2015-16 Math Intervention Webinar Series Resources
Session 4: Use Visual Representations
GENERAL RESOURCES
Achieve the Core. http://achievethecore.org/
National Council of 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. http://www.mathrecovery.org
Universal Design for Learning: Guiding principles
http://www.udlcenter.org/aboutudl/udlguidelines/principle1#principle1_g2
UW-Milwaukee School of Education Core Math Partnership / Dr. DeAnn Huinker, Project Directo
http://uwm.edu/education/research/centers/cmser/core-math
What Works Clearinghouse Practice Guides (U.S. Department of Education & Institute of Education Sciences)
http://ies.ed.gov/ncee/wwc/MathHome.aspx
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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.
http://www.broward.k12.fl.us/studentsupport/ese/PDF/CRAApproachinMath.pdf
Boaler, J. (2015). Visual math improves math performance. https://www.youcubed.org/think-it-up/visual-mathimproves-math-performance
Center for Implementing Technology in Education. Learning mathematics with virtual manipulatives.
http://www.cited.org/index.aspx?page_id=151
Echevarria, J., Vogt, M., & Short, D. J. (2010). Making content comprehensible for elementary English Learners
The SIOP model. New York, NY: Pearson. http://learningstrategieseng491.weebly.com/visual-aids.html
Note that these resources are provided for informational purposes only. The Wisconsin RtI Center does not
recommended or endorse any specific products or programs.
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2015-16 Math Intervention Webinar Series Resources
Session 4: Use Visual Representations
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. http://www.wismath.org/resources/Documents/DHuinker
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 20094060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education
Sciences, U.S. Department of Education. Retrieved from
http://ies.ed.gov/ncee/wwc/publications/practiceguides
Kiuhara, S., & Witzel, B. (2014). Focus on inclusive education: Math literacy strategies for students with learning
difficulties. Childhood Education, 90(3), 234-238. http://dx.doi.org/10.1080/00094056.2014.912067
LD Online. Using visual representations in mathematics. http://www.ldonline.org/article/61885
LD@School. Using the concrete-representational-abstract approach to investigate adding and subtracting
integers. http://ldatschool.ca/wp-content/uploads/2014/07/CRA_integers_final_accessible1.pdf
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, 3947.
Stancampiano, J. (2013). Benefits of Visual Facilitation in the classroom.
https://www.trainingindustry.com/content-development/articles/the-benefits-of-visual-facilitation-in-theclassroom.aspx
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. http://web.njcu.edu/sites/faculty/dbennett/uploads/tcm2010-08-38a_marshall.pdf
MathVIDS. Concrete - Representational – Abstract Sequence of Instruction.
http://fcit.usf.edu/mathvids/strategies/cra.html
Mind Research: Teaching math visually
http://www.mindresearch.org/home
Moschkovich. J. (2013). Understanding language: Principles for mathematic instruction for English Language
Learners. http://tinyurl.com/hbxnw2g
Open University (UK): Using visualisation in maths teaching. http://www.open.edu/openlearn/education/usingvisualisation-maths-teaching/content-section-0h
PowerUp Visual representation teaching guide
http://powerupwhatworks.org/strategy-guide/visual-representations-teach-tech
TED Talk: Teaching without words.
Note that these resources are provided for informational purposes only. The Wisconsin RtI Center does not
recommended or endorse any specific products or programs.
2
2015-16 Math Intervention Webinar Series Resources
Session 4: Use Visual Representations
https://www.youtube.com/watch?v=2VLje8QRrwg
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
http://www.specialconnections.ku.edu/?q=instruction/mathematics/teacher_tools/concrete_to_representation
al_to_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.
http://www.catea.gatech.edu/scitrain/kb/FullText_Articles/Witzel_Using.pdf
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.
http://www.ldonline.org/article/61885/
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: http://www.learner.org/interactives/geometry/index.html
Educational Development Center Solve Me visual algebra puzzles: http://solveme.edc.org
Harcourt Math multimedia glossary: http://www.harcourtschool.com/glossary/math_advantage
NCTM Illuminations: http://illuminations.nctm.org/Default.aspx
NRICH Mathematics: http://nrich.maths.org
Open source interactive HS math textbooks. http://www.mathopenref.com/index.html
YouCubed tasks using visual representations: https://www.youcubed.org/tasks/
OUTCOME STUDIES SUPPORTING THE USE OF VISUAL REPRESENTATIONS
The Access Center. Concrete-representational-abstract instructional approach.
http://www.broward.k12.fl.us/studentsupport/ese/PDF/CRAApproachinMath.pdf
Center for Implementing Technology in Education. Learning mathematics with virtual manipulatives.
http://www.cited.org/index.aspx?page_id=151
Educational Development Center Transition to Algebra series findings.
http://www.heinemann.com/shared/onlineresources/E05750/TTA_Research.pdf
Note that these resources are provided for informational purposes only. The Wisconsin RtI Center does not
recommended or endorse any specific products or programs.
3
2015-16 Math Intervention Webinar Series Resources
Session 4: Use Visual Representations
Mind Research: Outcomes for students using Spatial-Temporal (ST) Math
http://www.mindresearch.org/stmath/
Park, J., & Brannon, E. (2013). Training the approximate number system improves math proficiency. Association
for Psychological Science, 1–7. http://2015.laschool4education.com/wpcontent/uploads/2014/10/PSYS482944.pdf
United States Math Recovery Council Research. http://www.mathrecovery.org/pdfs/how-it-works/MathRecovery-Research-White-Paper.pdf
What Works Clearinghouse Practice Guides (U.S. Department of Education & Institute of Education Sciences)
http://ies.ed.gov/ncee/wwc/MathHome.aspx






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
http://ies.ed.gov/ncee/wwc/publications/practiceguides
DISCOURSE STRATEGIES TO USE WITH VISUAL REPRESENTATIONS
Boaler, J. Number Talks. https://www.youcubed.org/from-stanford-onlines-how-to-learn-math-for-teachersand-parents-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.
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