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devil duck

Not quite a book review

shalmestere brought home an advance reader's copy of The Math Myth (to be published in March 2016), thinking I might be interested. The main point of the book is that American schools, from middle school through college, require students to take a lot of math courses that they will never use, that do not make them better thinkers, that do not increase their earning ability or their competence as citizens of a democracy, but that do serve to filter out and discourage a lot of kids from reaching their potential in non-mathematical fields.

Which is almost certainly true. I've actually had occasion to use a little bit of calculus on the job (in doing analysis of algorithms), and in answering idle-curiosity physics problems, and I've used trigonometry to design tents, and I've used both trigonometry and linear algebra to write graphics programs, but 99.99% of the U.S. population will never need to do any of those things, either on the job or in private life. Most people need to be able to do arithmetic (with the aid of a calculator, but they need enough of a feel for numbers that they can tell whether the answers are at all plausible), and read a graph, and it would be nice if they knew that correlation isn't causation, and what statistical significance means. As a logician, I'd like it if ordinary citizens knew that "not all cats are grey" is equivalent to "at least one cat is not grey", and that "if that's a duck, then I'm Henry Ford" is not equivalent to "if that's not a duck, then I'm not Henry Ford".

Anyway, the author documents vast numbers of students whose only academic problem is an inability to pass such irrelevant math classes (middle school, high school, or college), but who are denied the opportunity to study Shakespeare or Swahili or spot-welding. He points out that most of the doomsaying about an imminent shortage of STEM-qualified workers comes from employers who have a strong vested interest in creating an overabundance of such workers. And he likes to illustrate things with sample test questions.

Here's a question he likes:

A rectangular-shaped fuel tank measures 27-1/2 inches in length, 3/4 of a foot in width, and 8-1/4 inches in depth. How many gallons will the tank contain? (231 cubic inches = 1 gallon)

(a) 7.366 gallons
(b) 8.839 gallons
(c) 170,156 gallons

He likes this because it tests "did you read the question carefully?" -- specifically, did you convert 3/4 of a foot into 9 inches -- and do you know what needs to be multiplied and what divided? He says if you failed to notice the "feet", you would get the incorrect answer (a) (in fact, he's misplaced a decimal point: you would get .7366 gallons, which you should also be able to rule out through common sense because a tank that big has got to hold more than a gallon!)

Here's a question he doesn't like:

Two charges (+q and -q) each with mass 9.11 x 1031 kg, are place 0.5 m apart and the gravitational force (Fg) and electric force (Fe) are measured. If the ratio Fg/Fe is 1.12 x 10-77, what is the new ratio if the distance between the charges is halved?

(a) 2.24 x 10-77
(b) 1.12 x 10-77
(c) 5.6 x 10-78
(d) 2.8 x 10-78

I have to confess I do like this question, because it doesn't require doing any arithmetic at all, only remembering that both gravitational and electrical forces follow an inverse-square law. Although if you have two masses of almost 1032 kg half a meter apart from one another, they're both black holes and you have bigger things to worry about than measuring the forces between them.

However, I don't see a lot of benefit in asking this question on an MCAT (which is where it allegedly came from). Yes, identifying the relevant and irrelevant features of a problem is important to a doctor, but physics isn't.

For a certain board game, two dice are thrown to determine the number of spaces to move. One player throws the two dice and the same number comes up on each of the dice. What is the probability that the sum of the two numbers is 9?
(a) 0
(b) 1/6
(c) 2/9
(d) 1/2
(e) 1/3

Again, he doesn't like this question, and I do: it requires no arithmetic, no probability, no combinatorics, only the ability to see past the irrelevant stuff to what matters.

Is this what they call a "trick" question? One that requires common-sense reasoning, not just the application of a memorized procedure? If so, I'm all for them.

Anyway, I've only read a quarter of the book; we'll see what else he has to say.
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I think I"m more on your side that not on those two questions, but the gravitational/electrical one requires sufficient background in physics to be able to recognize that it isn't a math problem, but a reasoning one. The last question, is much more accessible as a reasoning problem.
when does a math problem become a math problem and not a reasoning problem? I was developing the opinion that much of what maths is, is figuring out exactly how to apply your basic arithmatic.