text here The Beginning Set Caroline is 8 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 7 th Grade Released Test 2006 What has to happen to Brittany’s age to change it to Caroline’s age? X 4 Caroline’s age is 4 times Brittany’s age?

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 Problem Activity

VDOE 7 th Grade Released Test 2006 Change Problem Activity

VDOE 7 th Grade Released Test 2006

Group Problem Group set problems involve understanding the part to whole relationship.Group set problems involve understanding the part to whole relationship. The whole is equal to the sum of its parts.The whole is equal to the sum of its parts. Is there a better way? (Jitendra, 2002)

A farmer has 6 cartons of specialty eggs for sale. Each carton contains 12 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 6 th Grade Released Test /3 of 72 Or 24 2/3 of 72 Or 48 Or 72 Eggs Is the information about other eggs nice to know or necessary?

The Concrete Group Rotates To The Representational Station Group Problem Activity The Abstract Group Rotates To The Concrete Station The Representational Group Rotates To The Abstract Station

Group Problem Activity VDOE 6 th Grade Released Test 2007

Group Problem Activity VDOE 6 th 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 Problem Focus on 2 setsFocus on 2 sets Each has smaller or larger valueEach has smaller or larger value Each has the same unit of measureEach has the same unit of measure Is there a better way? (Jitendra, 2002)

1/8 inch = 1 foot Actual Patio Length Compared Set Difference Set Referent Set 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 length on the blueprint? VDOE 8 th Grade Released Test 2007 Blueprint Patio Length 14 feet Scale 1 3/4 inches What do you have to do with the actual patio length and scale to get the blueprint length?

The Concrete Group Rotates To The Abstract Station Compare Problem Activity The Abstract Group Rotates To The Representational Station The Representational Group Rotates To The Concrete Station

Compare Problem Activity VDOE 8 th Grade Released Test 2007

Compare Problem Activity VDOE 8 th Grade Released Test 2007

Sources Cited Coleman, D. (2006). The Impact of Graphic Organizers on the Instruction of Solving Word Problems. In An Action Research Project (Presented to the Shawnee Mission Board of Education, pp. 1-8). Shawnee Mission, KS: Brookridge Elementary School. Retrieved May 3, 2008, from Shawnee Mission School District Web site: Jitendra, A. (2002). Teaching Children Math Problem-Solving Through Graphic Representations. Teaching Exceptional Children, 34(4), Retrieved May 1, 2008, from Maccini, P. & Gagnon, J. (2005). Math Graphic Organizers for Students With Disabilities. In Ideas That Work U.S. Office of Special Education Programs (American Institute For Research, pp. 1-8). Washington, DC: U.S. Department of Education. Retrieved May 3, 2008, from The Access Center: Improving Outcomes for All Students K-8 Web site: Montague, M. (2005). Math Problem Solving for Upper Elementary Students With Disabilities. In Ideas That Work U.S. Office of Special Education Programs (American Institute for Research, pp. 1-13). Washington, D.C: U.S. Department of Education. Retrieved May 4, 2008, from The Access Center Improving Outcomes for All Students K-8 Web site: National Center on Accessing the General Curriculum. (2003). Graphic Organizers and Implications for Universal Design for Learning: Curriculum Enhancement Report. In Hall, T. & Strangman, N. (Ed.), Ideas That Work (NS GOUDL.5, pp. 2-27). Washington, DC: U.S. Department of Education. Retrieved May 2, 2008, from The Access Center: Improving Outcomes for All Students K-8 Web site: ​ / ​ What is Universal Design for Learning? (2007). Retrieved May 1, 2008, from Center for Applied Special Technology Web site: