Longitudinal study of children’s reasoning about space and geometry

Designing Learning Environments for Developing Understanding of Geometry and Space

Volumn , Issue , 2012, Pages 137-168

  Lehrer, Richard ^a   Jenkins, Michael ^a   Osana, Helen ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85070622380     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9780203053461-12     Document Type: Chapter

References (37)

1. Anderson, J. R. (1983). The architecture of cognition. Cambridge, MA: Harvard University Press.
2. Baltes, P., Reese, H. W., & Nesselroade, J. R. (1977). Life-span developmental psychology: Introduction to research methods. Monterey, CA: Brooks/Cole.
3. Braine, L. G., Schauble, L., Kugelmass, S., & Winter, A. (1993). Representation of depth by children: Spatial strategies and lateral biases. Developmental Psychology, 29, 466-479.
4. Bruer, J. T. (1994). Schools for thought: A science of learning in the classroom. Cambridge, MA: MIT Press.
5. Burger, W., & Shaughnessy, M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17, 31-48.
6. Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C, & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499-531.
7. Case, R. (1985). Intellectual development. New York: Academic Press.
8. Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching (pp. 420-464). Reston, VA: National Council of Teachers of Mathematics.
9. Eilan, N., McCarthy, R., & Brewer, B. (1993). Spatial representation. Cambridge, MA: Black-well.
10. Ellis, S. A. (1995, April). Developmental changes in children’s understanding of principles and procedures of measurement. Paper presented at the biennial meeting of the Society for Research in Child Development, Indianapolis, IN.
11. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht, the Netherlands: Reidel.
12. Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education Monograph, No. 3.
13. Goodnow, J. (1977). Children drawing. Cambridge, MA: Harvard University Press.
14. Henderson, D. W. (1996). Experiencing geometry on plane and sphere. Upper Saddle River, NJ: Prentice Hall.
15. Hoffer, A. (1983). Van Hiele-based research. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 205-227). New York: Academic Press.
16. Kosslyn, S. M. (1980). Image and mind. Cambridge, MA: Harvard University Press.
17. Kosslyn, S. M., Heldmeyer, K. H., & Locklear, E. P. (1977). Children’s drawings as data about internal representations. Journal of Experimental Child Psychology, 23, 191-211.
18. Kosslyn, S. M., Margolis, J. A., Barrett, A. M., Goldknopf, E. J., & Daly, P. F. (1990). Age differences in imagery abilities. Child Development, 61, 995-1010.
19. Lehrer, R., Knight, W., Sancilio, L., & Love, M. (1989, March). Software to link actions and descriptions in pre-proof geometry. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.
20. Lehrer, R., & Littlefield, J. (1993). Relationships among cognitive components in Logo learning and transfer. Journal of Educational Psychology, 85, 317-330.
21. Miller, K. F., & Baillargeon, R. (1990). Length and distance: Do preschoolers think that occlusion brings things together? Developmental Psychology, 26, 103-114.
22. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
23. Olson, D. R. (1970). Cognitive development: The child’s acquisition of diagonality. New York: Academic Press.
24. Piaget, J., & Inhelder, B. (1948/1956). The child’s conception of space. London: Routledge and Kegan Paul. (Original work published 1948)
25. Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child’s conception of geometry. New York: Basic Books.
26. Romberg, T, Tornrose-Dyer, M., & Harvey, J. G. (1994). Developing mathematical power (Vol. 2). Chicago: Encyclopaedia Britannica Educational Corporation.
27. Siegler, R. S. (1981). Developmental sequences within and between concepts. Monographs of the Society for Research in Child Development, 46 (2, Serial No. 189).
28. Siegler, R. S. (1986). Children’s thinking. Englewood Cliffs, NJ: Prentice Hall.
29. Siegler, R. S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.
30. Sigel, I. E. (1993). The centrality of a distancing model for the development of representational competence. In R. R. Cocking & K. A. Renninger (Eds.), The development and meaning of psychological distance (pp. 141-158). Hillsdale, NJ: Lawrence Erlbaum Associates.
31. Smith, L. B. (1989). A model of perceptual classification in children and adults. Psychological Review, 96, 125-144.
32. Towell, G., & Lehrer, R. (1995). A knowledge-based model of geometry learning. In T. Petsche, S. J. Hanson, & J. Shavlik (Eds.), Computational learning theory and natural learning systems (pp. 55-74). Cambridge, MA: MIT Press.
33. van Hiele, P. M. (1959). Development and the learning process. In Acta Paedogogica Ultrajectina (pp. 1-31). Groningen, the Netherlands: Wolters.
34. van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando, FL: Academic Press.
35. Wagman, H. G. (1975). The child’s conception of area measure. In M. F. Rosskopf (Ed.), Children’s mathematical concepts; Six Piagetian studies (pp. 71-110). New York: Teachers College Press.
36. Willats, J. (1977). How children learn to represent three-dimensional space in drawings. In G. Butterworth (Ed.), The child’s representation of the world (pp. 189-202). New York: Plenum.
37. Willats, J. (1984). Getting the drawing to look right as well as to be right: The interaction between production and perception as a mechanism of development. In W. R. Crozier & A. J. Chapman (Eds.), Cognitive processes in the perception of art (pp. 111-126). Amsterdam: Elsevier.