The nature of arguments provided by college geometry students with access to technology while solving problems

Journal for Research in Mathematics Education

Volumn 41, Issue 4, 2010, Pages 324-350

  Hollebrands, Karen F ^a   Conner, Annamarie ^b   Smith, Ryan C ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF GEORGIA   (United States)

Author keywords

College mathematics; Geometry; Proof; Reasoning; Technology (general)

Indexed keywords

EID: 77954718640     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. Castellanos, J. (2007). NonEuclid. Retrieved September 15, 2006, from http://www.cs.unm.edu/~joel/NonEuclid/NonEuclid.jar
2. Chazan, D. (1993). High school geometry students'justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24, 359-387.
3. de Villiers, M. (1998). An alternative approach to proof in dynamic geometry. in R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 369-394). Mahwah, NJ: Erlbaum.
4. de Villiers, M. (1999). Rethinking proof with the Geometer's Sketchpad. Emeryville, CA: Key Curriculum Press.
5. Edwards, L. D. (1997). Exploring the territory before proof: Students' generalizations in a computer microworld for transformation geometry. international Journal of Computers for Mathematical Learning, 2, 187-215.
6. Hadas, N., Hershkowitz, R., & Schwarz, B. B. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics, 44, 127-150.
7. Hollebrands, K. (2007). The role of a dynamic software program for geometry in the strategies high school mathematics students employ. Journal for Research in Mathematics Education, 38, 164-192.
8. Hollebrands, K., Laborde, C, & Sträßfier, R. (2008). Technology and the learning of geometry at the secondary level. in M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Vol. I. Research syntheses (pp. 155-206). Charlotte, NC: information Age.
9. Hoyles, C, & Healy, L. (1999). Linking informal argumentation with formal proof through computerintegrated teaching experiments. in O. Zaslavsky (Ed.), Proceedings of the 23rd annual conference of the international Group for the Psychology of Mathematics Education: Vol. 3 (pp. 105-112). Haifa, Israel: Technion Printing Center.
10. Inglis, M, Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: the importance of qualification. Educational Studies in Mathematics, 66, 3-21.
11. Jahnke, H. N. (2008). Theorems that admit exceptions, including a remark on Toulmin. ZDM Mathematics Education, 40, 363-371.
12. Kakihana, K., Shimizu, K., & Nohda, N. (1996). From measurement to conjecture and proof in geometry problems: Students' use of measurements in the computer environment. in L. Puig & A. Gutierrez (Eds.), Proceedings of the 20th annual conference of the international Group for the Psychology of Mathematics Education: Vol. 3 (pp. 161-168). Valencia, Spain: University of Valencia.
13. Laborde, C, Kynigos, C, Hollebrands, K., & Sträßer, R. (2006). Teaching and learning geometry with technology. in A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 275-304). Rotterdam, the Netherlands: Sense Publishers.
14. Lavy, I. (2006). A case study of different types of arguments emerging from explorations in an interactive computerized environment. Journal of Mathematical Behavior, 25, 153-169.
15. Leung, A., Chan, Y, & Lopez-Real, F. (2006). instrumental genesis in dynamic geometry environments. in L. H. Son, N. Sinclair, J.-B. Lagrange, & C. Hoyles (Eds.), Proceedings of the 17th study conference of the international Commission on Mathematical instruction: Digital technologies and mathematics teaching and learning: Rethinking the terrain. Part 2: Contributions (pp. 346-353). Vietnam: Hanoi University of Technology.
16. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
17. Noss, R., & Hoyles, C. (1996). Mathematics education library: Vol. 17. Windows on mathematical meanings: Learning cultures and computers. Dordrecht, the Netherlands: Kluwer.
18. Schoenfeld, A. H. (1986). On having and using geometric knowledge. in J. Hiebert (Ed.), Conceptual and procedural knowledge: the case of mathematics (pp. 225-264). Hillsdale, N J: Erlbaum.
19. Stephan, M., & Rasmussen, C. (2002). Classroom mathematical practices in differential equations. Journal of Mathematical Behavior, 21, 459-490.
20. Toulmin, S. (1958). The uses of argument. New York: Cambridge University Press.
21. Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando, FL: Academic Press.
22. Verillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10, 77-101.