By the time I had grabbed my iPhone, slid to unlock, put in the passcode, found Calculator, punched in the numbers, punched in the right numbers, and read her the result, my wife had easily figured the answer to a tax problem on a scrap of paper. Worth her studying math for 12 years in school?
“No,” is the clear answer given by Simon Jenkins in yesterday’s Guardian.com, “For Britain’s pupils, maths is even more pointless than Latin.” I completely agree. For one thing, except for what she regards as the most useless subject of all times, Euclidean geometry, she wasn’t doing math, or “maths,” as they say over there, at all. She was, basically, learning to replace a calculator.
Now although such a skill may come in handy at times, it’s not mathematics. Mathematics is proving theorems — thinking up and solving puzzles. Now I happen to think that’s a wonderful field; I have a Ph.D. in it myself. I totally agree with GH Hardy, quoted by Jenkins as remarking that mathematics “must be justified as art if it can be justified at all.” I don’t find it at all unusual, for example, that mathematicians will praise an exceptionally elegant new proof of an already established theorem.
What should children be taught in school? My answer: how to go out into the world, find stuff, decide whether it’s right, and use it. They should always be working on something, on writing or making or building something. When they’ve developed the appropriate level of proficiency, they can move on. I have no idea how much of this should be done in formal classroom settings.
Boyd suggested that such ability is the secret to success in life.
We can’t just look at our own personal experiences or use the same mental recipes over and over again; we’ve got to look at other disciplines and activities and relate or connect them to what we know from our experiences and the strategic world we live in. Strategic Game 45
Musashi said much the same thing way back in 1645, and he was only interested in killing people with swords:
- Cultivate a wide range of interests in the arts
- Be knowledgable in a variety of occupations
- Nurture the ability to perceive the truth in all matters
- Perceive that which cannot be seen with the eye
[From the last section of the “Earth” book, in the Book of Five Rings.]
So a familiarity with mathematics and its results, particularly statistics, which is necessary in order to develop “the ability to perceive the truth in all matters,” probably belongs in everybody’s repertoire of skills. But that’s as far as I would go. After that, the abilities to read, think, write and communicate become vastly more important. Oh, and let’s not forget the arts. Where would Apple be today if Steve Jobs hadn’t sat in on that calligraphy course?
Slightly East of New 
Good post, Chet. It is a theme that has been repeated many times over the course of my life by teachers and mentors who cared about truly guiding young people into an unknown future. I am equally sure that it has been repeated through the ages past. No matter what specialized area of interest we use as a vehicle to move forward in life, we must strive to expand our knowledge and viewpoint widely across multiple disciplines. The old adage, ” jack of all trades, master of none” comes to mind. I have met many people in my life who lived by that axiom, but whom I considered some of the most well-rounded and wise ones I have ever known.
Another appellation is “Renaissance Man” as the modern connotation infers. John Boyd was a textbook example. The human ability to assimilate many concepts and obtain more than superficial understanding is one of the greatest gifts we have. It is also a singular deficit among a seeming majority of humans nowadays, where facts and understanding of cause and effect seem to be a lost art.
Anybody happen to recall Robert Heinlein’s comment on this subject?
I agree that math is very important, and has an effect on thinking processes well beyond
the specific subject.
It is not however for everybody.
The BIG difficulty I experienced was in the manner in which it’s taught. It’s setup very deliberately to facilitate a certain failure rate. And that never seems to change, as
my daughter struggled greatly, throughout high school, in that subject
exclusively.
But rather than adapt to the failure rate, they apparently stick to the very same methods,
drills and explanations, and there can only be one reason for that.
I did not do particularly well in math, until, I studied the practical application in the feild
of electrical and electronic engineering, and my interests in astronomy, physics, and music, where upon, I picked it up rather well, in fact quite well to a level that suited my purpose, to an applied sci level.
M
The way mathematics is taught today is an emphasis on rote. There is no emphasis on thinking. It is mostly memory work. People are concerned about the answer and the grade, not the thinking process that got to it.
A republic if we can keep it? Well that requires that the bulk of the population be one capable of thinking. That does not seem to be happening today. There seems to be a powerful part of American culture that hates the very idea of thinking.
– Chris