Article in the journal "Perspectives on Languages and Literacy"

MATH EDUCATION FOR CHIlDREN WITh LANGUAGE-BASED LEARNING DIFFICULTIES (LBLD)

by Gayle Porter Lewis and Stephen Wilkins

For decades, responsible structured language educators have sought to apply that which works in reading instruction for the benefit of students’ math learning. To an extent, adherence to the similarities of teaching the abstract symbols of language and the abstract symbols of mathematics makes perfect sense. In other ways, the prin- ciples of multisensory structured language have been a false guide. This article seeks to explain why math educa- tion for students with LBLD should be redesigned.

The principles of a structured approach to teaching children to read, such as Orton Gillingham, provide significant insights into how to teach these same children to succeed in math. For example, instruction should be structured, systematic, sequential, multisensory, and properly aligned with what a child knows at the point of instruction. Further, the concept of diagnostic and prescriptive instruction is ideal for children in the early stages of learning arithmetic computation.

Teachers who base today’s lesson on a careful analysis of how the student performed yesterday are on the right track. Formulative assessment is essential in determining the pacing and movement of a successful math program. Similarly, teachers who are well-schooled in multisensory teaching know that hands-on materials that employ all the senses are likely to be far more effective than lesson after lesson from a prescribed and scripted textbook.

However, there is one major red herring within the principles of systematic phonics instruction that has trapped language-trained teachers and tutors into a less promising approach to helping children with LBLD learn math. Whereas the principles of Orton-Gillingham style reading instruction insist on a deductive approach (in which each sound-symbol connection is taught explicitly), math instruction should be largely an inductive activity in which children seek meaning in numbers. That is, teachers and tutors drill children to learn sound-symbol associa- tions. This approach is appropriate because there is no intrinsic meaning in a symbolic representation of a sound such as /b/. The opposite is true in the symbolic representa- tions of quantity, which we call numbers. Children cannot really explore the meaning of a phoneme; it needs to be taught directly. However, children can easily discover the relationship among numbers and develop their own meaningful schema. There is a strong meaning-symbol association with numbers.

Nancy Krasa and Sara Shunkwiler’s book, Number Sense and Number Nonsense, tracks the research and logic behind this fundamental difference. While it makes perfect sense to work with phonogram cards to cement sound-symbol relationships in children with LBLD, an analogous drill with math facts is an unwise way to begin math instruction. rather, teachers who support their

students’ pursuit of understanding the relationships among numbers are providing the most meaningful instruction; from the base of number sense, children with significant LBLD, memory, and processing speed issues will become better at computation.

Three small independent schools (Churchill School in St. Louis, Missouri; Sally Borden School in Dartmouth, Massachusetts; and Carroll School in Lincoln, Massachu- setts) are beta testing a different approach to math instruc- tion for children with LBLD. The program includes three essential components that are significantly different from a textbook approach:

1) Development of number sense—students work through a program that helps them induce meaning from the quantity-symbol associations in mathe- matics through visual-spatial and hands-on experiences;

2) Computational fluency—children move from the physical representations of numbers systematically until the symbol representations make enough sense to promote computational speed and accuracy; and

3) Thinking—the program focuses largely on develop- ing logical reasoning skills in children so that they see themselves as problem solvers in mathematics, rather than followers of rote algorithms and prescribed procedures.

The prospect of harnessing the strengths in children with LBLD to learn mathematics is the inherent concept of this approach to math instruction. Children who already see patterns and solutions where typical brains don’t are far more likely to succeed in a math program that encourages them to create meaning rather than to memorize and follow textbook prescriptions.

References

Krasa, K., & Shunkwiler, S. (2009). Number sense and number nonsense: Understanding the challenges of learning math. Baltimore: Paul H. Brookes.

Gayle Porter Lewis is the Math Department Chair at the Carroll School in Lincoln, Massachusetts. As a lifelong math educator, she has pursued curricula and approaches that hold the best opportunity for students with language based learning difficulties to be successful math students.

Stephen Wilkins is the Head of Carroll School in Lincoln, Massachusetts. Prior to his current position, he was Head of Proctor Academy in Andover, New Hampshire and Director of Jemicy School in Owings Mills, Maryland. Steve holds a master’s in education from the Harvard Graduate School of Education. He is a lecturer in the master’s in education program at Lesely University in Cambridge, Massachusetts.

The International Dyslexia Association Perspectives on Language and Literacy Summer 2010 13