Assessinghigh school students’ understanding of geometric proof

Canadian Journal of Science, Mathematics and Technology Education

Volumn 4, Issue 2, 2004, Pages 223-242

  McCrone, Sharon M Soucy ^a   Martin, Tami S ^a  

^a ILLINOIS STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85011479696     PISSN: 14926156     EISSN: 19424051     Source Type: Journal    
DOI: 10.1080/14926150409556607     Document Type: Article

References (26)

1. Balacheff, N. (1991). Treatment of refutations: Aspects of the complexity of a constructivist approach to mathematics learning. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 89-110). Dordrecht, The Netherlands: Kluwer Academic.
2. Chazan, D. (1993). High school geometry students’ justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24(4), 359-387.
3. 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.
4. de Villiers, M. (1999). Rethinking proof with the Geometer's Sketchpad. Emeryville, CA: Key Curriculum Press.
5. Dreyfus, T., & Hadas, N. (1987). Euclid may stay—and even be taught. In M.M. Lindquist & A.P. Shulte (Eds.), Learning and teaching geometry, K—12 (pp. 47-58). Reston, VA: National Council of Teachers of Mathematics.
6. Dreyfus, T., & Hadas, N. (1996). Proof as answer to the question why. International Reviews on Mathematical Education, 25(1), 1-5.
7. Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44, 5-23.
8. Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A.H. Schoenfeld, J. Kaput, and E. Dubinsky (Eds.), CBMS issues in mathematics education. Providence, RI: American Mathematical Society.
9. Hart, E.W. (1994). A conceptual analysis of the proof-writing performance of expert and novice students in elementary group theory. In J.J. Kaput & E. Dubinsky (Vol. Eds.), MAA Notes: No. 33. Research issues in undergraduate mathematics learning: Preliminary analyses and results. Washington, DC: Mathematical Association of America.
10. Healy, L., & Hoyles, C. (1998). Technical report on the nationwide survey: Justifying and proving in school mathematics. London: Institute of Education, University of London.
11. Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24(4), 389-399.
12. Hoyles, C. (1997). The curricular shaping of students’ approaches to proof. For the Learning of Mathematics, 77(1), 7-16.
13. International Association for the Evaluation of Educational Achievement. (1995). Released advanced mathematics items: Population 3. Third international mathematics and science study [TIMSS]. The Hague, The Netherlands: Author.
14. Martin, T.S. (1997). Calculus students' abilities to solve geometric related rate problems and their understanding of related geometric growth factors. Unpublished doctoral dissertation, Boston University, Boston, MA.
15. Martin, T.S., & McCrone, S.M. (2001). Proof principles questionnaire. Illinois State University, College of Arts and Sciences. Available: http://www.cas.ilstu.edu/proofproject/webpage/(accessed 1 March, 2004).
16. Martin, T.S., & McCrone, S.M. (2002). Proof construction assessment: Rubric. Unpublished assessment instrument.
17. Martin, W.G., & Harel, G. (1989): Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41-51.
18. McCrone, S.M., & Martin, T.S. (2002). Proof construction assessment. Illinois State University, College of Arts and Sciences. Available: http://www.cas.ilstu.edu/pr00Q3r0ject/webpage/(accessed 1 March, 2004).
19. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
20. Senk, S.L. (1985). How well do students write geometry proofs? Mathematics Teacher, 78(6), 448-456.
21. Senk, S.L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20(3), 309-321.
22. Simon, M.A., & Blume, G.W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. Journal of Mathematical Behavior, 15, 3-31.
23. Steffe, L., & Thompson, P. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A.E. Kelly & R.A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267-306). Mahwah, NJ: Erlbaum.
24. Tashakkori, A., & Teddlie, C. (1998). Mixed methodology: Combining qualitative and quantitative approaches. Thousand Oaks, CA: Sage.
25. Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. Chicago: University of Chicago Press.
26. Williams, E.R. (1979). An investigation ofsenior high school students’ understanding of the nature of mathematical proof. Unpublished doctoral dissertation, University of Alberta, Edmonton, AB.