Friday, July 28, 2006

Bad Textbooks

I've been doing a little light reading on topology. The sort of stuff that I probably should have learned in any of the handful of topology courses that I took either as an undergrad or in grad school -- or just by osmosis. Before heading to the library, I first referred to my office bookshelf and its cache of textbooks from those courses that I took long ago and the textbooks I acquired when my previous job threatened to have me teach the geometry course when its long-term instructor went on sabbatical.

That gives me two classes of textbook: the real math books, densely packed with symbology, from my own education (things like Munkres or Massey) and an assortment of colorful texts with lots of exposition and context and plenty of white space, mostly designed for lower-tier math majors (such as "math for secondary ed"), and mostly written by people I've never heard of. (A third type of book is a single text in a class by itself: Henderson. I can not tell where it falls on the brilliant/insane spectrum. I can tell that it is not the sort of book that I'd just refer to casually: you need to commit to Henderson to get anything from it.)

With the real math books, I have trouble figuring out where to start reading. Everything is presented in a flat yet fiercely interconnected way, and I can't easily identify where to pick up the strand of what interests me. If I can find the start of the idea and track down the prerequisite concepts, I'm OK; the math is presented in a clear and compact manner.

The books meant for somewhat dim math majors? Oh my fucking word. Yes, they do a great job of chopping the material up into bite-sized pieces. With paragraph upon paragraph of English text, I can identify the motivation and the context of each topic and get a decent sense of the big picture. But the way they write about the math? I just sit there going "wtf, wtf, wtf?" I can not make heads or tails of it! I look at the diagram, re-read the sentence, and still have no clue why that could possibly be true or even what it means. No wonder the students struggle.