The Relationship between Pre-service Teachers` Geometric Reasoning and their van Hiele Levels in a Geometer`s Sketchpad Environment

- Journal title : Research in Mathematical Education
- Volume 19, Issue 4, 2015, pp.229-245
- Publisher : Korea Society of Mathematical Education
- DOI : 10.7468/jksmed.2015.19.4.229

Title & Authors

The Relationship between Pre-service Teachers` Geometric Reasoning and their van Hiele Levels in a Geometer`s Sketchpad Environment

LEE, Mi Yeon;

LEE, Mi Yeon;

Abstract

In this study, I investigated how pre-service teachers (PSTs) proved three geometric problems by using Geometer`s SketchPad (GSP) software. Based on observations in class and results from a test of geometric reasoning, eight PSTs were sorted into four of the five van Hiele levels of geometric reasoning, which were then used to predict the PSTs` levels of reasoning on three tasks involving proofs using GSP. Findings suggested that the ways the PSTs justified their geometric reasoning across the three questions demonstrated their different uses of GSP depending on their van Hiele levels. These findings also led to the insight that the notion of "proof" had somewhat different meanings for students at different van Hiele levels of thought. Implications for the effective integration of technology into pre-service teacher education programs are discussed.

Keywords

geometric reasoning;pre-service teacher education;van Hiele levels;geometric proofs;

Language

English

References

1.

Battista, M. & Clements, D. (1995). Connecting Research to Teaching: Geometry and Proof. Math. Teach (Reston) 88(1), 48-54. ME 1996b.01051

2.

Burger, W. & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. J. Res. Math. Educ. 17(1), 31-48. ME 1986e.09027

3.

Cobb, P. & Gravemeijer, K. (2008). Experimenting to support and understand learning processes. In: A. E. Kelly, R. A. Lesh & J. Y. Baek (Eds.), Handbook of design research methods in education: Innovations in science, technology, engineering, and mathematics learning and teaching (pp. 68-95). New York: Routledge.

4.

Corbin, J. & Strauss, A. (2008). Basics of qualitative research (3rd ed.). Thousand Oaks, CA: Sage Publication.

5.

Crowley, M. L. (1987). The van Hiele Model of the Development of Geometric Thought. In: M. Lindquist (Ed), Learning and Teaching Geometry, K-12, 1987 Yearbook of the National Council of Teachers of Mathematics (pp.1-16). Reston, VA: NCTM. ME 1988x.00341

6.

De Villiers, M. (1991). Pupils' needs for conviction and explanation within the context of geometry. Pythagoras (Pretoria) 26, 18-27. ME 1992d.00245

7.

De Villiers, M. (2003). Rethinking proof with the Geometer's Sketchpad. Emeryville, CA: Key Curriculum Press. ME 2000d.02607

8.

De Villiers, M. (2004). Using dynamic geometry to expand mathematics teachers' understanding of proof. Int. J. Math. Educ. Sci. Technol. 35(5), 703-724. ME 2004d.05037

9.

Driscoll, M. (2007). Fostering geometric thinking. Portsmouth, NH: Heinemann.

10.

Eves, H. (1972). A survey of geometry. Boston, MA: Allyn & Bacon.

11.

Gawlick, T. (2005). Connecting arguments to actions - dynamic geometry as means for the attainment of higher van Hiele levels. ZDM, Zentralbl. Didakt. Math. 37(5), 361-370. ME 2005f.02677

12.

Goldenberg, E. P. & Cuoco, A. A. (1998). What is Dynamic Geometry? In: R. Lehrer & D. Chazan (Eds.) Designing learning environments for developing understanding of geometry and space (pp. 351-368). Mahwah, NJ: Lawrence Erlbaum Associates. ME 1998f.04240

13.

Govender, R. & de Villiers, M. (2003). Constructive evaluation of definitions in a dynamic geometry context. J. Korean Soc. Math. Educ. Ser. D 7(1), 41-58. ME 2003d.03244

14.

Gutierrez, A . (1992). Exploring the links between van Hiele levels and 3-dimensional geometry. Topologie Struct. 18, 31-48. ME 1995a.00083

15.

Haja, S. (2005). Investigating the problem solving competency of preservice teachers in dynamic geometry environment. In: H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th annual conference of the International Group for the Psychology of Mathematics Education (PME 29, Melbourne, Australia, July 10-15, 2005.), Vol. 3, (pp. 81-87). Melbourne, Australia: University of Melbourne, Dep. of Science and Mathematics Education. ME 2008a.00355

16.

Hollebrands, K. F. (2007). The role of a dynamic software program for geometry in the strategies high school mathematics students employ. J. Res. Math. Educ. 38(2), 164-192. ME 2007a.00324

17.

Jackiw, N. (2001). The Geometer's Sketchpad [Software]. Berkley, CA: Key Curriculum Press.

18.

Laborde, C. & Laborde, J. (2008). The development of a dynamical geometry environment. In: M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: vol. 2. Cases and perspectives (pp. 31-52). Charlotte, NC: Information Age Publishing (IAP) / Reston, VA: NCTM. ME 2011a.00351

19.

Lee, M. Y. (2015). The Relationship between Pre-service Teachers' Geometric Reasoning and their van Hiele Levels in a Geometer's Sketchpad Environment. In: O. N. Kwon, Y. H. Choe, H. K. Ko & S. Han (Eds.), The International Perspective on Curriculum and Evaluation of Mathematics - Proceedings of the KSME 2015 International Conference on Mathematics Education held at Seoul National University, Seoul 08826, Korea; November 6-8, 2015 (Vol. 3, pp.299-214). Seoul, Korea: Korean Society of Mathematical Education.

20.

Mayberry, J. (1981). An investigation of the van Hiele levels of geometric thinking in undergraduate preservice teachers. Dissertation Abstracts International, 42/01A, 2008A.

21.

Mudaly, V. & de Villiers, M. (2000). Learners' needs for conviction and explanation within the context of dynamic geometry. Pythagoras (Pretoria) 52, 20-23. ME 2001b.0145

22.

Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. Teaching and Teacher Education 21(5), 509-523.

23.

Olive, J. (2000). Using Dynamic Geometry Technology: Implications for Teaching, Learning & Research. Paper presented at TIME 2000 An International Conference on Technology in Mathematics Education. Auckland, New Zealand, 11-14.

24.

Patsiomitou, S.; Barkatsas, A. & Emvalotis, A. (2010). Secondary students' dynamic reinvention of geometric proof through the utilization of linking visual active representations. Journal of Mathematics and Technology 5, 43-56.

25.

Senk, S. (1989). Van Hiele levels and achievement in writing geometry proofs. J. Res. Math. Educ. 20(3), 309-321. ME 1990b.01262

26.

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.