## February 16, 2006

### More on the CMP Math Curriculum

The problems with CMP go far beyond failing to reach parents. One big problem is that the edifice of mathematics is so huge. Think of how long it took mathematicians to discover all of it. When one tries to use the discovery paradigm as the sole model for math lessons, all of the time available is spent in discovery process of basic concepts. There isn't time for more than a cursory look at any topic. There isn't any work on hard problems related to basic concepts. There isn't time to master computational aspects of basic concepts. Everyone learns 1/2 + 1/4, but no one learns how to find the least common denominator of 1/14 and 1/35. The people who promote a constructivist approach to math set up a false dichotomy between traditional math which teaches one to memorize formulas and tables of computations, and discovery math which teaches one to really understand how math works. I actually had a TAG resource teacher say this to me very patronizingly. "We don't teach math anymore the way that YOU learned it. Now children really understand math when they learn it." Excuse me, but traditional math was never like that. Tradtional math presents concepts AND teaches understanding of concepts. One learns formulas AND why they work. One also does large numbers of progressively more difficult computations to become skilled at them. The problem with traditional math is that large numbers of students don't understand the concepts as presented and try to get by with memorizing and manipulating formulas which they don't understand. They also don't master the computational aspects and try to make up for this deficit by using calculators inappropriately.

When I was TAing calculus in grad school, a typical scenario would be the student who never understood the algebra lesson about what a logarithm is and tried to memorize the associated list of formulas to get by. Now here we are in logs again. The student doesn't understand the algebra of logs, misplacing minus signs willy-nilly, so is destined to fail at calculus. In addition he doesn't really have a good handle on the multiplication tables, so every example has to be presented sooo slowly for him to follow. Why does this happen? Well it may be that some kids don't have enough mathematical talent/interest to master the material, but I don't believe it. In countries like Singapore and my husband's native country of Finland, everyone learns this math and learns it pretty well. I don't believe the gene pool is so radically different there. I think it has to do with expectations and foundations. If you live in a culture where everyone knows math and expects everyone else to know it, people will learn it. Math is built like a brick wall, bottom up. You have to learn the foundations properly and well to get along well further on. At each step, mastery requires doing lots of problems until they are like second nature. Learning some fuzzy understanding of the basic concept doesn't cut it here. You have to do lots of problems. You have to work hard. You can't do trigonometry if basic calculation is slow and difficult. It's no different than athletic training. You don't go out and run a marathon without practice and sweat. The problem needs to be fixed at the elementary level and also in our society with its dysfunctional attitude toward math. I think the people who promote curricula like CMP see this as a way to reach the kids with low math skills. These kids can at least get some kind of tenuous connection to math this way. But it is absolutely hopeless as a preparation for rigorous college-prep math. Of course the way to cure that is, guess what, put discovery math into the college-prep courses since with CMP as a background the kids will never be able to master real math. At West the Algebra text has been replaced with Discovery Algebra, and soon, I believe, Geometry will follow. Check it out at www.keypress.com. Maybe I'm wrong. Maybe this math is the way to go for the non-mathematical kids. But then they should have an alternative curriculum for kids who really like math and expect to need it in their careers. This CMP stuff(along with Everyday Math) just makes kids who like math scream in agony. It's torture. If you have a kid who's managing fine in CMP, it's likely the teacher is heavily supplementing with outside resources. But of course they can't let the brightest kids go. It would be (gasp!) tracking, and in any case the lesson structure requires that the bright kids be there to facilitate success in the group and help others along. I recommend you save your \$30,000. Do not invest more money in this curriculum. It's just throwing good money after bad.

I know that the people who create and implement these curricula have good intentions. They want the kids to learn. I know they don't intend to pull the schools down. There's some kind of mass delusion that has infected the education researchers, and we have to deal with the consequences.

Full disclosure. We are a family of math nerds. My husband is a math prof at UW and I have a master's degree in math. I run a math olympiad group at my children's elementary school and assist in the classroom whenever the teachers can use my assistance. We do Singapore Math at home to fill in the gaps in school instruction and do math for fun at the dinner table. I just made the painful decision to move my soon-to-be-middle-schooler daughter to private school next year, in part (but only a small part) to avoid CMP.

Posted by Jim Zellmer at February 16, 2006 2:34 PM