Jargon Miscues a Student’s Mathematical Thinking in an Online Proofs Course: A Reflective Study of an Email Intervention

Abstract

An online intro-to-proof course provided an unexpected opportunity for a series of email exchanges that yielded insights into one student’s mathematical thinking and the ambiguous role of mathematical jargon in miscuing this student’s reasoning. The jargon deals with the notation $\underset{x\to a}{lim}f\left(x\right)$, which encapsulates multiple conceptual meanings: the process of taking the limit, the question of if the limit exists, and if the limit exists, its value. As a matter of jargon, the statement $\underset{x\to a}{lim}f\left(x\right)=L$ was used in context for L to retain these multiple meanings, so L no longer represented merely a value. In computational calculus, this is of no consequence but in a course involving limit proofs, it led to confusion.

KEYWORDS:

• Jargon
• miscue
• proof
• misconception
• limit
• intervention
• online

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Barry Cherkas

After 50 years of classroom teaching, Barry Cherkas tackled the challenge of moving his in-class proofs course online. He notes with delight that student evaluations of the online course get higher marks than the in-class course. This octogenarian supplements the recreations of his mathematical life with almost daily fun runs of mountain biking.