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Nonstandard Student Conceptions About Infinitesimals

Robert Ely 

March 2010, Volume 41, Issue 2, Page 117

Abstract:
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.

Keywords:
Case Study Methods
Calculus and Higher Level Mathematics
Curriculum Developer
Conceptual Development
Higher Education
Grades 9-12
Higher Education
Numbers and Operations