Why I hated the New Math (published 22 Feb 1984)

Published in the Arkansas Gazette, on the op-ed page, February 22, 1984.

If a can of light beer contains 96 calories and this amount is one-third fewer calories than the amount in a can of regular beer, how many calories are in a can of regular beer?

Light beer is too light for my taste, and so is most American beer, but the label on a can of light beer recently provided me with the above problem.  It is a simple algebraic problem.  It can be solved without setting up an equation, but the basic thought process involved is nevertheless a kind of implicit way of doing algebra.

Before readers with a distaste for algebra start scattering like a covey of quail taking flight, I should say that I too once loathed any implicit or explicit form of algebra.  After I loathed it until I could loathe no more, I started ignoring it.  Unfortunately for me, I was enrolled in an Algebra II class in high school at the time.

About three years after that fiasco, spelled with a capital ‘F,’ I enrolled in a basic electronics class at a vocational-technical school.  The night I first opened the book I’d bought for that class was the first night I’d ever wanted to stay home with a textbook instead of going out with friends.  The book had some simple equations in it, but they were equations that not only made sense to me, they also made want to learn more about the subject.

Since then, that is what I’ve been doing.  And learning more about electronics at the theoretical level, where my main interest lies, has meant learning a lot of math and physics, both of which I now enjoy doing.  (I think “doing” is the proper word to use.  I’m not just studying math and physics at school—I’m using them every day and learning more about them on my own.)

So the question I am now pondering is:  Why did I not become at least slightly interested in algebra when I was first exposed to it?

My answer to that question may be of interest to those people who are now trying to make some improvements in the teaching of mathematics.  My answer is that  I could not swallow the so-called “new math.”

My problem with “modern” algebra was my inability to accept the abstract concepts presented by the textbooks.  The concepts were presented as postulates, from which proven statements were later extracted.  I could not muster any interest in the postulates because to me they were dogmatic proclamations with no immediate relevance.  My fellow students and I were, in effect, being told not to do any thinking for ourselves until all the laws had been laid down—until, in other words, we had been told how to think.

We were, however, supposed to be impressed with what we were told.  My high school algebra book, at the end of the first paragraph of the first chapter, told me that it would be my “privilege” to learn about  sets and about the “postulational basis of algebra,” both of which had in the recent past been studied only in graduate courses at the great universities!

These are not words that impress a high school student.  They more likely impress only the textbook writing team that wrote them.

I don’t think high school students should even have to put up with words like “postulational,” but the new math textbooks are, or at least were, full of such graduate math course verbiage.

The new math was not much of a success with my fellow high school students either.  I seem to remember them complaining about having to do  an occasional “word problem” or two.  I now think we were being taught badly, mainly as a result of the textbook’s emphasis on abstract algebra, because word problems are the only real problems.  The rest of algebra is learning and applying rules for manipulating numbers and learning to solve equations.  Learning the rules is certainly necessary, but if a person cannot apply those rules to real problems, what is the use of teaching him or her the rules?

In my case, if someone had presented me with a practical problem and allowed me to try to solve it, and then had helped me understand how algebra could be used to solve it, I would have developed an appreciation for math much earlier in my life.

I hope that now, with a renewed interest in improving science and math teaching, students will b e taught how to use mathematics.  Indeed, the only way to learn it is to use it, and to practice using it, and the same thing applies to learning physics.  What is needed now is not an emphasis on “computer literacy,” but an emphasis on mathematical literacy.  A computer is a very easy tool to learn to use; it gives immediate response to one’s programming errors.  Developing mathematical problem-solving skills takes years.  There is no way to do it other than to work a lot of problems, and that is not as much fun as computer programming.

For the most part, working problems is done with a pencil and paper, and a good eraser.

So now we are left with the big question:  how many calories are in a can of regular beer?  My answer is 144.

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Let's hope Common Core Math is better than the New Math. It seems to be better from what I saw when I looked at the website.  By the way,"one-third fewer calories" on the can of Lite beer is a sort of trick.  People I asked about it often thought it meant one-third the calories, but the word "fewer" should tell you differently.  What it means is more commonly stated in percentage terms, as in 33% fewer calories. This is like a piece of clothing in a store on sale for 33% off.  Which means you pay 2/3 of the original price.  And so with Miller Lite:  it has 2/3 the calories of regular Miller.

The algebra way, however, is the way I thought of it.  Let x be the unknown regular beer calories.  Then x minus one-third of itself is equal to 96,

x - x/3 = 96  or taking out common x factor,   x(1 - 1/3) = x(2/3) = 96, and there's your 2/3 amount.