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American Thinker
American Thinker
17 Feb 2024
Arnold Cusmariu


NextImg:End math requirements, says Washington Post opinion editor

Travis Meier, opinion editor for The Washington Post, got on LinkedIn to brag about his first WaPo column titled "The trouble with schools is too much math," calling it a “major moment.”

As the author of the recently published Logic for Kids, I thought I’d take a close look.

Alas, the article is nothing to brag about. While Meier makes some good points, he also harbors serious misconceptions about logic, overlooks serious problems with mathematics instruction, and would do away with a key component of mathematics with us since Euclid. I sent him an email suggesting he study my book. No reply as of this writing.

Meier may well be right that most people “have no use for imaginary numbers or the Pythagorean theorem” and that “more than three-fourths of the population spends painful years in school futzing with numbers.” Many computations can be done by simple calculators and, in technical jobs, by sophisticated software such as Matlab. The convoluted mess known as Common Core, which has caused massive headaches among students, parents, and teachers alike, goes unmentioned, however. My critique of Common Core is here and here.

Meier’s proposal that schools “end useless math requirements” will elicit howls of protest (laughter?) from the education establishment in this country and, indeed, probably worldwide as well. He wants to dump those requirements in favor of “something more useful.” Like what? Meier answers, “applied logic.” What’s that? Let’s take a close look at Meier’s exposition of this idea, quote:

This branch of philosophy [logic] grows from the same mental tree as algebra and geometry but lacks the distracting foliage of numbers and formulas. Call it the art of thinking clearly.

But wait, there’s more, quote:

“Logic teaches us how to trace a claim back to its underlying premises and to test each link in a chain of thought for unsupported assumptions or fallacies. People trained in logic are better able to spot the deceptions and misdirection that politicians so often employ. They also have a better appreciation for different points of view because they understand the thought processes that produce multiple legitimate conclusions concerning the same set of facts.”

Too much “futzing with numbers” is not the problem with mathematics instruction. The problem is exemplified by this astonishing admission in a recent geometry textbook, quote:

We have said that theorems are going to be proved by logical reasoning. We have not explained what logical reasoning is, and in fact, we don’t know how to explain this in advance. As the course proceeds, we will get a better and better idea of what logical reasoning is, by seeing it used, and best of all by using it yourself. This is the way that all mathematicians have learned what a proof is and what it isn’t. (My italics).

As a mathematics major in college, I can attest from personal experience that the logical structure of mathematical proofs is never made explicit. What we get is a proof sketch, which leaves it to students to fill in the logic blanks (good luck) and repeat the reasoning process for other theorems (good luck). Here is a sample, from a well-known analysis textbook by Edmund Landau (page 9):

Theorem 12: If x < y, then y > x.

Proof: Each of these means that y = x + v for some suitable v.

Got that? A logically explicit version of Landau’s proof is on pp. 271-275 of my article on logic in mathematics education, available here.

Finally, it seems not to have occurred to Meier that his proposal to end mathematics requirements means doing away with teaching mathematical proofs, a key component of mathematics since Euclid; and, paradoxically, also teaching the logic behind proofs, however cursorily. Maybe Meier should try proving the Pythagorean Theorem using “practical logic.”   

Arnold Cusmariu is a frequent contributor to American Thinker. He retired from the Central Intelligence Agency in 2010, where he worked as an analyst, analytic methodologist and analytic tradecraft instructor. A short article describing these duties can be read here.

Image: Pixabay / Pixabay License