Last Tuesday I went to a public forum co-sponsored by a local activist group, Where's the Math?, and the Washington state PTA. (Though the PTA, through its executive director, Jean Carpenter, was careful to make it clear that it was not endorsing the group or the ideas presented in the forum.)
What I learned at the forum supported the opinion I had come to some years ago: Our math curriculum is mediocre, at best. As a result, our public school students are not learning the math they need for many occupations, or even the math they need to understand many public policy questions. The students who are hurt most are those with poor, or poorly educated, parents. Students whose parents have more resources can tutor them, or can buy extra help for their children at tutoring centers, such as those run by Kumon.
My understanding of this problem has come from reading; parents often come to the same understanding more directly, when they are shocked to find out what their children are studying, or, often, what they are not studying. That's what happened to Shalimar Backman, the remarkable woman who cofounded Where's the Math?, after learning that her son was not being taught how to do long division, or much else in the way of real mathematics. She was first shocked, and then mobilized, by what she learned about the math curriculum in her son's school.
Something similar happened to University of Washington Atmospheric Sciences Professor Clifford Mass when he saw how little his oldest son was learning. (As a good father, with considerable resources, he tutored his son, enrolled him at Kumon, and did everything else he could to make up the deficit in math. But not every child has a father who takes an interest in his schooling, much less a college professor father who takes an interest in his schooling.)
Given his own mathematical skills, it was only natural that Mass would want to measure what students entering the University of Washington knew. Fortunately, his department has been giving the same math test to entering students for years, and so he could compare scores for the last decade or so. Students coming to the UW have higher and higher grades, he told us — and lower and lower scores on that math test.
What caused this decline? Much of it was caused by the math curriculum used in Washington state (and in most other states). In 1989, the National Council of Teachers of Mathematics adopted a math curriculum based on "constructivist" ideas, which was soon widely used across the United States. Constructivist ideas seem, frankly, so bizarre to me, that I will quote a semi-official description of them, as I did in this post, rather than try to describe them.
Students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or otherwise attempt to 'transfer' mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions. A critical aspect of the approach is a decomposition of each mathematical concept into developmental steps following a Piagetian theory of knowledge based on observation of, and interviews with, students as they attempt to learn a concept.
Or to put it crudely, the students are to figure out thousands of years of mathematical ideas on their own, without much help from their teachers. That's a little unfair, but not entirely.
That's the bad news, but there was good news at the forum, too. Comparative international studies have shown that we can markedly increase what our students learn about mathematics just by changing the curriculum, which is far easier than changing the teachers or the schools. To change the curriculum, Washington state would have to pass a law, and the public schools would have to buy new textbooks. Neither would be terribly expensive, or difficult.
Tomorrow, I will have more on this forum, but now I have to go cover the immigration demonstration in Seattle.
Cross posted at Jim Miller on Politics.
(The constructivist approach should not be confused with an earlier fad, the new math, which was so memorably satirized by Tom Lehrer. In fact, some call the constructivist approach the "new-new math", just to avoid that confusion.)
Posted by Jim Miller at May 01, 2006 01:26 PM | Email ThisMy thoughts were that tells only part of the story, it should have gone on to say
* if you were ‘taught’ by a pathetic failure – thank the NEA.
* if you were forced to listen to some leftwing moonbat go on ad infinitum about the virtues of an economic model that is responsible for the suffering of hundreds of millions of people – thank the NEA
* if all you learned during your years in the ~ $10,000/year public education system is how to put a condom on a banana – thank the NEA
I’m sure that there are those who can do better than I have but this is just a start
... the PTA, through its executive director, Jean Carpenter, was careful to make it clear that it was not endorsing the group or the ideas presented in the forum.
Did the representatives of Wheres The Math? happen to mention if they were endorsing the PTA?
"People in this world who know math take money from people who don't know math."
*If you believe that there are no wrong answers, thank the NEA
*If your child missed class to participate in an anti-war demonstration, thank the NEA
If your child attended school for half the summer due to an illegal teacher's strike, thank the NEA
Wow! This is fun.
By the way, I'm a proud parent of a 13 year old daughter who is at highschool and college level in all of her subjects. She attends Pine Lake Middle School in Sammamish. Some public schools are doing it right I guess.
Posted by: Jeffro on May 1, 2006 03:48 PMThis penalized schools with AP classes and students who took harder classes. An A in a regular or easy class was given more weight than a B in an honors or AP class. At our high school it led to students who took easy classes for four years, and got mostly A's got accepted to UW, but those who challenged themselves didn't.
That is now changing. The admittance director has realized that someone who works hard in AP Calc and gets a B is a better student than someone who breezes through pottery class with an A.
I agree that the movement towards "discovering" math concepts needs to be tossed out. Bellevue has figured this out, and is revamping its curriculum. The comment that it takes a state law to do this is just wrong. Each district has the ability to set their own curriculum.
Frankly, I don't want a state law dictating the curriculum. Our schools (Bellevue) are better than others in the state, and I don't want them dumbed down in order to make everything uniform.
Posted by: Janet S on May 1, 2006 04:04 PMAfter someone has had to figure something out a few times, the person will likely recognize the situation if it reappears. Concentrated drill and practice may not be fun, but it does expedite the process. Attempting to perform long multiplication before learning the 9x9 'times tables' is not impossible, but is apt to be an exercise in frustration. Better to focus on getting the 9x9 tables learned as quickly as possible so that when doing long multiplication the partial-products will be known instinctively.
One thing that may sometimes be helpful is to let students know that certain collections of information are inter-releated; it's not necessary to memorize everything, but after deriving things that weren't explicitly remembered they may become second-nature. For example, much in electronics may be summed up by two equations: E=IR and P=EI. One may not remember that P=I^2R, or that I=E/R, but it's easy enough to figure out. Someone who uses electronics very much may not memorize all 12 of the formulae involving P, E, I, and R, but would likely remember all the ones that person uses regularly.
Posted by: supercat on May 1, 2006 05:02 PMMy friend's kid was entering middle school and I asked what the curriculum offered. I was dumbfounded when I heard. I told her that kids in third world countries get a better education. She told me that only Algebra is required to graduation from high school?!! When I was in school, I was forced to take Calculus; Algebra was taken in 7th grade. I also asked if the school had any AP classes, she said no, because no one could perform at that level; well duh, if you don't teach the kids the basics how do you expect them to do advanced work.
Another bit of evidence. Notice there are no schools from Seattle,only Bellevue. Go figure.
Newsweek
http://www.msnbc.msn.com/id/12532678/site/newsweek/
Finally, I've always wondered why the big companies in Seattle recruit so heavily from outside the state. I meet MBA's, Engineers, Scientists, etc. from every part of the nation except UW. Okay, maybe one or two, but that doesn't explain the masses of out of state professionals. I've meet one from U of Texas, two from Florida State, one from Tennessee and the rest from your assorted California and Ivy league schools.
The only conclusion I can come to is that UW grads are so ill prepared that companies have to look out of state for acceptable talent. This does not speak well for UW or Washington education.
Posted by: mobius on May 1, 2006 07:16 PMWhere is the uproar...?
If Bush had said something as...Young women are having difficulty in learning Math...we need to close this gap. It would be front-page headlines and the led story at 5:00, every PC pun dent would be asking for impeachment and his head on a platter!!!
Andy yous are right, if dares one thing a Bookie knows its math. Setting odds, trackin what is owed, running numbers yous name it, wid out math I am out of Biz, and believe yous me, dare are many saps out dare dat do not know de odds.
Forgetaboutit