a theoretical mathematician evaluates constructivist math

This statement, from a theoretical mathematician, was first posted to the Bridgewater-Raritan Parents Math Forum.

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.