OPTING OUT…OF MATH


Lately, there has been a lot of press, fanfare and pride in having one’s child opt out of testing for Common Core.  I am not a fan of standardized tests, but I took them every year in elementary and high school.  Perhaps the stakes weren’t high then, or maybe I did well enough on them so it didn’t matter.  My teachers didn’t teach to a test.  They taught material, and we were supposed to learn it.

I have taken more than one proud teacher to task for bragging about how many kids aren’t going to take the test.  “What,” I ask, “do you plan to put into place to know that a student is competent to advance to the next grade?”  At this point, I usually hear complaints about how teachers aren’t listened to, rather than specifics about how to make something better.  It’s easy to complain about something; it is a lot more difficult to put oneself on the line and offer something different.

At Lane Community College, where I am a volunteer math tutor, a recent editorial in the school newspaper suggested the school get rid of any math requirement, with the headline “Math-free degrees make sense.”  Some quotations:

  • “Many of those careers don’t require people with math skills.”
  • “For some college programs, not all, math is completely unnecessary.”
  • “However, for some students, any math is a hindrance to getting a degree.”
  • “When students have to subjects they are not suited to, rather than attending classes of…relevance…they become stressed and tired.”
  • “Granted, those going onto (sic) four year colleges would still have to study math.”
  • “What matters to employers is that job applicants have the necessary knowledge and skills to get the job done.”
  • “Choosing between a job candidate who had to study math…and one who didn’t…employers simply wouldn’t care.”
  • “These days (sic) technology handles all the math most people will ever need.”
  • “I’m not saying no to math in education altogether.  I’m saying it’s the responsibility of earlier education.   Remedial math should be the choice of the individual, not a community college mandate.”
  • “A more practical…alternative would be where students learn…how compound interest works, how monthly payments enslave people…”

My first reading of the article was that is was sarcasm, but I soon realized it was not.  The editor-in-chief of the paper has her picture present, and she looks like she is within a decade of my age.  I had a choice between a 250 word letter to the editor or a 600 word opinion piece.  I chose the latter.  I will expand upon it a little more.

It’s unfortunate that the Suze Orman Show is now gone, for Ms. Orman embodied the importance of math in finance and in life.  Those who sought help from her did not fully understand its importance, as the “Can I Afford It?” and “How am I Doing?” segments showed.  

My student who wanted to be a stockbroker couldn’t understand why he was learning logs, until I showed him how to determine the doubling time of money with 5 calculator strokes (72 divided by the interest rate in per cent is number of years), proving it in two lines (proof below).  He was amazed.  Another was thrilled to discover that by knowing the volume of a cylinder, he could determine cubic inch displacement of an engine.  I have never forgotten the look on his face, when he realized his knowledge.  Math is important, can easily be made relevant, and—yes—even fun.   Having my advisor in graduate school look at a proof of the first and second moments of a previously unknown hypergeometric function, say “Good job,” was one of my highlights of two difficult years away from home.

I grew up in an era where people did the same job their entire life.  The world is rapidly changing; multiple careers during one’s lifetime are now the norm.  At 66, I have had three.  We can’t imagine what jobs will be needed 10 years from now, let alone 50.  The winners in this new world will be those who can adapt; math is the single most valuable subject I know that increases one’s adaptability.  I taught adults in their 30s who discovered that they were wrong, when they thought in high school they knew their career path. Suddenly, they needed an MBA to advance in their company.   When faced with linear regression in a business model, knowing the slope of a line becomes relevant, as does probability, difference between a mean and a median, servicing debt, survey design, and measuring quality, to name only a few.  Without math, the glass ceiling becomes cement. 

I have heard students complain, like Ms. S., that they wouldn’t use math they were learning.  I could easily fill this paper with counterexamples, and my primary career was a neurologist.  I didn’t start my third career, statistics, until I was 49, and I had to review calculus taken 32 years earlier in order to get accepted.  Math, like learning music, chemistry, or Spanish, takes work and practice.  If Ms. S. thinks that math is stressful and makes people tired, I can assure her that I survived the stress and fatigue of reviewing calculus on my own and two years of graduate school, 300 miles commuting each way.  I didn’t remember calculus, but once I began to review it, I discovered something important: “If one learns a subject well, and doesn’t use it, he will forget it.  BUT, once he sees the subject again, it is relearned quickly.”

I have long thought we need a parallel educational pathway where math requirements vary for students.  I agree that a community college should not be a high school finishing institution, but until elementary and high schools teach students how to add and subtract, learn the multiplication tables, know when a calculator result doesn’t make sense, allowing remedial math to be the choice of a Lane student is saying math doesn’t matter at all, countering Ms. S.’s claim.  Offering math-free diplomas to increase graduation numbers is an astoundingly bad idea.  Our society needs proof of agreed-upon minimum math competence before a student  graduates from high school. Until then, Lane students must deal with the “stress” of learning math.  Life is tough. In the meantime, I hope Ms. S. understands that teaching compound interest to become financially literate requires algebra: Stating I=prt doesn’t allow one to understand continuous compounding any more than showing me middle C on a keyboard and thinking I can find D major.  For those who think math is worthless, I’m at Lane twice weekly by choice, to help students learn math.  To me, those 8 hours are almost a sacred calling.  Yes, sacred, not scared.

[A piece of wood was 40 cm long and cut into 3 pieces.  The lengths in cm are:

2x-5 

x+7

x+6   Add:

4x+8  = 40

4x=32

x=8; pieces are 11, 15, and 14.  Even if you didn’t know this, x+7 is larger than x+6.  One piece has to be at least 14 cm, so x has to be 7 or greater.  Put in some numbers.

What is the length of the longest piece?  15 cm.  7% of American 8th graders got it right; 53% of Singaporean.]

********************************************************************

Compound interest that can be taught for financial literacy (not difficult, but if you haven’t had algebra?):

Continuously compounded (the easiest):

P=Po exp^(rt) ; P= principal  Po=starting principal, exp= e (2.71828); r=rate, t=time. Don’t worry about e; ln takes it away just like division takes away multiplication, subtraction takes away addition.  Can you imagine doing that without knowing algebra?  Yes, e=[1+(1/n)]^n, as n gets large or ∑[1+(1/n!)] summing from 1 to infinity, but without algebra?

2P=Po e^rt; P=2Po, because money has doubled, (2Po/Po)=e^rt; ln2=rt

ln2/r= t; 0.693/r = t   69.3/r (%)  =t   round to 72/r=t, because 72 is divisible by many numbers.  That is 6 lines, but 8 small equations fit in 2 lines.

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