What on earth is a straight line? What can we learn from an epistemological episode in eighth grade?

Johannes Paasonen

doi:10.7146/nomad.v2i3-4.146135

Authors

Johannes Paasonen

DOI:

https://doi.org/10.7146/nomad.v2i3-4.146135

Abstract

A detailed account of a spontaneous discussion in eighth grade of the nature of geometrical objects is given and related to constructivistic learning theory. The pupils were quite eager and able to discuss such subjects as infinity and more generally the process of abstraction inherent in geometrical concepts. Discussions of this type in class are advocated in order to encourage pupils to problematize concepts and procedures often regarded as self-evident, to spot and discuss pupils' misconceptions, and thus to attempt to raise the level of abstraction in mathematical communication and concept formation in class.

References

Caravita, S., & Halidén, O. (1994). Reframing the Problem of Conceptual Change. Learning and Instruction, 4(1). https://doi.org/10.1016/0959-4752(94)90020-5

Noddings, N. (1990). Constructivism in Mathematics Education. In R. B. Davis, C. A. Maher, & N. Noddings (Eds.), Constructivist Views on the Teaching and Learning of Mathematics. Reston, Va.: National Council of Teachers of Mathematics.

Paasonen, J., & Salmela, M. (1994). Introducing graphs of polynomial functions in lower secondary school with the aid of the graphic calculator. In M. Ahtee, & E. Pehkonen (Eds.), Constructivist viewpoints for school teaching and learning in mathematics and science. Department of Teacher Education. University of Helsinki. Research report 131.

Repo, S. (1992). Undervisning av begreppet derivata enligt den konstruktivistiska inlärningssynen. Nytt om data i skolan 1. Nordiska ministerrådets dataprogramgrupp.

Rowell, J. A., Dawson, C. J., & Lyndon, H. (1990). Changing misconceptions: a challenge to science educators. International Journal of Science Education, 12(2). https://doi.org/10.1080/0950069900120205

Schoenfeld, A. H. (1992). Radical Constructivism and the Pragmatics of Instruction. Journalfor Research in Mathematics Education, 23(3). https://doi.org/10.2307/749123