### The term ahead

Headed over to the island yesterday to get my teaching schedule, find a place to live, and to touch base with the other instructors. Succeeded on two and a half of those counts: most of the other instructors weren’t around, but I am allowed to work rather autonomously anyway, so I’m not terribly worried. I shall spare you the details of the apartment-finding process is one I shall spare you, save to say that it resulted in me finding an apartment and was therefore worth the encounters with crazy landlords, the “oh, no one told you we’d rented that place out a month before you phoned us?” waste of time, and the broken-down car. I have an apartment. Furnished, above ground, and cheaper than the one I’m in now.

I got my hands on the two textbooks I’ll be working with. The precalculus one is shrink-wrapped, and I haven’t opened it yet, because precalculus textbooks are like mint-condition comics, though the reason they depreciate as soon as you open them are different. The finite mathematics text is Sullivan and Mizrahi’s book of the same title, and I hate it already. The first section leads the hapless reader through a ten-page song-and-dance about how to graph a straight line, complete with the now-ubiquitous sidebars exhorting students to *get out their graphing calculators* and see for themselves what the graph of 2x+3y=6 looks like. I weep. I reckon the authors are being paid by the word (with the word-equivalence of the pictures computed as per usual); how else to explain the ten-question symposium on how to compare rental-car rates, or the section devoted to families of lines passing through a single point? Really, WHY? I read through the thirty-five-odd pages on line-graphing, and by the time I was done, I no longer understood the concept. The authors, sadly, seem to have bought into the idea that the more little tricks students have to remember, the better they’ll understand the material. Hogwash. I’ve had far greater success - both in teaching and in learning - figuring out how to motivate the material, and stopping short of the rules and mnemonics that treat half a dozen almost-identical cases separately.

Anyway, it’s a pity, because the last month of the course is probability, which is fun and relevant, and there are some business and economics applications pertaining to matrices sprinkled throughout the book, but the first month seems to be designed with the intention of losing everyone. I remember questions like the ones in the first chapter: questions I’d been able to solve ten years before, and ones that hardly lent themselves to the tools presented in the chapter. One imagines the authors agonizing over the layout of the text:

“Applications; we need *applications*! I know - you *could* use linear algebra to compute the number of ten-cent cups of lemonade Little Suzy has to sell in order to recover the $1.50 she spent on the can of Country Time mix!”

“Hey, and what about if the cost of paper cups goes up! Or if half of the lemonade spills? I think you’re onto something!”

Point is, I have the freedom to teach as I see fit, using the textbooks as much, or as little, as I want. Needless to say, I’m gravitating toward the latter. I plan to incorporate a lot of stuff about estimation into my precalculus class, as too many students are graduating from university (well, from high school) with no concept, let alone motivation, of how to figure out if their answer makes sense. Distance travelled in ten seconds by a car starting from rest and speeding up to 20 m/s? One kilometer. Or negative eight meters. Which leads to law students, like one I met last year, accepting uncritically “statistics” such as the one revealing that twentysomethings’ income has declined by 95% over the last two decades. 95%! In two decades! (”Are you denying the *facts*?” he asked me when I, well, apparently denied them.)

My question for y’all: can you recommend any good supplementary texts, or other books, for precalculus and discrete math classes? For the latter, I’m planning to use John Allen Paulos’ Innumeracy for real-life examples involving probability and the consequences of trusting intuition. His *A Mathematician Reads the Newspaper* might be worth dusting off as well. Any other suggestions?

Precalculus is a bit more difficult; Amazon.com lists 933 books under a search of the term, and unless the field has been revolutionized recently, they’re very similar. Still, I’d love to hear some ideas.