What a strange question to ask, especially on an MAA website. I hope it has attracted the reader’s attention and curiosity. The words of the title, in themselves, pose an important and controversial question, but the statement is not complete. The whole question is: "Do we teach too much mathematics but not enough about it?" In my experience, I have taught mathematics for over fifty years, covering a broad spectrum of people and situations: from pre-school to graduate classes and from intercity America to the rural compounds of lesser-developed countries. Always, I have been plagued by the students’ recurring questions—“What is this stuff good for?” “When will I ever use this?”—and still further perplexed by an adult’s apologetic confession that he or she “never liked mathematics and was confused by it.” Elementary school teachers, if given a choice, will opt out of teaching mathematics in favor of other subjects. Mathematics has a bad reputation! This negative situation seems universal.
In attempts to isolate and remedy these situations of frustration, I have come to believe that the fault most often can be found in the ways we teach mathematics. Too often instruction consists mainly of sequences: concept, exercises, repeat; or definitions, algorithms, practice, test. Teach the mechanics—impart the skills. I know, I’ve been there, we must get through the syllabus! But mathematics has a story to tell; it has a structure, a history and a purpose. All these factors, if recognized and acted upon, do in fact lead to better appreciation and understanding of the subject and eventually to an improved student performance. However, most often, they are neglected or minimized. Better teaching would stress the affective aspects of mathematics teaching and learning—what we might call ‘humanizing mathematics’, that is, better exposing and building upon its historical, societal and cultural connections. We might also think of this as ‘doing a better job of selling the subject', thus responding to the complaint: "What is this stuff good for?”