I read this article on cnn’s website today. It’s about how parents today are often rebelling against the new constructivist math programs (TERC, Chicago Math, etc) that have taken over the elementary (and some middle) school’s math curriculums by teaching them traditional problem solving skills like long division.
As a former math teacher, I have been preached to by both sides of this war, and believe me if you think the parents are up in arms, you should see the behind the scenes wars carried out in Math Department meetings.
I am a firm traditionalist, which puts me in a solid minority—the ones who admit it. Most math teachers I know are, to some degree, supporters of traditional math at least some of the time. But because the schools we teach (in my case taught) for effectively gagged us, we taught the traditional math furtively with a worksheet here or a side note (here’s one more way to do it) there.
As I contemplate Emby’s education, which as the child of two parents who view education as their only religion, I have no guilt and no hesitation over stating now, when she still has 16 weeks until she’s born (as of midnight) that she will be getting traditional math every day at home.
As a middle school teacher, few things pissed me off more than getting “advanced” sixth graders who didn’t know their times tables. Who couldn’t divide to save their lives. Who had gotten straight A’s from the constructivist program, but were going to get nowhere in Algebra without serious review. I spent every September each year doing review and basic curriculum to get them ready for the exam that would determine if they would be admitted to the exam schools in Boston—things they SHOULD have known by sixth grade.
I then had to teach elementary school for the last two years and I got down and dirty in constructivist curriculum…and it only made me hate it more. Not because I didn’t understand it–I’m a solid math student and teacher, but because giving students three approaches to learning multiplication in three days only confused them, and that the curriculum expected it and said “hey, that’s cool, they’ll get it again next year, so move onto this other topic” convinced me beyond a shadow of a doubt that it is harmful and wrong.
Why is it wrong to do constructivist approaches for 8 years? Because they don’t do it AT ALL in high school. There is no way to do a constructivist approach to teaching Calculus. To understand why Calculus works, you need to know HOW TO DO CALCULUS, which is why it’s a very advanced math course that you can’t take at MIT until you’ve taken something like 3 or 4 other Calculus courses. The same, at heart, is also true of advanced Algebra. Doing proofs is learning the why’s of Geometry, but if you are faced with a Geometry problem, you need to have your formulae memorized and ready to go.
I see the constructivist approach as working for some kids (and hey, maybe Emby would be one of these…but I doubt it) but generally it’s something that should be used in a supplementary capacity for a kid who isn’t getting it.
Honestly, it’s times like this that I think putting my Master’s Degree in Education to it’s best use will mean homeschooling my kids.
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July 21, 2008 at 7:30 am
Brian
I think you are pretty much right on. On the other hand, of course different approaches to any problem are better than just one. But that’s not really what “constructivists” do. They seem to “teach” nothing. Different methods are not necessarily the problem, it’s that some people seem to think they are “magic.” Like if you just expose children to them, they will “get” it. It’s like you said- “giving students three approaches to learning multiplication in three days only confused them” It’s the limited time, and the limited expertise of the constructivist, (and of course, the fact that programs like TERC are just stupid).
The false dichotomy of “traditionalist” verses “progressive” is never helpful, though. If you find something that works, hammer away at it. For example, the “standard” algorithm for multiplication is not “standard” in some countries that blow our doors in with math. There are much better algorithms, but they have to actually be taught, not just by show-and-tell, and not by some pie-in-the-sky “reformist.” And these algorithms are more helpful in high school than the “standard.”
If I may be so bold, may I refer you to The Math Mojo Chronicles” for a post about this issue?
I think if we had teachers like yourself using some time-tested methods like Trachtenberg and others (not for everything, of course), our kids would probably get more “juice” out of math then if they had decades of “constructivist” pap. Your frustration with “advanced” kids who didn’t know squat should be universal. How in the name of education can schools do that to kids? It’s like selling them a car as a “brand new Ferrari” and giving them an Edsel. When they find out they’ve been cheated, they’ll resent Edsels and Ferraris, and they absolutely hate the salesmen.
Keep fight it the good fight!
– Brian (a.k.a. Professor Homunculus at MathMojo.com )
July 23, 2008 at 2:49 pm
dobeman
Ha! I read the article too, and I do it the old fashioned way. Truly, I read their description of how the “new math” teachers do it, and after about the fifth step, I was completely lost!
My problem with this all is, if you’re going to give kids 2-3 hours of homework a night, parents should be able to help where possible. Teaching this new process exclusively means parents either have to learn it themselves, or they end up looking dumb in front of their kids.
July 23, 2008 at 11:30 pm
whenwillitbemyturn
Brian–I agree that it’s a false dichotomy. In a truly great math program kids would get an approach that makes sense to them, AND that will serve them in the future. I totally agree that some combination of the two could work, with the constructivist serving as a supplement or alternative approach for kids who don’t easily understand traditional math. I’ve seen it be helpful. But lack of depth in these constructivist approaches just make it all that much worse. How do expect a kid to learn how to multiply large numbers in a week or two and then move on? What ever happened to practicing skills? Why am I teaching third graders to find a mean when they can’t really divide, and the program doesn’t expect the skill to be mastered until 5th or 6th grade???
Dobeman–some schools offer support to parents, but it’s usually two or three nights in a year…not enough to fully teach the parents how to do the math their kids are doing. And without support, many kids will stumble. I had a lot of trouble in upper math because my parents had never taken it and I was on my own. But by 15 I understood how to self-advocate, ask for help, and where to look to get it. It’s an absolute joke to think that your average seven or ten year old is that mature or self-actualized.
July 31, 2008 at 7:48 pm
Brian Foley
I’m in total agreement. It’s not that “constructivism” per se is wrong, it’s just that if you don’t provide the time, expertise and resources to take advantage of it, you should stay away from it.
It drives me nuts when I give school or afterschool programs about math, magic and meaning, and a teacher says, “Oh, yeah, I already know that stuff. I’ve taught it to the kids.”Of course the kids don’t have a clue about it. That’s another problem with our schools, most often we teach by show-and-tell, and you can’t get any depth that way. We teach “about” something, rather than teaching the thing itself.
At any rate, I really like your post and your blog, and am about to social-bookmark it on about 20 sites. People ought to know about it.