Components of Effective Mathematics Instruction (page 2)

By — LD Online
Updated on Feb 25, 2011

Grade Five and Beyond

In grade five and beyond, general education instruction in math focuses a great deal on advanced concepts and reasoning (e.g., what a variable or a function is), learning of complex computational algorithms (e.g., those involved in adding and subtracting fractions and decimals), and more difficult kinds of verbal problem-solving (e.g., problems with multiple steps). By grade five, automatic recall of number facts is well-developed in most normally-achieving youngsters. However, youngsters with math disabilities often continue to struggle with math skills far below grade expectations, including not only automatic recall, but also many computational algorithms and math concepts. A thorough evaluation that assesses a range of important math skills is essential, because children can have different strengths and weaknesses even within the domain of math, and knowing the pattern of strengths and weaknesses is central to instructional planning. For instance, a child who has good conceptual abilities but whose difficulties center on automatic recall and computation will need a different kind of instructional program than will one whose main difficulties are conceptual in nature.

As children advance into middle and high school, tracking of students into different levels of math (e.g., an accelerated track, a grade-level track, and a remedial track) is typical. Also, science courses begin to draw more heavily on mathematics skills, and students with math disabilities may begin to experience more difficulties in science. Providing intensive remediation of basic math skills to students who need it remains essential in these grades, not only to help students acquire the skills needed for everyday life, but also because math achievement serves as a gateway for higher education and for many occupations.

Examples of Sources

Peer-reviewed journal articles:

Carnine, D. (1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130-141.

Cawley, J., Parmar, R., Foley, T., Salmon, S., & Roy, S. (2001). Arithmetic performance of students: Implications for standards and programming. Exceptional Children, 67, 311-330.

Fuchs, L., & Fuchs, D. (2001). Principles for the prevention and intervention of mathematics difficulties. Learning Disabilities Research & Practice, 16, 85-95.

Maccini, P., & Gagnon, J. (2002). Perceptions and application of NCTM Standards by special and general education teachers. Exceptional Children, 68, 325-344.

Other helpful sources:

Curriculum and evaluation standards for school mathematics. (2000). Reston, VA: National Council for Teachers of Mathematics.

Fuchs, L., & Fuchs, D. (2003). Enhancing the mathematical problem solving of students with mathematics disabilities. In H. L. Swanson, K. R. Harris, & S. Graham (Eds.), Handbook of Learning Disabilities (pp. 306-322). New York: Guilford.

Geary, D. C. (1996). Children's mathematical development. Washington, DC: American Psychological Association.

Rivera, D. P. (1998). Mathematics education for students with learning disabilities: Theory to practice. Austin, TX: Pro-Ed.

Stein, M., Silbert, J., & Carnine, D. (1997). Designing effective mathematics instruction: A direct instruction approach (3rd edition). Upper Saddle River, NJ: Merrill.

Stevenson, H.W. & Stigler, J.W. (1992). The learning gap. New York, NY: Summit Books.

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