From the table of contents of a precalculus text – written by the same three folks who wrote the piece of shit I’m valiantly trying to teach from – that I’m using for supplementary examples:
1. Functions, Graphs, and Models….1
1.1 Using graphing utilities…2
Page 2! They really cut to the chase, don’t they? The good people at Texas Instruments, along with their shareholders, must be very pleased. Anyway, let’s see what the book has to say about functions, starting on page 1. In full, emphasis added:
THE FUNCTION CONCEPT IS ONE OF THE MOST IMPORTANT ideas in mathematics. The study of either the theory or the applications of mathematics beyond the most elementary level requires a firm understanding of functions and their graphs. In the first section of this chapter we discuss the techniques involved in using an electronic graphing device such as a graphing calculator or a computer. In the remaining sections, we introduce the important concept of a function, discuss properties of functions and their graphs, and examine specific types of functions. Much of the remainder of this book is concerned with applying the ideas introduced in this chapter to a variety of different types of functions, as is evidenced by the chapter titles following this chapter. Efforts made to understand and use the function concept correctly from the beginning will be rewarded many times in this course and in most future courses that involve mathematics.
So, in other words, we’re going to put the cart right here, and leave the horse six time zones behind us. But don’t worry, in Section 1.2 we’ll get to meet the horse. Isn’t that exciting? In particular: note the conspicuous absence of, oh, say, the definition of “function” from the entire introduction of Chapter 1; note also the lack of references to, for example, a single instance of what we might be using functions for. All we know so far is, they sure are useful! And we can use computers to study them!
In the sidebar is a list of topics that students are advised to review – yes, I’m laughing too – before delving into the useful, rewarding, and tech-savvy world of functions; but then, we’re done with that intro, and we turn the page to learn that
[t]he use of technology to aid in drawing and analyzing graphs is revolutionizing mathematics education. Your ability to interpret mathematical concepts and to discover patterns of behaviour will be greatly increased as you become proficient with an electronic graphing device.
Makes you wonder what people did before there were graphing calculators. I imagine my parents and grandparents sitting around in caves, clad in fur, with fires burning in front of them, etching misshapen circles in the mud with sticks. The same circles, every goddamned time, because they couldn’t discover patterns of behaviour from one circle to the next. And forget parabolas! But then, along came graphing calculators, and God Himself smiled down upon the mathematics classroom.
Honestly, this is delusional. The bulk of my students come to me “proficient with an electronic graphing device”, and their mathematical skills end right there. They don’t use their calculators to help them graph functions; they use them as an excuse to whine that I make them graph functions by hand. They don’t find patterns; why would they? they have machines for these sorts of things.
I have yet to hear of a single mathematics educator, save an author of the new edition of a textbook – now compatible with the latest graphing utilities! – whose experience differs from mine.