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I am a theoretical mathematician (Ph.D. UCLA 1996), who taught as an Adjunct Assistant Professor at UCLA for 2 years ('96-'98), and then as an Assistant Professor at Illinois State University (ISU) for 4 more years ('98-'02). In addition to my experience teaching college math and computer science, through interaction with many of my colleagues at ISU I became well-versed in issues of Mathematics Education. (ISU has one of the largest Math Ed. programs in the country.) In fact, many of my fellow faculty were involved in drafting the NCTM standards, both past and present.
Both my daughter (eighth grade) and my son (fourth grade) have used EDM exclusively for their in-school math instruction. As a mathematician I find the program abysmal, and I know that I am not alone (amongst mathematicians and others) in this assessment.
Let me share with you a portion of an email that I sent to our local (Hollis, NH) school board. This should serve to encapsulate (at least in part) my position on EDM.
As you could tell, I am passionately opposed to the use of Everyday Math (EDM). My experience with it, both personal and professional, has been uniformly negative. I also have large amounts of anecdotal evidence that confirms that the only way our kids learn any math while using EDM in school is when parents become frustrated and just teach them math the "old fashioned" way.
What I object to is the "Emperor's New Clothes" syndrome: everybody telling me how great this program is, but there being absolutely no evidence that it provides any benefit at all. What is particularly telling are the words and phrases that its advocates use: "It makes math more enjoyable," or "The kids really like the games." Of course they do!
What I believe has happened is that the teachers have been sold a bill of goods: most elementary and middle school teachers, while being dedicated and tireless in their devotion to wanting to teach our children, have not received adequate training in mathematics. (This I can attest to from first-hand experience; I once taught Calc I to a group of students destined to be "math teachers." I failed half of them (many couldn't do high school algebra). What was particularly disturbing was the fact that failing my class did not dissuade them from wanting to be teachers, it merely "redirected" them: without passing Calculus they simply could no longer be Secondary (i.e., High School) math teachers; Calculus, it seems, wasn't required for Elementary or Middle School (math) teachers.)
Hence, when a program (endorsed by "experts") comes along and tells them that they can do a better job teaching math by having the kids participate in group activities, making it "relevant" to their "everyday" lives, the teachers rush to adopt it: who wouldn't? However, the hard yet honest fact is that math is difficult, and requires work, dedication and perseverance to master. As Euclid said, "There is no royal road to mathematics."
But beyond all this, what troubles me most is the fundamental philosophical flaw in EDM: It ignores the core beauty and power of mathematics, viz., that it is an edifice constructed out of pure reason, all of whose inferences and deductions flow logically and unarguably from more basic facts. EDM asks the students to flit willy-nilly from room to room or even floor to floor in this structure, without ever exposing them to the skeleton, the underlying architecture.
The basic premise of EDM, so much so that its part of its name, that math should be valued or appreciated only insofar as it can be applied to "everyday things," is worse than misguided, it is a lie promulgated by people who, quite frankly, don't understand the first thing about mathematics. (Example: Do we study "Everyday English Literature?" Why do we still read Shakespeare? Are people really worried about being encountered by three old women stirring a big pot, and wanting to know how to deal with them?)
Let me recount for you what I used to tell all my students the first day of class: Being in a (math) class is like buying a membership to Gold's Gym. If you come to class, sit passively by, and then complain that you didn't learn anything, that you just don't "get it," that is akin to walking into the gym a month after you bought your membership and complaining that you haven't gotten any stronger, even though you come to the gym everyday and watch people work out. Being in a class, or in school, provides only the opportunity to learn, the teacher is there to facilitate the learning process, but the effort must emanate from the student.
In short, the "guided instruction" methodology, however well-intentioned, is in fact, "misguided": Imagine paying a tennis or golf pro to help improve your game, only to have her tell you to "try and discover the right method to strike the ball on your own." You would be justifiably outraged; you pay someone who is a better tennis player / golfer than you to teach you the right way to do it. Human minds are not designed to do math (unlike, say, to learn language); they need to be taught the right way to do it."
I hope that it comes through in what I have written that I am not blaming the teachers. In my (admittedly limited) experience, many of them are similarly frustrated by having to adhere to an administration-mandated (math) curriculum that they neither support nor believe in. I have rarely met a teacher who is not extraordinarily dedicated to her students, and I absolutely do not want anything I say to be construed as being critical of the job that they do. My point here was merely to demonstrate that some teachers (as well as administrators, school board members, etc.) are insufficiently trained to evaluate properly the merit of their math curriculum, and so rely upon others (like the NCTM) to do so for them.
Tony Falcone, Ph.D
This passage is beautiful:
The basic premise of EDM, so much so that its part of its name, that math should be valued or appreciated only insofar as it can be applied to "everyday things," is worse than misguided, it is a lie promulgated by people who, quite frankly, don't understand the first thing about mathematics. (Example: Do we study "Everyday English Literature?" Why do we still read Shakespeare? Are people really worried about being encountered by three old women stirring a big pot, and wanting to know how to deal with them?)
The night before Tony's statement appeared on the B-R Mathforum I had been trying to explain to Ed why constructivist math, from the perspective of a real mathematician, isn't even math.
Of course, I can't really explain it, not off the cuff at any rate.
Then Tony's statement landed in my email queue.
We are all lucky to have it.
22 comments:
"theoretical mathematician"
Isn't that redundant?
I have no idea!
I'm assuming it's not, since that's the phrase he used to describe himself.
I don't think that "theoretical mathematician" has to be redundant.
Brown University, for example, has an "Applied Math" department. I expect that the mathematicians working there are applied mathematicians :-) So specifying that you do the sort of math that isn't useful outside math itself doesn't have to be redundant.
According to Wikipedia, applied math "concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains."
-Mark R.
He asks: "Do we study 'Everyday English Literature?' Why do we still read Shakespeare?" as if the answer is self-evident. It isn't. There have been attempts in the past to make reading/literature much more "practical". There will be more in the future, I expect.
-Mark R.
"The night before Tony's statement appeared on the B-R Mathforum I had been trying to explain to Ed why constructivist math, from the perspective of a real mathematician, isn't even math."
You could say that math is "constructed" from things like definitions, identities, axioms, and proofs. It is very clear and very exact. Understanding and mastering these constructs makes you a good mathematician.
This is not what constructivist math constructs. All they try to construct is a simplified, low level understanding of how easy problems work. They might show you graphically how to divide 2 1/2 pies into 5 pieces. That's it. You don't construct how to do this with proper mathematics. You don't construct how to do this symbolically. You could call what they do a simplified visual aid. It may be helpful for simple problems, but it won't help when you have to divide (3x-5) by 3/x. It's not math and it's not even construction.
Thanks, Catherine, for the links. I love the quote about Shakespeare. Somehow, I've got to find a way to get the Board members in my town that influence curriculum to notice these things. One of our Board members is a physicist. He joined the Board after EM was implemented. Maybe I can make some inroads there.
Of course, the fact that I have trouble being civil to any of the Board members at the moment won't help.
"One of our Board members is a physicist."
You have to be careful. Does he or she have kids in the schools? Does he or she get to see what comes home as homework? Some of these people like the general happy "understanding" talk, but haven't looked at the details. I remember thinking of how I would improve the math education I received. I was quite surprised when I looked at the details of reform math.
There is also the question of what, exactly, is wrong. Some parents see that their kids are doing fine. They know the times table. They make sure that they know how to do fractions.
Perhaps they just haven't gotten to middle school yet. Perhaps they haven't realized that the K-8 curriculum can't get their kids to honors math in high school without a lot of work on their part. But some parents feel that it is their duty to do more at home. They don't see anything wrong with that. A couple of well-educated parents are on our school committee. Their primary goal is to work within the system. They know that there are issues, but they are working on them.
I see it almost as a blind spot. Their kids are doing fine, so what's the problem? Then again, both parents do lots of extra work with their kids at home. They think this is normal. They care about thier kids. Unfortunately, they assume that all parents have basically smart kids and do what they do at home.
Excellent points, Steve.
As long as tests scores remain high, there is little incentive to engineer a big change. Teachers and administrators are happy. I'm not the only unhappy parent, but with high test scores and lots of supplementation, it is really difficult to get people to change.
If a board member has a bright kid who doesn’t need much teaching, then his reaction might be “what’s the big deal?”. That would have been me if someone had brought this to my attention when my son was sailing through elementary & middle school math. This only became important when my younger child started having difficulties with math.
The initial contacts I’ve made with our BOE & school have yielded responses that indicate their attitudes are similar to those that have been discussed here before.
The BOE is mostly hands off because they don’t want to “micro-manage”.
The school professes desire for parental involvement, but text book selection is best left to the school because they see hundreds of students and are in the best position to evaluate these things. When I mentioned the inclusion of parents on the selection committee I could almost hear a gasp of horror.
Don’t worry, the school’s priority is “balance”. Of course this means constructivist books with some rote learning thrown in for us educational Luddites.
Catherine or anyone else,
Do you know about any more of these parent groups similar to the Bridgewater-Raritan Forum?
If there are more, could you give us names &/or links?
I tried searching Yahoo Groups, but did not have much luck. Finding out about these and learning what these parents are saying is very helpful. The statement from Tony Falcone is full of gems.
As I’ve mentioned, I might start a group in my town.
I'm sure Mark is right - I was forgetting that "Applied Math" can be (or is) considered a separate category.
I believe Harvard has a major called "Applied Math." (not fact-checked)
He asks: "Do we study 'Everyday English Literature?' Why do we still read Shakespeare?" as if the answer is self-evident. It isn't. There have been attempts in the past to make reading/literature much more "practical". There will be more in the future, I expect.
That's already happened with the attacks on "Dead White Males" etc.
So far this year Christopher has read THE OUTSIDERS.
That's it.
7th grade
All they try to construct is a simplified, low level understanding of how easy problems work.
I've been trying to find the language to express this.
The "problems" in constructivist math aren't problems for anyone who knows math.
I always say, "Enrichment means giving students beginning algebra problems without teaching them algebra" or "giving students long division problems without teaching them long division" - but it doesn't quite work.
I see it almost as a blind spot. Their kids are doing fine, so what's the problem? Then again, both parents do lots of extra work with their kids at home. They think this is normal. They care about thier kids. Unfortunately, they assume that all parents have basically smart kids and do what they do at home.
How are the disadvantaged kids doing?
Or are they all in special ed?
That's the question.
Don’t worry, the school’s priority is “balance”. Of course this means constructivist books with some rote learning thrown in for us educational Luddites.
Throw me a bone!
I'm saying ALL curricular decisions must be joint decisions of:
teachers
content specialists (real content specialists, not educators who think they're content specialists)
parents
checks and balances
"How are the disadvantaged kids doing? Or are they all in special ed? "
There are no disadvantaged kids around here, so if they are not in special ed, it's their own fault.
There are no disadvantaged kids around here, so if they are not in special ed, it's their own fault.
Really?
None?
I need to find out our exact statistics.
Horrible moment at the Board meeting the other night where one of the principals said something like, "X City in Rockland has 22% black students and we have 12% so our achievement is better."
Something like that - this is NOT a direct quote.
One of the parents there was incensed; so was Ed.
I've discovered, however, that this isn't racism in the sense we all thought.....it's not that ed-school trained educators think black kids can't learn.
They think the exact same thing about my kid - about lots of the kids - they do about black kids.
They think pushy white parents are deluded about their kids' abilities or "maturity level" etc.
I have to find out, specifically, how many kids we have who are defined as disadvantaged.
I'd bet the ranch they're all either in special ed - high end special ed - or on "AIS" or "building services."
I'll bet the ranch because I already asked this question of a pal who had a daughter in high-end special ed. (We're in low-end special ed.)
I was asking her about disadvantaged kids: how are they doing?
She said, "I know how they're doing; they're all in special ed with 'Jane.' It's the disadvantaged kids and 'Jane.'"
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