But perhaps, like me, you still want a textbook to offer your students as a one-stop resource for the material you'll be thinking together about in the course. For me, the most important function of the textbook is providing homework problems for my (college) students to use to practice. I also want the mathematical progression of ideas to be recorded somewhere that the students can easily access.
So what makes a good textbook?
At the least, it needs to:
- do the math properly,
- be written in good pedagogical style,
- provide problems that progress from simple (so the students who want to learn the ideas through the problems can) to deeply thought-provoking, including problems that address whatever twists and turns can come up with the material.
- ?? (What other criteria would you add?)
I told my pre-calc students I'd help them get print copies of one of the open source books I listed, with just the sections they'll need included. But I'm not particularly happy with either one. One thing I do like is that the personalities of the author teams shine through in both of them. (1 pedagogical point earned.)
Here are a few of the things I noticed:
Stitz and Zeager seem to be going for better mathematical reasoning than the commercial textbooks. On page 11:
... the distance formula. Mostly I like what they're doing here. (Many texts treat it as separate from the Pythagorean theorem, which makes me cringe.) But I would not ask 'Do you remember why ...' here. I'd ask if they know why, understand why, or can figure out why. Remembering is for factoids, and why questions should not be thought of as having that sort of answer. I'm reminded of my post on teaching for understanding. Just as the word 'understand' can have deeper and shallower meanings, so can the word 'why'.
Also the use of 'extract' is a bit archaic. It refers to the process used before calculators (bc?) for finding square roots. Nowadays we 'take' the square root of both sides.
Lippman & Rasmussen are probably less likely to include an archaic term like 'extract', but they have other problems. On page 158, in a list of 6 vocabulary words referring to polynomials, they include:
A term of the polynomial is any one piece of the sum, that is any aixi. Each individual term is a transformed power function.
Does 'piece' do anything to define 'term'? When I'm teaching, I sometimes say 'chunk' myself, but I think we do this because we see the terms as standing separately. Our students don't yet see that. So I try to always add in something more helpful like 'terms are separated by a plus or minus'. If you're going to define things in a math book, your definition must give more information than the original word did. 'Any aixi' does that, by example, but a definitional phrase would be helpful.
On the next page, they say:
For any polynomial, the long run behavior of the polynomial will match the long run behavior of the leading term.They give no indication of why this is true. I do not want to encourage students to think of math as a bunch of little bits and pieces strung together with no rhyme or reason. Really, it's just the opposite - one huge coherent edifice, full of beauty and mystery. I want students to try to figure out things like long run behavior, based on what they already know.
From the little bit of checking I've done, I'm guessing I prefer having students use the Stitz & Zeager, even though the Lippman & Rusmussen may have more cool problems. I like how Stitz and Zeager write, and the feel they give is usually one of reasoning things out. I'll go with it, and maybe I can send them my suggestions for improvements. (Yeay for open source.)
Thinking about all this makes me want to write my own textbook. That's probably way more work than I want to take on, but I do like writing about math. Maybe some day...