Friday, June 23, 2006

Math Curriculum Adoption

From what I heard at this week's Board meeting, the math curriculum adoption decision for middle schools is incredibly upsetting to many people.

Today's article in the PI, Schools move toward uniform math lesson, has some details.

Can anyone who has been involved in this issue either post comments here or send me some information to post?


Anonymous said...

I don't like reform math because I don't think it accomplishes the ambitious goal it aims for and leaves students without the more modest achievements that they really need.

I would say that math ability consists of three parts: understanding, knowledge, and skills.

The understanding element is all kind of conceptual, for example the idea that area is two-dimensional and volume is three dimensional so the volume of a cylinder is going to be the area of one of the circular ends times the height.

The knowledge part is largely rote memorization with a bit of conceptual understanding as a back up. For example, the formula for the volume of a cylinder is pi times the radius squared times the height. You might be able to figure that out from a solid understanding of the concept, but you'd have to both have an extraordinarily solid understanding and be pretty damn good at that sort of thing. Even still, you would have to know the formula for the area of a circle which simply is not obvious. The best way to know that formula is to just be taught the formula and remember it.

Math skills are just that: skills. Skills require practice. The best way to get good at calculating the volume of cylinders is to calculate the volume of about a hundred cylinders.

Reform math focuses on the concepts, provides none of the knowledge, and provides inadequate skill practice. I helped my daughter with her math homework almost every day this past year. Nowhere in her book are the formulas (pardon my failure to use the pretentious Latin plural ending for this word) for anything. I had to keep telling her over and over again the formula for the area of a circle, the formula for the volume of a cylinders, cones, and spheres.

She's a bright girl, but there is no way that she - or great majority of students in her class - could deduce these formula for themselves, yet, astonishingly, that was the expectation of the textbook writer.

The writer did leave a "trail of breadcrumbs" that might lead a student to a solid understanding of the concept, but that trail is a whole lot easier to follow when you already have the knowledge.

So I see the noble goal of reform math is to outfit students with a profound understanding of the concepts so that they could figure out the formulas. That would be great. But if the students fall short of that ambitious goal they have nothing. Whereas if the students were given the knowledge they could do the practice to gain the skills. Then, once they have the knowledge, I think it would make the concepts more accessible. I think that the knowledge should come first, then the practice, then we can show them (or guide them to discover) the concepts. For example, I provided the formula for the volume of a cylinder above. Can you see that it consists of the formula for the aread of a circle (pi times radius squared) times the height? And once you see that in the formula, isn't it easier to understand it as a concept? Doesn't it at least support your efforts towards understanding? And - most important - even if you never achieve a profound understanding of the relationship between two dimensional area and three dimensional space, at least you can competently calculate the volume of a cylinder.

Reform math doesn't work because it neglects two of the three critical elements of math ability. It leaves out knowledge entirely and skimps on the skill-building practice.

Beth Bakeman said...

For those of you, like me, who want to learn more about math in our schools, there have been many Seattle Times letters to the editor on this issue recently.(http://archives.seattletimes.nwsource.com/cgi-bin/texis.cgi/web/vortex/display?slug=sunlets18&date=20060618&query=math)

Specifically, regarding the curriculum the Seattle School Board just adopted for middle school, there is an interesting article about the Olympia School District putting the same decision on hold. (http://www.theolympian.com/apps/pbcs.dll/article?AID=/20060523/NEWS/60523003)