CTK Insights

22 Apr

Regarding the Mess We Are In

Dr. Harry Elmer Barnes (discredited in his late life for the denial of Holocaust) opined in the New York World-Telegram (during the Great Depression, probably around 1932):

The fact that men like President Cleveland had not the slightest grip on the mathematical and scientific facts which have created the modern world is one reason why we are in our present mess.

It appears that Harry Elmer Barnes' advice went unheeded - I have not heard that any one had ever suggested to institute math testing for elected officials, let alone of the President.

In 2009, during an economic downturn, Dr. Arthur Benjamin also suggested a remedy for the economic ills of the country:

I think if our students, if our high school students — if all of the American citizens — knew about probability and statistics, we wouldn’t be in the economic mess that we’re in today.

Now, I greatly respect Dr. Arthur Benjamin (I own three of his books and find him a great teacher, lucid writer and math expositor. I regularly run into his articles in various MAA publications.) But, unless it was a prunk, it proves that all the claims that math education may positively affect thinking ability of students and subsequently of more general population contain a logical error.

It is often asserted that, mathematics being a deductive science, the study of mathematics is bound to have a positive effect on students' thinking ability. The evidence that this is so is mostly anecdotal. The evidence that there are other and more effective ways to improve students' thinking (and along the way their math scores) is traditionally and consistently being ignored.

The underlying assumption that we - the humans - think logically and use logic to arrive at everyday conclusions or conclusions of longer impact has been long undermined by the research of psychologists and economists (see the works of Daniel Kahneman, Brafman brothers, Dan Ariely, Johnathan Haidt and many others.)

I may be mistaken, but it seems to me that the idea that study of mathematics leads to a betterment of the general thinking ability contains if not a plain logical flaw then at least an overlooked ambiguity. It's implicit in that belief that improved general thinking would bring about positive effects like avoidance of economic downturns, and in lifes of individuals would lead to reaching better, more advantageous decisions. Would not that mean that (at least in the limit - so to speak - when all think masterfully), all would be expected to arrive at the same conclusions? If so, then the argument is patently based on a faulty assumption. As a matter of fact, mathematicians - those ultimate, professional thinkers - would not agree as a group (i.e. arrive logically at the same conclusion) on almost any trifle or a matter of importance.

There are republican and democrat mathematicians. There are among them liberals and conservatives, good investors and bad investors, happily married and multiply divorced ... There are mathematicians on both sides of the math wars; there were mathematicians who promoted the New Math and those who warned about its dangers.

Mastering mathematics may make life more interesting by providing more ground for wonderment and delight. Given certain aptitude, maths could be fruitfully used as a professional tool. I submit that in some cases a mathematical study could be as useful as a critical thinking course in teaching one to better organize one's thoughts. The history of math education refutes any claim to the universality of positive effects it may have. In this respect I side with D. E. Smith who would give a chance to study mathematics to every student, just to try and see, and have a chance - without being penalized - to choose some other interest:

I believe it to be our duty to stand solidly against the lowering of the standard of mathematics that shall make of it only a science that immediately instead of potentially practical. I believe that we should open the door of the great field of algebra and geometry to every boy and every girl in our country. If they fail, let them substitute some other science for this, but offer them the chance.

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