Civil disagreements with Lynne Varner and Bruce Ramsey, members of the Seattle Times editorial board is a weekly feature of the Ed Cetera blog. Bruce and Lynne often disagree on major issues. Here they take on the fight in the Seattle Schools over which high-school math books to buy, which is partly an argument about how to teach math.

Bruce Ramsey: Lynne, the Seattle Public Schools are on the verge of choosing a new set of math books for high school. This is the great chance to junk the “reform math” and get back to the real thing. Given the choice they have, I’d go with the Prentice-Hall books, and not the “Discovering” books, by Key Curriculum Press, that the district wants.

Part of the “reform” math is jettisoned either way. That’s the “integrated” part, which means mixing together algebra and geometry, and jumping back and forth in a system called spiraling. My son had that approach in middle school in the Integrated 1, Integrated 2, Integrated 3 books, and he said it was chaotic. Both of the new series—Discovering and Prentice-Hall, are single subject: Algebra One, Algebra Two, and Geometry. That’s better.

But the Discovering books keep the “reform math” method of inductive learning and group learning. For example “Discovering Geometry” introduces the student to isosceles triangles by having him draw an angle on paper, select a point A on one of the rays, then fold the paper so that the rays match up, and select a point B under the point A. Then draw a line from A to B, completing a triangle. Then the book says to measure the angles inside the triangle at points A and B. “What relationship do you notice?” it says. And it says, “Compare results in your group.”

What Discovering wants you to discover is that the two angles are the same; try it again with a different starting angle and find that the two derived angles are the same again; and you come to the conclusion that when two sides of a triangle are the same, two angles will be, also.

Maybe it will take you half an hour to do this, check your work and have a class discussion about it. Maybe it will take the whole hour. Prentice-Hall simply says it right up front: A triangle with two sides the same length is an isosceles triangle. And if the two sides are the same, the two angles opposite them will be the same, also. Prentice-Hall immediately goes on to prove that this is so. The Discovering book does not prove this, or any other theorem of geometry, until after page 690--practically an appendix.

Discovering is an inductive book, and Prentice-Hall is a deductive book. Induction is a fine method for history, but geometry is a deductive discipline and was taught that way for centuries, until the last few decades. Prentice-Hall’s deductive book strikes me as straightforward and logical: Euclid updated. Discovering’s inductive book strikes me as roundabout—a kind of math my son Morgan, a high-school senior, knows and detests. He calls it “bassackwards math.”

I’d go with Prentice-Hall.

Lynne Varner: Hi Bruce. On one small part we agree: the Seattle School Board should not adopt a math textbook tomorrow night. It is too divided over the Discovering math choice for anyone to trust that the decision will be implemented with the right amount of district support.

I've heard principals like the book. Teachers are all over the map about it. I seconded our editorial urging the board to back off any decision until they can justify it with a better reason than because something has to be done.

Something does. I won't go as far as you, Bruce, and pick a textbook. Too much money is at stake for a choice that, in my case, would be based on personal preferences rather than imperical knowledge about how high school students in Seattle learn math. Math instruction has been hijacked enough by the culture wars, I won't add a salvo.

Reformers and traditionalists alike wants students leaving school with strong math skills. We may like to pontificate over isosceles and equilateral triangles, but which textbook, given the right amount of supporting materials and teacher preparation, will help students learn geometry best?

The State Board of Education's recommendations cannot be discounted. But what I like about the Discovering textbook is likely what detractors hate about it. It is extremely dependent on supporting materials and instruction. It's success relies on a group, rather than solo, effort. If a textbook was meant to suffice alone, why send my child to school at all. Why not simply shut him in his bedroom with a Prentice-Hall textbook?
Guess I made a choice after all.