The role of representation(s) in developing mathematical understanding

Theory into Practice

Volumn 40, Issue 2, 2001, Pages 118-127

  Pape, Stephen J ^b   Tchoshanov, Mourat A ^a  

^a UNIVERSITY OF TEXAS AT EL PASO   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035593613     PISSN: 00405841     EISSN: None     Source Type: Journal    
DOI: 10.1207/s15430421tip4002_6     Document Type: Article

References (31)

1. Arnheim, R. (1969). Visual thinking. Berkeley: University of California Press.
2. Brenner, M.E., Mayer, R.E., Moseley, B., Brar, T., Duran, R., Reed, B.S., & Webb, D. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34, 663-689.
3. Bruner, J. (1966). Toward a theory of instruction. Cambridge, MA: Belknap Press.
4. Caine, R., & Caine, G. (1994). Making connections: Teaching and the human brain. New York: Addison-Wesley.
5. Chabris, C., & Kosslyn, S. (1998). How do the cerebral hemispheres contribute to encoding spatial relations? Current Directions in Psychology, 7, 8-14.
6. Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23, 2-33.
7. DiSessa, A.A., Hammer, D., Sherin, B., & Kolpakowski, T. (1991). Inventing graphing: Meta-representational expertise in children. Journal on Mathematical Behavior, 10, 117-160.
8. Greeno, J.G., & Hall, R.P. (1997). Practicing representation: Learning with and without representational forms. Phi Delta Kappan, 78, 361-367.
9. Hall, N. (1998). Concrete representations and the procedural analogy theory. Journal of Mathematical Behavior, 17, 33-52.
10. Herscovics, N. (1996). The construction of conceptual schemes in mathematics. In L. Steffe (Ed.), Theories of mathematical learning (pp. 351-380). Mahwah, NJ: Erlbaum.
11. Hiebert, J. (1988). A theory of developing competence with written mathematical symbols. Educational Studies in Mathematics, 19, 333-355.
12. Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: Macmillan.
13. Janvier, C., Girardon, C., & Morand, J. (1993). Mathematical symbols and representations. In P.S. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 79-102). Reston, VA: National Council of Teachers of Mathematics.
14. Krutetskii, V. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
15. Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-58). Hillsdale, NJ: Erlbaum.
16. Maher, C.A., & Speiser, R. (Eds.). (1998a). Representations and the psychology of mathematics education: Part I [special issue]. Journal of Mathematical Behavior, 17(1).
17. Maher, C.A., & Speiser, R. (Eds.). (1998b). Representations and the psychology of mathematics education: Part II [special issue]. Journal of Mathematical Behavior, 17(2).
18. Mc Kim, R. (1972). Experiences in visual thinking. Monterey, CA: Brooks/ Cole.
19. Meira, L. (1995). The microevolution of mathematical representations in children's activity. Cognition and Instruction, 13, 269-313.
20. Mitchell, W. (1994). Picture theory. Chicago: University of Chicago Press.
21. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
22. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
23. National Research Council. (1996). National science education standards. Washington, DC: National Academy Press.
24. Perkins, D.N., & Unger, C. (1994). A new look in representations for mathematics and science learning. Instructional Science, 22, 1-37.
25. Presmeg, N.C. (1999, October). On visualization and generalization in mathematics. In F. Hitt & M. Santos (Eds.), Proceedings of the twenty first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 151-155). Columbus, OH: Clearinghouse for Science, Mathematics, and Environmental Education.
26. Seeger, F. (1998). Representations in the mathematics classroom: Reflections and constructions. In F. Seeger, J. Voigt, & V. Werschescio (Eds.), The culture of the mathematics classroom (pp. 308-343). Cambridge, UK: Cambridge University Press.
27. Tchoshanov, M. (1997). Visual mathematics. Kazan, Russia: ABAK.
28. Vellom, R.P., & Pape, S.J. (2000). EarthVision 2000: Examining students' representations of complex data. School Science and Mathematics, 100, 426-439.
29. Wheatley, G.H. (1997). Reasoning with images in mathematical activity. In L.D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 281-298). Mahwah, NJ: Erlbaum.
30. Wileman, R. (1980). Exercises in visual thinking. New York: Hastings House.
31. Yakimanskaya, I. (Ed.). (1991). The development of spatial thinking in schoolchildren. Reston, VA: National Council of Teachers of Mathematics.