2015-16 Math Intervention Webinar Series Resources

Session 4: Use Visual Representations

GENERAL RESOURCES

Achieve the Core.

National Councilof Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.

National Research Council. (2001). Adding it up. Division of Behavioral and Social Sciences and Education, Center for Education & Mathematics Learning Study Committee (authors).Findell, B., Jane Swafford, J., & Kilpatrick, J. Editors. Division of Behavioral and Social Sciences and Education. Washington, DC: The National Academies

Press.

National Research Council. (2005). How Students Learn: History, Mathematics, and Science in the Classroom. Committee on How People Learn, A Targeted Report for Teachers. M.S. Donovan and J.D. Bransford, Editors. Division of Behavioral and Social Sciences and Education. Washington, DC: The National Academies

Press.

United States Math Recovery Council.

Universal Design for Learning: Guiding principles

UW-Milwaukee School of Education Core Math Partnership / Dr. DeAnn Huinker, Project Directo

What Works Clearinghouse Practice Guides (U.S. Department of EducationInstitute of Education Sciences)

  • Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students
  • Teaching Math to Young Children
  • Improving Mathematical Problem Solving in Grades 4 Through 8
  • Developing Effective Fractions Instruction
  • Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools
  • Encouraging Girls in Math and Science

USING VISUAL REPRESENTATIONS TO SUPPORT CONTENT LEARNING – TEACHER RESOURCES

The Access Center. Concrete-representational-abstract instructional approach.

Boaler, J. (2015). Visual math improves math performance.

Center for Implementing Technology in Education.Learning mathematics with virtual manipulatives.

Echevarria, J., Vogt, M., & Short, D. J. (2010). Making content comprehensible for elementary English Learners The SIOP model. New York, NY: Pearson.​

Goldenberg, E.P., Mark, J., Kang, J., Fries, M. Carter, C., & Cordner, T. (2015). Making sense of algebra: Developing students' mathematical habits of mind. Portsmouth, NH:Heinemann Publishing.

Huinker, D. (2015). Representational competence: A renewed focus for classroom practice in mathematics.Wisconsin Teachers of Mathematics, (67)2, 4-8. article.pdf

Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel,B. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC:National Center for Education Evaluation and Regional Assistance, Institute ofEducation Sciences, U.S. Department of Education. Retrieved from

Kiuhara, S., & Witzel, B. (2014). Focus on inclusive education: Math literacy strategies for students with learning difficulties.Childhood Education, 90(3), 234-238.

LD Online. Using visual representations in mathematics.

LD@School. Using the concrete-representational-abstract approach to investigate adding and subtracting integers.

Marshall, A., Superfine, A., & Canty, R. (2010). Star students make connections: Discover strategies to engage young math students in competently using multiple representations.Teaching Children Mathematics, (17)1, 39-47.

Stancampiano, J. (2013). Benefits of Visual Facilitation in the classroom.

Marshall, A. Superfine, A.C. & Canty, R. (August, 2010). Star students make connections: Discover strategies to engage young students in competently using multiple representations. Teaching Children Mathematics. Reston, VA: NCTM, 39-47.

MathVIDS.Concrete - Representational – AbstractSequence of Instruction.

Mind Research: Teaching math visually

Moschkovich. J. (2013). Understanding language: Principles for mathematic instruction for English Language Learners.

Open University (UK): Using visualisation in maths teaching.

PowerUp Visual representation teaching guide

TED Talk: Teaching without words.

Tripathi, P. N. (2008). Mathematical understanding through multiple representations. Mathematics Teaching In The Middle School. 12: 438-445

University of Kansas Special Connections: Concrete – Representational – Abstract Instruction

Witzel, B. (2005).Using CRA to teach algebra to students with math difficulties in inclusive settings. Learning Disabilities: A Contemporary Journal 3(2), 49–60.

Wright, R., Martland, J, & Stafford, A. (2006). Early numeracy: Assessment for teaching and intervention (Math Recovery). Thousand Oaks, CA: SAGE Publishing.

Wright, R. & Stanger, G. (2006). Teaching number: Advancing children's skills and strategies (Math Recovery). Thousand Oaks, CA: SAGE Publishing.

Zorfass, J., & Han, A. (2014). Using Visual Representation in Mathematics.

ONLINE VISUAL REPRESENTATION RESOURCES TO USE WITH STUDENTS

Early Learning Apps using visual representations: Friends of Ten, Ladybird Maths, and Count On It

Annenberg Learner Interactives:

Educational Development CenterSolve Mevisual algebra puzzles:

Harcourt Math multimedia glossary:

NCTM Illuminations:

NRICH Mathematics:

Open source interactiveHS math textbooks.

YouCubed tasks using visual representations:

OUTCOME STUDIES SUPPORTING THE USE OF VISUAL REPRESENTATIONS

The Access Center. Concrete-representational-abstract instructional approach.

Center for Implementing Technology in Education.Learning mathematics with virtual manipulatives.

Educational Development CenterTransition to Algebra series findings.

Mind Research: Outcomes for students using Spatial-Temporal (ST) Math

Park, J., & Brannon, E. (2013).Training the approximate number system improves math proficiency.Association for Psychological Science, 1–7.

United States Math Recovery Council Research.

What Works Clearinghouse Practice Guides (U.S. Department of EducationInstitute of Education Sciences)

  • Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students
  • Teaching Math to Young Children
  • Improving Mathematical Problem Solving in Grades 4 Through 8
  • Developing Effective Fractions Instruction
  • Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools
  • Encouraging Girls in Math and Science

Witzel, B. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from

DISCOURSE STRATEGIESTO USE WITH VISUAL REPRESENTATIONS

Boaler, J. Number Talks.

Chapin, S., O’Connor, C., & Anderson, N. C. (2013). Classroom discussions in math: A teacher’s guide for using talk moves to support the Common Core and more. Sausalito, CA: Math Solutions.

Humphreys, C. & Parker, R. (2015). Making number talks matter: Developing mathematical practices and deepening understanding, grades 4-10.Portland, ME: Stenhouse Publishing.

Parrish, S. (2014). Number talks: Helping children build mental math and computation strategies, grades K 5, updated with Common Core connections. Sausalito, CA: Math Solutions.

Schwan Smith, M. & Stein, M. K. (2011).5 practices for orchestrating productive mathematics discussions.Reston, VA: NCTM.

Wright, R. & Ellemor-Collins, D. (2012). Developing number knowledge: Assessment,teaching and intervention with 7-11 year olds (Math Recovery). Thousand Oaks, CA: SAGE Publishing.

Wright, R., Stanger, G., Stafford, A. & Martland, J. (2014). Teaching number in the classroom with 4-8 year olds (Math Recovery). Thousand Oaks, CA: SAGE Publishing.

Note that these resources are provided for informational purposes only. The Wisconsin RtI Center does not recommended or endorse any specific products or programs. 1