I share the basic concern about the quality of K-12 math education with the author of this article, but that article itself is a mess and hardly serves as a clear description of the state of things.
The author keeps wanting to conflate constructivism with postmodernism and multiculturalism and everything else bad under the sun, and in so doing none of the -isms he bandies around have any meaning at all. (How postmodern!) Constructivism is a particular approach to mathematics pedagogy that does in fact have its place. You don't have to be a tree-hugging peace-sign-wearing tofu eater to be a constructivist, and it's not a religion that must be adopted all or nothing.
And statements like this make me wonder if the author really understands what preparation for college really entails: "Integrated math has students using calculators in the early grades instead of having them master the basic math tables." Huh? "Basic math tables"? Does he think that I (as a college prof) want students who can recite trig and log tables from memory?
I'd advise the author to take a few deep breaths, talk to some college profs, and try again.
Texas is now mandating a graduation plan called "Four by Four" which means four science and four math classes for next year's incoming freshmen classes. On paper, it looks good. That is all of course based on the assumption that all kids can "do" this work. All kids can't I have kids now who are taking Algebra II for the second or third time. I have kids who are taking Chemistry for the second time. And they are seniors. While it's nice to think we can make all of these kids pass these classes, I anticipate that some will repeat once, and fail, and then drop out. Perhaps years down the road things will change, but let's face it, there are some kids who are just not ready to do anything beyond concrete reasoning. They are the reason the Jackass and Jack Black movies continue to rule the box office. Is this a good trend? No, but the alternative under current rules will mean that the teachers and districts will end up punished despite pulling all stops to get kids to be successful when the kids fail and drop out. That will lower AYP, districts will lost money and teachers will lose jobs despite their best efforts. Is this any way to encourage success? And in the meantime, how about the numerous kids that can't read and write? Or the ones who don't know ANYTHING about history? There's a link on my website to a blog at our local paper.
Based on my experience with constructivist math in the elementary schools (and beyond), I think "basic math tables" refers to a multiplication table.
When my daughter was in 8th grade, I had the opportunity to test the students on their knowledge of the multiplication tables. When a problem was difficult, the strategies I would see employed were skip counting and doing a nearby multiplcation and adjusting. They were tested through 12 x 12. I forewarned the students and told them if they were having trouble I wouldn't "hit them" with the same/similar problems over and over if they were having problems in a particular area. The following incident occurred multiple times on the x12's. The students would do fine with 1x12, 2x12, 3x12 and 4x12. When they got to 5x12 many would start struggling. I would see skip counting going on many times, but probably due to nervousness they struggled. I would suggest the following for 6 x 12...
Do you know what 6 x 10 is? The would answer 60 quite easily. Do you know what 6x2 is? Once again they would answer easily, 12. ... and 60 + 12 is?? And they would answer 72. For at least 50% of the students that were struggling, you could see their eyes light up. When other x12 problems occured, you could "see" them doing the calculations in their heads.
The students had never been taught the disbributive property of multiplcation. Why not? Because they were supposed to figure it out for themselves, and of course, then they wouldn't know it was the "distributive property".
My oldest daughter in now taking geometry. The teachers don't lecture. I don't get it.
What worries me is that when the chance to change things pops up in legislatures or on school boards, the decisions are made by people who weren't good at math. So they tend to go easy on the *poor kids* or think that some new "fun" teaching scheme is going to make it all better.
4 comments:
I share the basic concern about the quality of K-12 math education with the author of this article, but that article itself is a mess and hardly serves as a clear description of the state of things.
The author keeps wanting to conflate constructivism with postmodernism and multiculturalism and everything else bad under the sun, and in so doing none of the -isms he bandies around have any meaning at all. (How postmodern!) Constructivism is a particular approach to mathematics pedagogy that does in fact have its place. You don't have to be a tree-hugging peace-sign-wearing tofu eater to be a constructivist, and it's not a religion that must be adopted all or nothing.
And statements like this make me wonder if the author really understands what preparation for college really entails: "Integrated math has students using calculators in the early grades instead of having them master the basic math tables." Huh? "Basic math tables"? Does he think that I (as a college prof) want students who can recite trig and log tables from memory?
I'd advise the author to take a few deep breaths, talk to some college profs, and try again.
Texas is now mandating a graduation plan called "Four by Four" which means four science and four math classes for next year's incoming freshmen classes. On paper, it looks good. That is all of course based on the assumption that all kids can "do" this work. All kids can't I have kids now who are taking Algebra II for the second or third time. I have kids who are taking Chemistry for the second time. And they are seniors. While it's nice to think we can make all of these kids pass these classes, I anticipate that some will repeat once, and fail, and then drop out. Perhaps years down the road things will change, but let's face it, there are some kids who are just not ready to do anything beyond concrete reasoning. They are the reason the Jackass and Jack Black movies continue to rule the box office. Is this a good trend? No, but the alternative under current rules will mean that the teachers and districts will end up punished despite pulling all stops to get kids to be successful when the kids fail and drop out. That will lower AYP, districts will lost money and teachers will lose jobs despite their best efforts. Is this any way to encourage success? And in the meantime, how about the numerous kids that can't read and write? Or the ones who don't know ANYTHING about history? There's a link on my website to a blog at our local paper.
Robert,
Based on my experience with constructivist math in the elementary schools (and beyond), I think "basic math tables" refers to a multiplication table.
When my daughter was in 8th grade, I had the opportunity to test the students on their knowledge of the multiplication tables. When a problem was difficult, the strategies I would see employed were skip counting and doing a nearby multiplcation and adjusting. They were tested through 12 x 12. I forewarned the students and told them if they were having trouble I wouldn't "hit them" with the same/similar problems over and over if they were having problems in a particular area. The following incident occurred multiple times on the x12's. The students would do fine with 1x12, 2x12, 3x12 and 4x12. When they got to 5x12 many would start struggling. I would see skip counting going on many times, but probably due to nervousness they struggled. I would suggest the following for 6 x 12...
Do you know what 6 x 10 is? The would answer 60 quite easily. Do you know what 6x2 is? Once again they would answer easily, 12. ... and 60 + 12 is?? And they would answer 72. For at least 50% of the students that were struggling, you could see their eyes light up. When other x12 problems occured, you could "see" them doing the calculations in their heads.
The students had never been taught the disbributive property of multiplcation. Why not? Because they were supposed to figure it out for themselves, and of course, then they wouldn't know it was the "distributive property".
My oldest daughter in now taking geometry. The teachers don't lecture. I don't get it.
Chris
What worries me is that when the chance to change things pops up in legislatures or on school boards, the decisions are made by people who weren't good at math. So they tend to go easy on the *poor kids* or think that some new "fun" teaching scheme is going to make it all better.
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