CHAPTER 7: Mathematics as a Subject of Great Appreciation and Aesthetics

Something exciting is underway when it is difficult to label what one is observing with any known categories. This is the case with mathematics! Well, we might not think this way, depending on our personal experience with mathematics in school: the common experience of mathematics as an assemblage of hard-to-memorize procedures for manipulating meaningless symbols and even harder to remember facts without purpose is so prevalent in many cultures that school mathematics is routinely used as a definition of tedium, ennui, and a source of shame and indignation. School mathematics is typically accomplished, at least in the U.S., in the following fashion: the teacher checks on the understanding of the previous day’s lesson; the teacher then introduces a slightly new variation or addition to the previous lesson, moving students in a step-wise manner toward a comprehensive coverage of the month’s unit; students are given practice tasks to check their understanding of the day’s material, and work quietly in class on these tasks; students may then get a head start on the homework for the next day. This is usually a collection of many exercises that have the same structure as those practiced in class, so that homework is a “reinforcement” of that day’s material. Note that new material and homework in typical school mathematics is introduced and rehearsed in a manner that enables the student who is successful to passively experience instruction as easily understandable; the teacher’s job is to make learning as close to “not even realizing one is learning” as possible.