If you’ve ever struggled with your tax return, wondered how interest rates could stay so low, or tried to explain why raising taxes on employers is actually not conducive to job creation….
We need solid math education now more than ever. We are no longer an agrarian nation yet we teach math like we are.
Thirty years ago an ARM was attached to your body. Now it is attached to your credit report. An adjustable rate mortgage is not evil, but it is now maligned as so many folks feel like they have lost their homes to the ARM. In reality they lost their homes to poor judgment of risk. It’s kind of like building a house on sand, in a hurricane zone….
Smart or Foolish?
Which really brings us to a question of risk.
How risky is that (your idea goes here)?
Imagine for a moment that a stock you like has a 90% chance it will rise by 20%, and a 10% chance that it will fall to zero over the next year. Our current models for risk imply that there is a certain probability that an event will occur. So, we price the total cost of an investment based on those factors. So if you can buy at $10/share today, you can sell at $12/share or you lose the investment completely in one year.
The most straightforward approach is to price the total investment based on the proposed outcome proportion. To simplify, either the market rises 20% or it falls to zero.
$12*(90%) + $0*(10%) = $10.80
Since the $10.80 is above your purchase price, you are in the money and the investment looks good. But what did we really just do? We assumed that each dollar invested had equal probability and opportunity to earn that 20%. In effect, we implied that one share could gain 20% and one share could lose 100%. But that’s not really true. If one share gains 20%, all shares gain 20%. If one share loses 100%, all of the shares drop to zero. So, in reality, you either get $12/share or you get nothing. There is no $10.80. Average doesn’t actually exist. It is a construct.
We averaged all of the shares to simplify our decision, but we didn’t account for the actual risk. So we missed the point.
This isn’t a question about modeling stock prices and returns – there are certainly more elaborate methods to model prices – it’s simply to illustrate our tendency to dumb down the basic math and therefore the real risk of various proposals, because, most of us don’t really have the tools to understand the math.
Indeed the more I teach, the more I see, most of us don’t have the tools to balance our checkbooks. A few months ago I had a student tell me that he went to a school (NYC) that operated much like a Montessori – he was able to discover math at his own rate….
Well, he’s 25 now, a graduate of a very prestigious college, well employed, and he genuinely does not understand the purpose and function of fractions. Sure, he recognizes them when written out, but ask him to perform operations with fractions or to interpret a word problem, and he is two steps away from toast. Here’s the killer, he believes he is good at math because his teachers told him he was smart.
Sadly, this is nowhere near an isolated incident.
So, he has great self esteem, but he can’t calculate his mortgage payment on his own. As a consequence, we have ever more elaborate financial products rolling off the line and fewer and fewer people equipped to understand them. This is what leads to catastrophic failure – of banking systems and of entire economies.
We need more math education and less self esteem training. You bomb your multiplication tables, guess what, no gold star for you. Get back to the drawing board. You need those multiplication tables. As a society we cannot afford to both PAY for public education AND ignore the lack of results of that education.
No Child Left Behind gets a lot of grief in teaching circles, but the fact remains, we have a HUGE gap between those who understand math and those who can’t function in an increasing complex society. Which costs us more, under-educating the average population who then make catastrophic miscalculations or creating a super class of teachers and testing students on performance?
If we were just farmers growing crops and bringing them to market, we might be okay. But we offer the average high school grad an adjustable rate mortgage and a 401k. Perhaps it would be good idea to equip them with the tools to understand the consequences of their choices, never mind the innovation curve….
2 thoughts on “More Math Education, Less Self Esteem Training”
100 years ago math books like those in the Ray’s Arithmetic series had significant sections devoted to annual interest, settlement of accounts, and contingent annuities – maybe we should revive some of our past tradition!
Ahem, cough… should we just teach kids to be good at Microsoft Excel?
I kid. And fully agree. Nice post.
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