corporate textbooks and algebra

I read an NYT article about Connecticut schools taking Algebra I online and throwing out the 1000-page textbooks that dominate high school mathematics these days. This is a very good idea. Perhaps it is time to start counting the pages of math texts, or any text, in self-defense.

(Right: a page from Euclid's classic text which ran 13 books; no known page count.)

I tried tutoring high school math one of these dinosaurs and they truly get in the way of their subject. Does it really take 180 lesson days to cover algebra 1 or are we filling time because we have it? Do we even know the core content anymore? After the fun of doing good problems in Singapore's texts, the whole pedagogical enterprise of massive corporate texts seems useless.

WESTPORT, Conn. — Math students in this high-performing school district used to rush through their Algebra I textbooks only to spend the first few months of Algebra II relearning everything they forgot or failed to grasp the first time.

So the district’s frustrated math teachers decided to rewrite the algebra curriculum, limiting it to about half of the 90 concepts typically covered in a high school course in hopes of developing a deeper understanding of key topics. Last year, they began replacing 1,000-plus-page math textbooks with their own custom-designed online curriculum; the lessons are typically written in Westport and then sent to a program in India, called HeyMath!, to jazz up the algorithms and problem sets with animation and sounds.

“In America, we run through chapters like a speeding train,” said John Dodig, the principal of the 1,728-student Staples High School here. “Schools in Singapore and India spend more time on each topic, and their kids do better. We’re boiling down math to the essentials.”

The entrenched attitudes of textbook companies is indicated in the article by the stated reduction of a textbook from 1000 pages to 800 pages. An 800-page text for high school algebra, first part only, is absurd.

The makers of modern mathematics learned mathematics in substantially fewer pages. Precalculus mathematics alone in most high schools means 4-5 of these 1,000 page beasts. For a truly concise book, by a university professor, look at Precalculus Mathematics in a Nutshell (from the intro):

"Contrary to popular opinion, precalculus mathematics is not a shapeless mass that no one can hope to master. This clearly written book pulls together the essentials of geometry, algebra, and trigonometry in one clearly written and accessible volume, showcasing each subject in its own chapter with readable explanations, exercises, and fully worked-out solutions. When read as a whole, the book provides a thorough analysis of all three subjects; but each subject can be mastered independently from the others. " 119 pp.

This book, which includes exercises, comes to a total of 119 pages for all of precalculus mathematics. That's algebra 1 & 2, geometry, and trigonometry which in the corporate text version would be about 4000 pages.

So add some really good problems to do for fun. Another 200 pages of problems would make 319 pages of work.

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