The Importance of Mathematical Wording by Math Instructors

Abstract

At times we the math instructors in a classroom are not careful enough to use proper Mathematical wording, e.g. sin + cos = 1 without any reference to the angle. Improper Mathematical wording can be confusing to a student at any level, especially at high school and/or at a college freshman or sophomore level. It may hinder the students’ progress in the present and the subsequent math courses. Through our years of teaching, we have seen students struggle with many mathematical concepts. Oftentimes this difficulty does not arise with a lecture topic, but rather with the language and terminology that some of their previous teachers have used. (At times, most of us are guilty of this too.) In this paper we first discuss some examples of mathematical wording that can be confusing to students and then supplement it with worksheets in Appendix A that contain activities to substantiate the ideas discussed in the body of this paper. These activities can also be used in a classroom by an instructor as guided activities making students to do the work and the instructor to guide them along the way if and when help is needed by a student(s). As our first example, when the concept of vertical asymptotes and the method of how to find them is introduced, an instructor may say “If an x-value makes the denominator of a rational function zero, then the function has a vertical asymptote at that x-value.” The teacher may forget to add that it is true ONLY when the rational function is in the reduced form. For example, the function has only one vertical asymptote, x = 2, as it contains a removable discontinuity (a hole in its graph) at x = –3. We have encountered many students who have had a difficult time in recognizing when the graph of a function has a hole instead of a vertical asymptote. This is compounded by the fact that they do not see a hole in the graph when they use a graphing calculator to graph the function. Moreover, they have become accustomed to the above language and expect a vertical asymptote at x = –3. Another example is when we examine the special case of 0/0. As early as elementary school, students are told that “zero divided by any number is zero.” We think it is probably alright at that level, however, sometimes the 1 Goel and Reid: The Importance of Mathematical Wording by Math Instructors Published by Digital Commons @ the Georgia Academy of Science, 2012