An Investigation of Spatial-Geometrical Understanding in Students with Learning Disabilities

Abstract. Five- to 13-year-old children of average intelligence who had been identified as having learning disabilities (LD, n = 85) and not identified as having learning disabilities (NLD, n = 94) were individually tested for their ability to mentally anticipate and execute pegboard transformations of square and diamond figures, complete free-hand drawings of these figures, and draw figures on the Developmental Test of Visual Motor Integration. For students with LD and NLD alike: (a) age-related improvements in transformational strategies and in drawing were evident; (b) diamond figures were easier than square figures to transform but more difficult to draw; and (c) significant intra- and intertask correlations were obtained on pegboard and free-hand drawing tasks. These findings are consistent with predictions derived from Piagetian theory and suggest that a general spatial-cognitive mechanism determined performance on the tasks administered. On most tasks, students with LD did not perform as well as same-aged students with NLD even though the effects of IQ were reduced via matching and statistically controlled. The LD-NLD group differences are interpreted as reflecting delayed development in this general spatial-cognitive mechanism in students with LD rather than a specific skill deficit in visual-perceptual processing. Diagnostic and remedial implications of the findings and interpretation are discussed. The performance of students with learning differences (LD) in the area of mathematics has received increased attention in recent years. Much of this research has focused on computation and word problems. According to Rivera (1997): Although much has been learned about the mathematical skills of students with learning disabilities, research is needed in other mathematics areas, such as place value, geometry [italics added], fractions, measurement, and so forth ... [A] great deal of work remains to be done in developing a better understanding of specific difficulties in other mathematics concepts and skills. (p. 9) The present study investigated aspects of spatial-geometrical understanding in students with learning disabilities aged 7 to 13 years old. Specifically, we investigated performance on individually administered tasks that required students to draw and to anticipate and execute transformations of square and diamond figures. According to the curriculum and evaluation standards adopted by the National Council of Teachers of Mathematics (NCTM, 1989), K-8 students should be able to: describe, model, draw, and classify shapes; investigate and predict the results of combining, subdividing and changing shapes (K-4 standard #9); visualize and represent geometric figures with special attention to developing spatial sense; explore transformations of geometric figures; and understand and apply geometric properties and relationships (G5-8 standard #12). Research on tasks involving manipulation of geometric shapes and relationships is needed, not only because of the general paucity of research in geometry noted by Rivera (1997), but also because geometry is an important area of mathematical problem solving (Patton, Cronin, Bassett, & Koppel, 1997) where children with LD are able to draw on their strengths and achieve success using problem-solving strategies relative to their abilities (Swanson, 1993; Thornton, Langrall, & Jones, 1997; Wansart, 1990). Further, visualization techniques such as drawing diagrams are helpful in solving problems for many students with LD (Montague, 1997) although the extent and manner to which manipulatives should be used are controversial (Carnine, 1997). More controversial is the opinion that the standards in the NCTM reform (1989) on spatial skills for students with LD are detrimental and that their inclusion in curricula for students with LD reflects our inability to learn from past errors (Hofmeister, 1993; Mercer, Harris, & Miller, 1993). …