Interpreting student understanding in geometry: A synthesis of two models

Designing Learning Environments for Developing Understanding of Geometry and Space

Volumn , Issue , 2012, Pages 109-136

  Pegg, John ^a   Davey, Geoff ^b  

^a UNIVERSITY OF NEW ENGLAND   (Australia)

^b Christian Heritage College   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70449574060     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9780203053461-11     Document Type: Chapter

References (39)

1. Biggs, J., & Collis, K. (1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.
2. Biggs, J., & Collis, K. (1991). Multimodal learning and the quality of intelligent behavior. In H. Rowe (Ed.), Intelligence, reconceptualization and measurement (pp. 57-76). Hillsdale, NJ: Lawrence Erlbaum Associates.
3. Bruner, J. S. (1964). The course of cognitive growth. American Psychologist, 19, 1-15.
4. Burger, W. R, & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17, 31-48.
5. Campbell, K., Watson, J., & Collis, K. (1992). Volume measurement and intellectual development. Journal of Structural Learning and Intelligent Systems, 11, 279-298.
6. Case, R. (1992). The mind’s staircase: Exploring the conceptual underpinnings of children’s thought and knowledge. Hillsdale, NJ: Lawrence Erlbaum Associates.
7. Clements, D., & Battista, M. (1992). Geometry and spatial reasoning. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York: Macmillan.
8. Collis, K. (1975). A study of concrete and formal operations in school mathematics: A Piagetian viewpoint. Melbourne: Australian Council for Educational Research.
9. Collis, K. (1988). The add up or take syndrome. In J. Pegg (Ed.), Mathematical interfaces (pp. 66-75). Adelaide: Australian Association of Mathematics Teachers.
10. Collis, K., & Biggs, J. (1983). Matriculation, degree structures, and levels of student thinking. Australian Journal of Education, 27 (2), 151-163.
11. Collis, K., & Romberg, T. (1991). Assessment of mathematical performance: An analysis of open-ended test items. In M. C. Wittrock & E. L. Baker (Eds.), Testing and cognition (pp. 82-130). Englewood Cliffs, NJ: Prentice Hall.
12. Darke, I. (1982). A review of research related to the topological primacy thesis. Educational Studies in Mathematics, 13(2), 119-142.
13. Dickson, L., Brown, M., & Gibson, O. (1984). Children learning mathematics: A teacher’s guide to research. East Sussex, UK: Holt, Rinehart and Winston.
14. Fischer, K. W., & Knight, C. C. (1990). Cognitive development in real children: Levels and variations. In B. Presseisen (Ed.), Learning and thinking styles: Classroom interaction (pp. 43-67). Washington, DC: National Education Association.
15. Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education Monograph, 3.
16. Gutiérrez, A., Jaime, A., & Fortuny, J. M. (1991). An alternative paradigm to evaluate the acquisition of the van Hiele levels. Journal for Research in Mathematics Education, 22, 237-251.
17. Hoffer, A. (1981). Geometry is more than proof. Mathematics Teacher, 74, 11-18.
18. Jurdak, M. (1989). van Hiele levels and the SOLO taxonomy. PME Proceedings, 13, 155-162.
19. Laurendeau, M., & Pinard, A. (1970). The development of the concept of space in the child. New York: International Universities Press.
20. Lesh, R., & Mierkiewicz, D. (1978). Perception, imaging and conception in geometry. In R. Lesh & D. Mierkiewicz (Eds.), Recent research concerning the development of spatial and geometric concepts (pp. 7-28). Columbus, OH: ERIC.
21. Levins, L., & Pegg, J. (1993). Students’ understanding of concepts related to plant growth. Research in Science Education, 23, 165-173.
22. Lidz, C. S. (1987). Dynamic assessment: An interactional approach to evaluating learning potential. New York: Guildford.
23. Little, J. (1980). The uncertain craft of mathematics. New Scientist, 626-628.
24. Lovitt, C, & Clarke, D. (1988). Codifying and sharing the wisdom of practice. In J. Pegg (Ed.), Mathematical interfaces (pp. 1-21). Adelaide: Australian Association of Mathematics Teachers.
25. Mayberry, J. (1981). An investigation of the van Hiele levels of geometric thought in undergraduate preservice teachers. Unpublished doctoral dissertation, University of Georgia. (University Microfilms No. DA 8123078)
26. Olive, J. (1991). Logo programming and geometric understanding: An in-depth study. Journal for Research in Mathematics Education, 22, (2), 90-111.
27. Olson, D. R., & Bialystok, E. (1983). Spatial Cognition. Hillsdale, NJ: Lawrence Erlbaum Associates.
28. Pegg, J. (1992a). Assessing students’ understanding at the primary and secondary level in the mathematical sciences. In J. Izard & M. Stephens (Eds.), Reshaping assessment practice: Assessment in the mathematical sciences under challenge (pp. 368-385). Melbourne: Australian Council of Educational Research.
29. Pegg, J. (1992b). Students’ understanding of geometry: Theoretical perspectives. In B. Southwell, B. Perry, & K. Owens (Eds.), Space-The first and final frontier (pp. 18-36). Sydney: Mathematics Education Research Group of Australasia.
30. Pegg, J., & Davey, G. (1989). Clarifying level descriptions for children’s understanding of some basic 2D geometric shapes. Mathematics Education Research Journal, 1 (1), 16-27.
31. Pegg, J., & Faithfull, M. (1995). Analyzing higher order skills in deductive geometry. In A. Baturo (Ed.), New directions in geometry education (pp. 100-105). Brisbane: Queensland University of Technology Press.
32. Pegg, J., & Woolley, S. (1994). An investigation of strategies used to solve a simple deductive exercise in geometry. In G. Bell, B. Wright, N. Leeson. & J. Geake (eds.) Challenges in mathematics education: Constraints on construction, (pp. 471-479). Lismore, New South Wales: Mathematics Education Research Group of Australasia, Southern Cross University.
33. Piaget, J., & Inhelder, B. (1956). The child’s conception of space. London: Routledge & Kegan Paul.
34. Piaget, J., Inhelder, B., & Szeminska, A. (1960). The child’s conception of geometry. New York: Basic Books.
35. Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry (Final report of the Cognitive Development and Achievement in Secondary School Geometry. Project) Chicago: University of Chicago, Department of Education.
36. van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. New York: Academic Press.
37. Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard University Press.
38. Watson, J., & Collis, K. (1994). Multimodal functioning in understanding chance and data concepts. PME Proceedings, 18, 369-376.
39. White, P., & Pegg, J. (1994). A description of student responses to restrictions on assumed knowledge. In G. Bell, B. Wright, N. Leeson, & J. Geake (eds.), Challenges in mathematics education: Constraints on construction (pp. 691-698). Lismore, New South Wales: Mathematics Education Research Group of Australasia, Southern Cross University.