Examples as Mediating Artifacts in Conjecturing

Chih-Hsien Huang^1,

¹Ming Chi University of Technology

Cite this paper:
Chih-Hsien Huang. Examples as Mediating Artifacts in Conjecturing. American Journal of Educational Research. 2016; 4(19):1295-1299. doi: 10.12691/education-4-19-3

Abstract

In this paper we report a study concerning examples as mediating artifacts in conjecturing. We used activity theory as an analytical framework to analyze students’ behavior and the process of conjecturing. The results show that through the guidance of proceduralized refutation model, most of the students could find the common properties by generating examples, and develop the ability of generalization and further made conjectures.

Keywords:
activity theory example proceduralized refutation model

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Alcock, L. “Uses of examples objects in proving.” In Proceedings of the 28rd Conference of the International Group for the Psychology of Mathematics Education, PME, Vol. 2, 17-24, July, 2004.
[2]	Boero,P., Garuti, R. and Lemut, E. “About the Generation of Conditionality of Statements and its Links with Proving.” In Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, PME, vol. 2, 137-144, July, 1999.
[3]	Cole, M. and Engeström, Y. “A cultural-historical approach to distributed cognition.” In G. Salomon (Ed.), Distributed cognitions: Psychological and educational considerations. Cambridge University Press, New York, 1993, 1-46.
[4]	Dahlberg, R.P. and Housman, D.L. “Facilitating learning events through example generation.” Educational Studies in Mathematics, 33, 283-299. September. 1997.
[5]	Davydov, V. “Types of generalization in instruction.” Soviet Studies in Mathematics Education, 2, 90-102. March. 1972.
[6]	Goldenberg, P., and Mason, J. “Shedding light on and with example spaces.” Educational studies in mathematics, 69, 183-194. May. 2008.
[7]	Goodwin, C., and Heritage, J. “Conversation analysis.” Annual Review of Anthropology, 19, 283-307. September. 1990
[8]	Harel, G. “The development of mathematical induction as a proof scheme: A model for DNR-based instruction.” In S. Campbell, & R. Zazkis (Eds.), Learning and teaching Number Theory. Ablex Publishing Corporation, New Jersey, 2001, 185-212.
[9]	Harel, G. and Sowder, L. “Students’ Proof Schemes: results from exploratory studies.” In A. Schoenfeld, J. Kaput and E. Dubinsky (Eds.), Research on Collegiate Mathematics Education, Vol.3, M.M.A. and A.M.S. 1998, 234-283.
[10]	Hazzan, O. and Zazkis, R. “Constructing knowledge by constructing examples for mathematical concepts.” In Proceedings of the 21rd Conference of the International Group for the Psychology of Mathematics Education, PME, vol. 4, 299-306, July, 1997.
[11]	Kuutti, K. “Activity theory as a potential framework for human–computer interaction research.” In B. A. Nardi (Ed.), Context and consciousness: activity theory and human–computer interaction. MA: MIT Press, Cambridge, 1997, 17-44.
[12]	Leont'ev, A. N. Activity, consciousness, and personality. Prentice- Hall, New Jersey, 1978.
[13]	Lin, F. L. “Designing mathematics conjecturing activities to foster thinking and constructing actively.” The meeting of the APEC-TSUKUBA International Conference. Tokyo, Japan, December. 2006.
[14]	Mason, J. and Johnston-Wilder, S. Fundamental Construct in Mathematics Education. Routledge, Falmer. 2004.
[15]	Skemp, R. R. The Psychology of Learning Mathematics, Middlesex, UK: Penguin. 1971.
[16]	Skemp, R. R. “Goals of learning and qualities of understanding.” Mathematics Teaching, 88, 44-49. March. 1979.
[17]	Tall, D.O. and Vinner, S. “Concept image and concept definition in mathematics, with special reference to limits and continuity.” Educational Studies in Mathematics, 12 151-169. May. 1981.
[18]	Toulmin, S. The Uses of Argument, Cambridge University Press, Cambridge. 1958.
[19]	Vygotsky, L.S. “The genesis of higher mental functions.” In J. V. Wertsch (Ed.). The concept of activity. Armonk, New York, 1981, 144-188.
[20]	Watson, A. and Mason, J. “Extending example spaces as a learning/teaching strategy in mathematics.” In Proceedings of the 26rd Conference of the International Group for the Psychology of Mathematics Education, PME, Vol. 4, 378-385, July, 2002.
[21]	Zaslavsky, O. “Open-ended tasks as a trigger for mathematics teachers’ professional development.” For the Learning of Mathematics, 15 (3), 15-20. March. 1995.
[22]	Zaslavsky, O. and Shir, K. “Students’ conceptions of a mathematical definition.” Journal for Research in Mathematics Education, 36 (4), 317-346. July. 2005.