Two or three lifetimes ago, I was an Associate Professor at a small, liberal arts college, teaching, among other things, lifespan developmental psychology because, well, somebody needed to teach it and I had published several articles on assessment of families and other semi-related issues. One debate in the field, I learned, was how much of the purported decline in “fluid intelligence” was real and how much was just a function of the unwillingness of older people to solve pointless problems to please a researcher. I call this “the crotchety effect”.
I have been experiencing that effect a lot lately. I am reading a great book entitled , This will change everything, a product of edge.org , which is best described as a website full of people who think about things besides next quarter’s stock prices , whether their clothes are springtime fresh, what’s for dinner and who is president of the country club. Several of the chapters were the expected emerging science/ technology. We’ll be able to know our own DNA so we can predict if we will get Alzheimer’s at 65 or ovarian cancer at 40, we’ll have robots that we can love, or as close a facsimile as most marriages anyway, we’ll have genetically engineered children to be faster, smarter, stronger. A chapter I read this morning really struck me. The author, Frank Tipler, said something like this:
What will change everything is the enormous decline in the number of people going into science and mathematics. Steven Hawking and the other less well-known but equally brilliant and creative scientists will soon retire and I do not see anyone coming up to replace them.
The author goes on to note that this decline is even greater than has been realized within America because such a growing proportion of our graduate programs are filled with students from other countries. Where I disagree with this chapter is the assertion is due to the ability of graduates entering finance to make three times the salary the author was receiving as a tenured professor. I don’t think too many people in previous generations entered science or mathematics because they expected it to pay better than any alternative. In fact, I think the reverse is true. I see many more people now, especially those from outside the U.S., who are entering these fields precisely because they expect to make a very comfortable living. Thirty-five years ago, when I was a college freshman, most of my friends in engineering or computer science majored in that because it interested them.
I had enough courses in business and economics to major in either field but I had business on my transcript because I thought it was more likely to get me a job. Statistics, economics and computer science classes I took just because I thought they were interesting, for the same reason I listen to National Public Radio, or read the New York Times , and devoted about as much serious study to them as an undergraduate. HOWEVER, after I graduated, I never gave another thought to net present value, whatever it was I was supposed to have learned in finance or industrial psychology, while I continued to read every day about statistics, programming and systems design.
In this country, we have a great faith in the ability of science and technology to “fix things”, everything from the mortgage crisis to AIDS. Yet, few people want to be making or maintaining that science and technology. Even the people that say they do only want to do so tangentially. I was quite disappointed today looking at the National Science Foundation SMETE Digital Library. There is some good stuff, for example, MIT Open Courseware is a gift to the nation and God bless ’em. Honestly, though, it is over and above what the average undergraduate and many graduate students can comprehend on their own. That doesn’t mean it isn’t great for those above average students in motivation or intellect. On the other hand, a lot of what I found in the digital library was fluff – links like “What famous mathematicians had birthdays today?” or “Biographies of famous women mathematicians.”
Okay. Stop right there damn it! You know what would help my beautiful little girl have a better chance of being a mathematician? If Mommy sits down with her and says,
“You know what a normal distribution is, my angel? You don’t? Well, it looks like this, with a few people very far below average, most of the people are average, and a few people way above average. Then, there are other distributions. This one is skewed. You can measure how different something is from normal. You can look at it, or you can use numbers … “
This is exactly what I did tonight, drawing a histogram on a white board that, for some unknown reason, was in the middle of the living room floor when I walked in.
Why has the quality of our students declined so precipitously? I’m really not sure but I think a big part of the reason is that our demands on them have dropped dramatically. My mother, my high school teachers, my siblings and my professors as an undergraduate could all line up to be first to tell you that I was not a particularly good student. In college, I went to more parties than I did classes. I studied mathematical statistics, Fortran, BASIC programming, Differential and Integral Calculus – because those were – you’re not going to believe this – ways to MEET MY GENERAL EDUCATION REQUIREMENTS. Yes, your random, relatively unmotivated college freshman whose main priority was which frat party to attend on Friday night was expected to prove the central limit theorem, find a derivative and write a subroutine just because those were the sorts of things a well-rounded educated person was expected to know.
So, I took classes in high school, like matrix algebra, analytic geometry and Calculus because it is what was offered and my teachers taught me far better than I deserved. You could take general math but then all of your friends made fun of you because you were stupid.
When I went to college, I had some of that stuff all over again and, with a little effort, kept the B average necessary to keep my scholarship and continue going to frat parties. I have to admit it wasn’t until I was in my mid-twenties, working on my second masters and Ph.D. that I became really motivated to learn statistics, and I haven’t looked back.
Three really, really key points here, though are:
A. I was prepared to learn by having been literally force-fed mathematics throughout school from middle school all the way to graduate school. No one, from Sister Marion, who taught me math in sixth grade, to Phyllis, my matrix algebra teacher at Logos High School, to Chris, my high school Calculus teacher, to Dr. Spitznagel who taught the statistics course I skipped every Friday as an undergraduate gave a damn if I wanted to learn it or not.
B. All of those people I mentioned knew math really,really well. I had the opportunity to learn from people who had every expectation in the world that I could and WOULD learn whatever it was they were teaching. If I had suggested getting extra credit for writing a paper on a famous woman mathematician they would have thought I had lost my mind.
C. Because of this, when I finally got interested in statistics, learning it was not insurmountable. Because I had matrix algebra in high school and in regional economics and urban economics in college, when I needed to learn the normal equations, I knew how to invert and transpose a matrix.
Things are different now. I have taught in North Dakota and California, and have friends at universities all over the country. We all see the same thing. Even at the doctoral level at the best universities, students do not have the same level of numeracy that your average, unmotivated party-going undergraduate did thirty-five years ago.
Unless we reverse it, this will change everything. And not in the good way.