Val,
Do you have some framework concepts like these that you've found useful in looking at math books?
Here's what I look for. I'd be very interested in learning about how anyone else approaches this task. In summary, I ask myself, "Does this book have ADHD?"
1. First, I look for distracting content. Distracting content includes irrelevant color photos, factoids in the margins, notes in the margins, "hints" and "tips" in the margins, and other margin content ("Go to...; "What you'll learn...And why," etc.). And colors. Lots of bright colors.
Examples. DD's (school)
Algebra[/i]-1/dp/0131339966/ref=sr_...=Prentice+hall+algebra+1] Algebra 1 book has 12 irrelevant color photos on pages 2-20. They include a girl climbing a rock, a guy who worked in a shoe factory in the 19th century (colorized to give him rosy cheeks), and a dude mowing his lawn. There's a "Real-World Connection" in the margin under the lawn mower photo. It tells us about the amount spent by Americans annually on lawn care. It's completely irrelevant, but it does make a good distraction for students who are bored with learning about what variables are.
There are also drawings of dollar bills and what appears to be a park (with a fountain!).
Alternatively, DD's (home)
Algebra 1 book (Richard Brown) has only 2 pictures on pages 1-20. Both are related to the word problems next to them. There is absolutely no content in the margins --- because the margins aren't wide enough for it.
We have an old copy of
Mary Dolciani's Algebra 1 book. Again, no content in the margins. Pictures are minimal and restricted to content between chapters, such as mini-biographies of mathematicians. The Brown book has these, too (Brown is a new edition of Dolciani's books).
Richard Rusczyk's
Introductory algebra book has no photos and no content in the margins, but there are drawings accompanying problems.
2. I look for actual text. Many modern textbooks skimp on explanatory text. All that stuff in the margins seems to be (IMO) an attempt to put prose into a sound-byte kind of format. Dolciani and Brown do the best job with the text, followed closely by Rusczyk. The text in the school's book is risible and limited to short paragraphs scattered throughout a section.
3. I look at the problems. Do they start easy and get harder? How many sections have a set of computational problems followed by a set of word problems? How often are you asked to write a proof from scratch? The problems in the school's book are mostly pretty same-y (forget proofs). They use what I see as tricks to make them "harder":
Simplify 2xyz + 4xy - 18zyx + 2xy. Basic variable expression problems in the other books are just...
harder because they're longer or have nested parentheses or whatever. No one is trying to trick you in the other three books.
4. Does the book toss out random concepts that are above the student's pay grade at that point and/or are off-topic? Or does it proceed in logical order from one idea to the next? Dolciani, Brown, and Rusczyk generally move in a logical way and go into depth. The other book tosses out random ideas and treats them superficially.
Examples. The school's book tosses out matrices on page 59 in a section on adding rational numbers. It provides exactly one sentence of information about them, unless you count the sentence that says, "The plural of matrix is matrices (pronounced MAY-truh-seez)." I don't count that sentence.
We return to MAY-truh-seez on page 79 and then meet them again on pages 394-5. Brown and Dolciani discuss them in depth in subsequent books. Rusczyk has a single problem about them on page 154 and a discussion of them on the next two pages. IMO, it's nice information but is maybe too much for someone who's supposed to be learning about solving systems of equations for the first time. But this is very different from the school's book's florid case of ADHD.
5. I look at layout. Is it easy to find my way? Do I know where I am? Brown wins hands down here. Sections always start on a new page and are clearly marked. The beginning and end of each set of problems is easy to see. Etc. Dolciani is second, with the school's book and Rusczyk coming in way below them. The school's book is just too full of distractions and is therefore beyond hope in this regard, whereas the Rusczyk book just needs (serious) help from usability guy and a typesetting/reformatting chick.
Okay, that was really detailed.
