March 2010, Vol. 41, Issue 2
Nonstandard Student Conceptions About Infinitesimals
Robert Ely
A
case study of an undergraduate calculus student’s nonstandard conceptions of
the real number line. Interviews with the student reveal robust conceptions of
the real number line that include infinitesimal and infinite quantities and
distances. Similarities between these conceptions and those of G. W. Leibniz
are discussed and illuminated by the formalization of infinitesimals in A.
Robinson’s nonstandard analysis. These similarities suggest that these student
conceptions are not mere misconceptions, but are nonstandard conceptions,
pieces of knowledge that could be built into a system of real numbers proven to
be as mathematically consistent and powerful as the standard system.
This article is available to members of NCTM who subscribe to
Journal for Research in Mathematics Education. Don't miss out—join now or upgrade your membership. You may also purchase this article now for online access.
Log In/Create Account
Purchase Article