Monday, December 11, 2017

Fear Of Math

Actually, Peggy Sue's life would have turned out better if she understood Algebra.  Maybe she wouldn't have ended up marrying that loser, Nicolas Cage.

Fear of math is rampant in the United States. The film clip above represents this typical fear - that an unexpected math test is coming, and it will be "hard" and that math is "hard" and not only that, useless in "real life" whatever that means.

But of course, the opposite is true.  Whether it is balancing a checkbook, understanding an investment, figuring out whether a political poll makes sense, understanding a politician's promises about taxes, financing a car or a house, taking out a student loan - just about anything involving serious issues in your life - revolves around mathematics.

Now, I'm not saying you need to study Calculus and Differential Equations or take Number Theory, but you should have a working understanding of basic mathematics, and by that, I don't mean memorizing the multiplication tables or doing your sums.

And sadly, I think the fear of math comes from poor math teachers.  In the 4th grade, we had a horrible teacher who taught us to memorize the multiplication tables.  That was pretty much the whole course.   The stupidest kids in the class could memorize the tables, but of course, they had little idea of what the answers actually meant.  It was all emphasis on rote learning and nothing on comprehension - an emphasis that the far-right thinks we should return to.   Citizens who comprehend are dangerous, whereas people who learn by rote can be easily manipulated.

As I noted before, in the first grade at Everett Elementary School in Lake Forest, Illinois, we were taught set theory and Boolean Algebra as part of this "new math" curricula, which was very controversial.   Twenty years later, a very frustrated Algerian teaching assistant tried to teach us these "high level" concepts as part of a course on microprocessor design.   He took us to task for being bored by it, and when we explained to him this was elementary school stuff here in the States, he flatly refused to believe us.

Anyway, my 4th grade teacher nearly held me back a year, as I could not memorize the multiplication tables.   Maybe I am Autistic, but 7 x 9 always stumps me.   This did not prevent me from taking three semesters of Calculus, Differential Equations, and Number Theory in college and scoring fairly well.  Of course, those courses teach (for the most part) comprehension not merely rote learning.  You can't fake your way through higher math by memorizing equations.

I think this failure in our educational system instills a fear of math in many people - a fear they carry with them their whole life.   As a result, their minds shut down whenever numbers are presented to them, and oftentimes, they cannot see through raw deals or understand things on a meta scale.

For example, on more than one occasion, I have had a conversation with Mark about the price of something.  He is a classic mathphobe, having been punished psychologically in many math classes in High School and College where getting the "right answer" was harped upon, but understanding mathematics was really not taught.

The conversation would go something like this:

ME:  So how much was the price of the item? 
MARK:  I don't know, I would have to look it up! 
ME:  More than a dollar and less than a million? 
MARK:  Well, of course it was! 
ME:  Well, compared to infinity, we've narrowed it down quite a bit!

Of course, he doesn't appreciate my sense of humor.  But I would continue to present similar outliers - $10 to $100,000 and so on, until he would zero in on a price of about $40 (or whatever) which would be within a few dollars of the actual price.   Frozen by fear of math, he didn't want to say "it was about forty bucks" because his math teacher beat into his head that there was only right answers, down to ten decimal places and anything else is wrong, wrong, wrong!

And this has a crippling effect, as you cannot figure things out in your head if you are convinced that every number has an exact value and what's more that exact value is actually important.   A professor in semiconductor design neatly proved this point to us in a final exam that had us solve one problem to determine the depletion region of a semiconductor transistor.   The equation involved was monstrous - having over a dozen difficult components.   Those of us who cranked through the equation to the bitter end would (if they were lucky) finished it just in the nick of time before the exam ended and likely get a "B" - as they would inevitably make a math error.  Those who didn't finish got a "C".

Those who saw the forest through the trees realized that the first four components of the equation were the most important, and the answer could be calculated in fifteen minutes if you dropped off the remainder of the equation.  They got an "A".   I got a "B" and a valuable lesson I should have already known as an instrumentation technician, that calculating things out to umpteen decimal places is an exercise in self-deception.  Just because an instrument reads out to ten decimal places in a digital display doesn't mean it is accurate to that amount!

In a later math course in Junior High, we had a better teacher, and he did a segment on rounding and estimating.   The idea was to get kids comfortable with coming up with rough answers to problems where exact numbers didn't matter.   For example, Joe wants to spread fertilizer on his lawn.  Each bag of fertilizer covers 10,000 square feet.  His lawn is 515 feet by 198 feet.   How many bags does he need?

If you estimate, and say his lawn is 500 x 200 feet (or 100,000 square feet) he needs 10 bags to get the job done.   The wrong answer would be 10.197 bags, as they don't sell 0.197 bags of fertilizer and spreading fertilizer is not an exact science.   Another good answer would be to say 11 bags, rounding up so there was a little left over.   But cranking out an exact number, in this case, was not necessary.  Rounding and estimating are better and faster tools than a calculator.

Most of the kids in class freaked out when handed this assignment.   There was no right answer down to ten decimal places.  There was no formula to memorize, or table to commit to.   You had to have a feel for numbers and how they worked.   Like I said, most kids freaked at this assignment, but I enjoyed it and did well.   And another kid in class, who was not a real math genius (in terms of getting "right" answers) also shined with it.  He later turned out to be a general contractor, where I presume estimating worked out very well for him.

And I have a friend like that, who was a contractor and later an HVAC Engineer, who never went to college and memorized equations.  But he could look at a building or a set of plans and tell you, without spending a lot of time with a pencil or calculator, how many 2 x 4's you'd need to build it and how many panels of oriented strand board - and maybe have one or two boards left over when you were done.   And I know this, because he planned and built our studio, and when it was all said and done, there were three studs and half a panel left over.

Having a feel for numbers is far more important than treating math as something "hard" that needs to be memorized in order to use it.   Once you understand mathematics at a gut level, memorizing 7 x 9 is really irrelevant in the greater scheme of things - provided you understand the answer is greater than 10 and less than 100.   You need exact numbers?  That's what calculators are for.

Sadly, few people seem to have this "gut feel" for numbers, but most have an inordinate fear of math.   They don't read the "fine print" on a contract because the math scares them.   They buy a car or a house or whatever, and all they want to know is the monthly payment.   So long as that number is less than their paycheck, they think they got a good deal.   But of course, shitty deals can be wrapped up in attractive monthly payments - which is how car salesmen sell cars.

It also explains why everything in your life is priced at $1.99 or $5.99 or $59,999.99 or whatever - because people don't bother to think that these numbers actually mean $2, $6, or $60,0000.    When it comes to rounding off numbers, it seems most of us only know how to round down.

I am not sure where to go with this, other than this idea that "you don't need math in real life" needs to be shouted down roundly.   You do need it.  And you need art class, and music, and English, and Physics, and Chemistry, and History, and all the rest of it - yes, even Gym.   Because ignorant people can be easily lead astray.

You can tell a mathphobe, because he is the one who believes that abolishing the "death tax" means he can leave his double-wide to his kids, tax-free.   And he also doesn't know what "marginal rate" means, but believes that cutting taxes of the very rich will somehow affect him.   People who are ignorant about numbers are always at the mercy of those who aren't.

And maybe that is why there is such hatred today toward Bankers, the "1%", Wall Street, Lawyers and whatnot - much of it couched in terms of anti-antisemitism as well.  Yes, bankers understand math better than the average person - which is why they come out ahead in financial deals and so many others do not.

Do the math - it is a mantra I have repeated many times in this blog.   And it is hard for me to "feel sorry" for "victims" of poor math comprehension - college students who borrow a hundred grand to go to school and then later find out they can never pay it back (or so they think).   Smart enough to be accepted at a prestigious college, not smart enough to understand compound interest, job market futures, or even the simple concept that borrowed money has to be paid back.

Do that math - it is your friend, and sometimes your only friend in a cold, dark, and cruel world.