Imagery and Fractions in Students Classified as Learning Disabled

Abstract

This article describes constructivist principles of learning in geometry specific to children's imaginal anticipations in line measurement and the related area of fractions. To assist with this discussion, seven sixth-grade students classified as learning disabled (LD) and receiving some type of special education service for mathematics were individually tested in tasks that investigated their imaginal anticipations of space and their representations of this understanding in the fraction symbol. Additionally, the investigation examined the effectiveness of constructivist teaching techniques in extending student thinking. All students perceived the most static elements of the line and could represent a metric unit. In the related area of fractions, they interpreted simple fractions as operational units. However, the majority of students were unable to coordinate and, thus, imagine the second-order nested hierarchies that could be inferred from the line. Similarly, they had difficulty coordinating the higher-order nested relationships necessary to interpret equivalent fractions intelligently. The students benefited from instruction that questioned their way of knowing and from manipulatives that served to support their reflections.