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I Love Math May 12, 2017

Posted by Peter Varhol in Uncategorized.
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There, I said it. You might think that it is a natural thing for someone with a math degree (among others) to say, but let me delve a little deeper into that statement.

I was never very good at math. I completely lost it at calculus, not being able to relate it to real world concepts.  I think our minds like to relate abstract ideas into something concrete, a part of our lives, and that’s very hard with calculus and beyond.

I tried again as a college freshman. No dice, so I ended up with a degree in psychology, although I took a number of science courses as electives.

Another psychology degree later, I started to feel the math itch again. As I took graduate statistics, experimental design, and did a thesis with a mathematical model of behavior in a game theory situation, I came to realize that, despite my relative incompetence, I could no longer shrug away my math jones.

Long story short, I moved to a new job, taught myself calculus and differential equations in the evenings and weekends over the space of a summer, and enrolled in a graduate applied math curriculum in the fall. I got through it in three years (with some undergraduate course supplements), and graduated in 1985 with an M.S.

Why do I love math? I think it’s because most of our thought processes are representational.  We express ideas and emotions in words, in pictures, and increasingly today in video.  But the fundamental representation of the world around us is through mathematics.

My problem, of course, is that I came of age about 25 years too early. At that time, other than teaching, the only mathematical job available was as an insurance actuary, which sounded like the equivalent of watching paint dry.

(Well, there were a couple of other options. I turned down a GS-12 from the NSA because I didn’t want to move back to the Baltimore area.  Of course, being a cryptologist would have been very interesting the last few years.  And there were beginnings of rumblings about highly-paid “quants” on Wall Street, but I didn’t want to live in Manhattan.)

Today, of course, I can be a data scientist, although this late in my career it would be problematic to make that change. I’m back to tinkering with neural networks and machine learning, and maybe I will make a go of something there.  But 25 years ago, the options in applied mathematics were much more limited.

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What is the Liberal Arts? April 26, 2017

Posted by Peter Varhol in Education.
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My B.A. degree is in the liberal arts. The diploma says psychology, but I also took substantial coursework in chemistry, biology, and physics.  Conversely, I took no English courses.

(To be fair, I wanted to take an English course, specifically, a writing course. My university required that I take an English placement test prior to doing so.  I did so, and placed out of the course that I wanted to take, and out of the next course, and was awarded six credits for my investment of an hour.  I never looked back.)

Today, liberal arts and humanities are on the proverbial ropes. This article in Wall Street Journal (paywall) describes how liberal arts programs in some schools are being expanded to include courses in mathematics and data analytics, in an effort to bolster the liberal arts with career learning.

Frankly, those courses, and other science topics should always have been there. In the dawn of the liberal arts education, the goal was to deliver a well-rounded individual who could opine and even work in a wide variety of different fields.  It led to a person who could be described as a “natural philosopher” who is educated and cultivated on a wide variety of topics, which relate to both social and science areas.

It’s only in more modern times that liberal arts curricula came to mean that the individual only had to study psychology, sociology, English, and political science. And that is wrong.  The liberal arts education has always been defined by a broad education without the depth of specialization.  Its intent is to drive rigor across traditional academic boundaries to enable its possessor to become a truly educated person.

But we got away from that at some point, with higher education permitted to define liberal arts as a much narrower take on a limited number of softer topics. Today’s so-called liberal arts is actually a bastardization of what it was intended to be.

The WSJ article positions the addition of math and science courses as a nod toward career training over life training. Ah, no.  Chosen well, what the math and science courses really do is round out a liberal arts education.  I understand that people need to get jobs, and such to get jobs, and such courses may help, but science and math are very much a part of life experience, no matter what field you may ultimately pursue.

Weapons of Math Instruction February 15, 2017

Posted by Peter Varhol in Education, Technology and Culture.
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That old (and lame) joke, of course, refers to Al-Gebra (algebra).  But the fear of math is very real.  For decades, many have hid behind the matra “I’m not a math person”, without exploring the roots of that statement.  This article, by Jenny Anderson on Quartz, offers hope that we may be able to move on from this false rhetoric.

I never understood math early, but I always loved it.  Post-BA degree, I taught myself calculus, and obtained an MS in applied math.

I taught various math and statistics courses to college students for 15 years.  I would like to think that my enthusiasm and down-to-earth explanations at the very least made it tolerable to them.  I still remember one student saying to me, “In elementary school, the teacher would preface the math lesson by saying, ‘I don’t want to do this any more than you do, but we have to, so let’s get it over with.’”  I think teaching is a very big part of the problem.  If teachers don’t like the topic, neither will their students.

I especially came to appreciate word problems, something that few if any students liked.  I had a method of dealing with them.  My original issue with word problems was that if I read it once and didn’t immediately see the solution, I would be stumped.  Instead, I taught people to read the problem first, to understand it without seeking a solution.  Then read it again, and highlight any information that seemed pertinent.  Then read it a third time, to pull out that information and see how it might help lead to a solution.  Then try a formula.  If it didn’t seem to work out, discard it and start back at step 1.

It is not hard, folks, though it does require overcoming age-old biases, as well as a willingness to be open to new ways of thinking.  Anderson notes that learning and applying math and quantitative methods requires a growth mindset.  That is, a willingness to get something wrong, and learn from it for the future.

As we move (or already have moved) into a data-driven world that requires an intimate understanding of how data shape our lives, we can no longer plead ignorance, or lack of ability.  If we plead lack of interest, we will be left behind.