I love old books, especially textbooks and particularly math textbooks. RightWingProf’s post here explains why, as he walks us through a page out of his old high school algebra textbook.

The excerpts in his post are typical of a lot of older high school texts in math. The language used in the problems is standard grade-appropriate English which a lot of students today, college students included, would be hard-pressed to understand on first reading. They problems don’t shy away from fractions or inconvenient numbers. (Why do so many high school math books these days think they’re offending somebody if they use the number -175/33 as an answer?) And, perhaps surprisingly, the problems are firmly rooted in practical applications and demand a lot of what I would call critical thinking from students. (Look at Exercise 13 at Prof’s post.) Somehow one might expect older books to be more theoretical and less practical, but actually the opposite was the case.

I tend to think that the information source you use for a class — whether it’s a book or some other selection of resources — will set the expectations for student performance in the class. I’ve been involved with the selection of textbooks for courses, and done reviews for several textbooks, and too many of them these days treat the students as if they were 8-10 years younger than they really are, which is dangerous.

**Update**: Via Myrtle’s blog, here’s a schedule for her use of this book in teaching her son algebra. Check out those topics! You won’t find those in most Algebra I books these days. She’s using this book along with Gelfand‘s algebra. Ambitious plan; lucky kid.

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Very good point. So true.

We are using that text with our son. I recently did a similar blog entry for the Algebra II text by the same author not so long ago. It is interesting to note how quickly the kiddies are moved along in terms of sophistication of language and terminology. The sample lesson I have is the introduction to logs.

From what I understand of the Algebra I book that RWP didn’t say, is that Allen states the 11 properties of a number field, along with some ordering properties and then proceeds to use those to prove about 40 different theorems in algebra. He transitions the students from supplying the justification of the steps, to supplying the entire proof. In the algebra one book they are two column, in the algebra two book they are to be written in paragraph form in a combination of prose and symbol.