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Shipman, Barbara A.; Shipman, Patrick D. – PRIMUS, 2013
We study situations in introductory analysis in which students affirmed false statements as true, despite simple counterexamples that they easily recognized afterwards. The study draws attention to how simple counterexamples can become hidden in plain sight, even in an active learning atmosphere where students proposed simple (as well as more…
Descriptors: College Mathematics, Undergraduate Study, Mathematics Instruction, Misconceptions
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Shipman, Barbara A. – PRIMUS, 2013
Traditional definitions, language, and visualizations of convergence and the Cauchy property of sequences convey a sense of the sequence as a potentially infinite process rather than an actually infinite object. This has a deep-rooted influence on how we think about and teach concepts on sequences, particularly in undergraduate calculus and…
Descriptors: College Mathematics, Mathematics Instruction, Mathematical Concepts, Undergraduate Study
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Jorgensen, Theresa A.; Shipman, Barbara A. – PRIMUS, 2012
This paper presents guided classroom activities that showcase two classic problems in which a finite limit exists and where there is a certain charm to engage liberal arts majors. The two scenarios build solely on students' existing knowledge of number systems and harness potential misconceptions about limits and infinity to guide their thinking.…
Descriptors: Majors (Students), Liberal Arts, Class Activities, Learning Activities
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Shipman, Barbara A. – PRIMUS, 2012
Differences in definitions of limit and continuity of functions as treated in courses on calculus and in rigorous undergraduate analysis yield contradictory outcomes and unexpected language. There are results about limits in calculus that are false by the definitions of analysis, functions not continuous by one definition and continuous by…
Descriptors: Comparative Analysis, Calculus, Mathematics Instruction, Undergraduate Study