The purpose of this study was to investigate students' use of visual imagery and its relationship to spatial visualization ability while solving mathematical word problems. Students with learning disabilities (LD), average achievers, and gifted students in sixth grade (N = 66) participated in this study. Students were assessed on measures of mathematical problem solving, visual imagery representation, and spatial visualization ability. The results indicated that gifted students performed better on both spatial visualization measures than students with LD and average-achieving students. Use of visual images was positively correlated with higher mathematical wordproblem—solving performance. Furthermore, the use of schematic imagery was significantly and positively correlated with higher performance on each spatial visualization measure; conversely, it was negatively correlated with the use of pictorial images.
Get full access to this article
View all access options for this article.
References
1.
Baddeley, A. (1992). Is working memory working? The fifteenth Barlett lecture. The Quarterly Journal of Experimental Psychology , 44A, 1—31.
2.
Baddeley, A.D., & Lieberman, K. (1980.). Spatial working memory. In R. Nickerson (Ed.), Attention and performance (Vol. 8, pp. 521—539). Hillsdale, NJ: Erlbaum.
3.
Battista, M.T. (1990). Spatial visualization and gender differences in high school geometry. Journal for Research in Mathematics Education, 21, 47—60.
4.
Ben-Chaim, D., Lappan, G., & Houang, R.T. (1988). The effect of instruction on spatial visualization skills of middle school boys and girls. American Educational Research Journal, 25, 51—71.
5.
Brown, D.L., & Wheatley, G.H. ( (1997). Components of imagery and mathematical understanding. Focus on Learning Problems in Mathematics, 19, 45—70.
6.
Burnett, S.A., Lane, D.M., & Dratt, L.M. (1979). Spatial visualization and sex differences in quantitative ability. Intelligence, 3, 345—354.
7.
Campbell, K.J., Collis, K.F., & Watson, J.M. (1995). Visual processing during mathematical problem solving. Educational Studies in Mathematics, 28, 177—194.
8.
Clements, D.H., & Battista, M.T. (1992). Geometry and spatial reasoning . In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420— 464). New York: Macmillan.
9.
Clements, M.A.K. (1982). Visual imagery and school mathematics. Part II. For theLearning of Mathematics2, 33—39.
10.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
11.
Denis, M. (1991). Imagery and thinking. In C. Cornoldi & M. A. McDaniel (Eds.), Imagery and cognition (pp. 103—131). New York : Springer Verlag.
12.
Farah, M.J., Hammond, K.M., Levine, D.N., & Calvanio, R. (1988). Visual and spatial memory: Dissociable systems of representation. Cognitive Psychology, 20, 439—462.
13.
Fennema, E. (1979). Women and girls in mathematics—equity in mathematics education. Educational Studies in Mathematics , 5, 126—139.
14.
Fennema, E., & Sherman, J. (1977). Sex-related differences in mathematics achievement, spatial visualization, and affective factors. American Education Research Journal, 14, 51—71.
15.
Fennema, E., & Tartre, L.A. (1985). The use of spatial visualization in mathematics by girls and boys. Journal for Research in Mathematics Education , 16, 184—206.
16.
Fuchs, L.S., & Fuchs, D. (2001). Principles for the prevention and intervention of mathematics difficulties. Learning Disabilities Research & Practice, 16, 85—95.
17.
Geary, D.C. (1996). Children's mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
18.
Geary, D.C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4—15.
19.
Grobecker, B., & De Lisi, R. (2000). An investigation of spatial—geometrical understanding in students with learning disabilities. Learning Disability Quarterly, 23, 7—22.
20.
Harris, L.J. (1981). Sex-related variations in spatial skill. In L. S. Liben, A. H. Patter-son, & N. Newcombe (Eds.), Spatial representation and behavior across the life span (pp. 83—125). New York: Academic Press.
21.
Hegarty, M., & Kozhevnikov, M. (1999). Types of visual—spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684—689.
22.
Hutchinson, N.L. (1993). Effects of cognitive strategy instruction on algebra problem solving with adolescents. Learning Disability Quarterly , 16, 34—63.
23.
Jencks, S.M., & Peck, D.M. (1972). Mental imagery in mathematics. The Arithmetic Teacher, 19, 642—644.
24.
Jitendra, A.K., & Hoff, K. (1996). The effects of schema-based instruction on the mathematical word-problem-solving performance of students with learning disabilities . Journal of Learning Disabilities, 29, 422—431.
25.
Jonides, J., & Smith, E.E. (1997). The architecture of working memory. In M. D. Rugg (Ed.), Cognitive neuroscience (pp. 243— 276). Cambridge, MA: MIT Press.
26.
Kaufmann, G. (1990). Imagery effects on problem solving. In P. J. Hampson, D. F. Marks, & J. R. E. Richardson (Eds.), Imagery, current development (pp. 169—196). London: Routledge & Kegan Paul.
27.
Kazdin, A.E. (1982). Single-case research designs: Methods for clinical and applied settings. New York: Oxford University Press.
28.
Kozhevnikov, M., Hegarty, M., & Mayer, R.E. (2002). Revising the visualizer— verbalizer dimension: Evidence for two types of visualizers. Cognition and Instruction , 20, 47—77.
29.
Kosslyn, S.M., & Koenig, O. (1992). Wet mind: The new cognitive neuroscience. New York: Free Press.
30.
Krutetskii, V.A. (1976). The psychology of mathematical abilities in schoolchildren . Chicago: University of Chicago Press.
Lean, G., & Clements, M.A.K. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12, 267—299.
33.
Marsh, L.G., & Cooke, N.L. (1996). The effects of using manipulatives in teaching math problem solving to students with learning disabilities. Learning Disabilities Research & Practice, 11, 58—65.
34.
McGee, M.G. (1979). Human spatial abilities: Psychometric studies and environmental, genetic, hormonal, and neurological influences. Psychological Bulletin, 86, 889—918.
35.
Miller, S.P., Butler, F.M., & Lee, K. (1998). Validated practices for teaching mathematics to students with learning disabilities: A review of literature. Focus onExceptional Children, 31, 1—24.
36.
Montague, M. (1996). Assessing mathematical problem solving. Learning Disabilities Research & Practice, 11, 238—248.
37.
Montague, M., & Applegate, B. (1993a). Mathematical problem-solving characteristics of middle school students with learning disabilities. The Journal of Special Education, 27, 175—201.
38.
Montague, M., & Applegate, B. (1993b). Middle school students' mathematical problem solving: An analysis of think-aloud protocols. Learning Disability Quarterly, 16, 19—32.
39.
Montague, M., & Applegate, B. (2000). Middle school students' perceptions, persistence, and performance in mathematical problem solving. Learning Disability Quarterly, 23, 215—227.
40.
Montague, M., Bos, C., & Doucette, M. (1991). Affective, cognitive, and metacognitive attributes of eight-grade mathematical problem solvers. Learning Disabilities Research & Practice, 6, 145—151.
41.
Owens, K.D., & Clements, M.A.K. (1998). Representations in spatial problem solving in the classroom. The Journal of Mathematical Behavior, 17, 197—218.
42.
Parmar, R.S., Cawley, J.F., & Frazita, R.E. (1996). Word problem solving by students with and without mild disabilities. Exceptional Children, 62, 415—429.
43.
Piaget, J., & Inhelder, B. (1966). Mental imagery in the child. New York: Routledge & Kegan Paul.
44.
Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). Garden City, NY: Doubleday.
45.
Presmeg, N.C. (1986a). Visualization and mathematical giftedness. Educational Studies in Mathematics, 17, 297—311.
46.
Presmeg, N.C. (1986b). Visualization in high school mathematics. For theLearning of Mathematics, 6, 42—46.
47.
Presmeg, N.C. (1997). Generalization using imagery in mathematics. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 299—312). Mahwah, NJ: Erlbaum.
48.
Smith, I.M. (1964). Spatial ability: Its educational and social significance . London: University of London Press .
49.
Swanson, H.L. (1989). Central processing strategy difference in gifted, normal achieving, learning disabled, and mentally retarded children. Journal of Experimental Child Psychology, 47, 370—397.
50.
Swanson, H.L., Carson, C., & Sachse-Lee, C.M. (1996). A selective synthesis of intervention research for students with learning disabilities: Is there general support for a strategy deficit model. In T. E. Scruggs & M. A. Mastropieri (Eds.), Advances in learning and behavioral disabilities (Vol. 10, Part A, pp. 51—180). Greenwich, CT: JAI Press.
51.
Tartre, L.A. (1990). Spatial orientation skill and mathematical problem solving. Journal for Research in Mathematics Education, 21, 216—229.
52.
Thornton, C.A., Langrall, C.W., & Jones, G.A. (1997). Mathematics instruction for elementary students with learning disabilities. Journal of Learning Disabilities , 30, 142—150.
53.
Van de Walle, J.A. (1998). Elementary and middle school mathematics: Teaching developmentally (3rd ed.). New York: Long-man.
54.
van Garderen, D. (2002). Visual imaging and mathematical word problem solving by students of varying abilities. Unpublished doctoral dissertation, University of Miami, FL.
55.
van Garderen, D., & Montague, M. (2003). Visual—spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18, 246—254.
56.
Wansart, W.L. (1990). Learning to solve a problem: A micro-analysis of the solution strategies of children with learning disabilities. Journal of Learning Disabilities, 23, 164—170, 184.
57.
Wechsler, D. (1976). Wechsler intelligence scale for children—Revised . San Antonio, TX: Psychological Corp.
58.
Wechsler, D. (1991). Wechsler intelligence scale for children (3rd ed.). San Antonio, TX: Psychological Corp.
59.
Wheatley, G.H. (1990). Spatial sense and mathematics learning. Arithmetic Teacher, 38,10—11.
60.
Woodcock, R.W., McGrew, K.S., & Mather, N. (2001). Woodcock-Johnson—III tests of cognitive abilities. Itasca, IL: Riverside .
61.
Woodward, J., & Montague, M. (2002). Meeting the challenge of mathematics reform for students with LD. The Journal of Special Education, 36, 89—101.
62.
Zawaiza, T.R.W., & Gerber, M.M. (1993). Effects of explicit instruction on math word- problem solving by community college students with learning disabilities. Learning Disability Quarterly, 16, 64—79.
63.
Zimmerman, W., & Cunningham, S. (1991). Editors' introduction: What is mathematical visualization? In W. Zimmerman & S. Cunningham (Eds.), Visualization in teaching and learning mathematics (pp. 1—7). Washington, DC: Mathematical Association of America .
