Teaching Abstract Concepts to Concrete Thinkers

Students with autism are, generally, concrete thinkers, which can make teaching math skills difficult.  As math work becomes more abstract, how can educators help these students build problem solving and application skills?  Jo Boaler, Professor of Mathematics Education at Stanford University, reports that brain evidence supports the use of visual approaches in mathematics and explains that when these approaches are used “mathematics changes for them, and they are given access to deep and new understandings” (Boaler, Chen, Williams, & Cordero, 2016)

Seeing is Understanding

Using visual representations helps give concrete structure to abstract concepts and, therefore, is a beneficial practice in math instruction for all students, particularly those with autism.  Research has shown that students who use concrete materials and visual representations develop more mathematical understandings and better apply these ideas to life situations (Harrison & Harrison, 1986; Fuchs, et al., 2008; Witzel, 2005).

To Learn More

Information on how to carry out the use of visual representations, as well as solutions to potential roadblocks, is available in the Institute of Education Science’s practice guide, Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools.

References

Boaler, J., Chen, L., Williams, C., & Cordero, M. (2016). Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning. Journal of Applied & Computational Mathematics,05(05).

Fuchs, L. S., Powell, S. R., Hamlett, C. L., Fuchs, D., Cirino, P. T., & Fletcher, J. M. (2008). Remediating Computational Deficits at Third Grade: A Randomized Field Trial. Journal of Research on Educational Effectiveness,1(1), 2-32.

Gersten, R. M. (2009). Assisting students struggling with mathematics: Response to intervention (RtI) for elementary and middle schools. Washington, D.C.: U.S. Dept. of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance.

Harrison, M., & Harrison, B. (1986). Developing numeration concepts and skills. Arithmetic Teacher,33, 1-21.

Witzel, B. S. (2005). Using CRA to teach algebra to students with math difficulties in inclusive settings [Abstract]. Learning Disabilities—A Contemporary Journal,32(2), 49-60.