Imagery and fractions in students classified as learning disabled

This article describes constructivist principles of learning in geometry sp ecific to children's imaginal anticipations in line measurement and the rel ated area of fractions. To assist with this discussion, seven sixth-grade s tudents classified as learning disabled (LD) and receiving some type of spe cial education service for mathematics were individually tested in tasks th at investigated their imaginal anticipations of space and their representat ions of this understanding in the fraction symbol. Additionally, the invest igation examined the effectiveness of constructivist teaching techniques in extending student thinking. All students perceived-the most static element s of the line and could represent a metric unit. In the related area of fra ctions, they interpreted simple fractions as operational units. However, th e majority of students were unable to coordinate and, thus, imagine the sec ond-order nested hierarchies that could be inferred from the line. Similarl y, they had difficulty coordinating the higher-order nested relationships n ecessary to interpret equivalent fractions intelligently. The students bene fited from instruction that questioned their way of knowing and from manipu latives that served to support their reflections.