Becoming an Expert Statistician (or Mathematician or Programmer)

It’s not often that you read a paragraph and it sticks in your mind for months. That this particular paragraph came not from some great literary work but rather from the proceedings of the annual meeting of the Association of Small Computer Users in Education is even more expected, but there it is. Douglas Kranch wrote:

“Expertise develops in three stages. In the first stage, novices focus on the superficial and knowledge is  poorly organized. During the end of the second stage, students mimic the instructor’s mastery of the domain. In the final stage, true experts make the domain their own by reworking their knowledge to meet the personal demands that the domain makes of them.”

This idea kept coming back to me in a lot of ways. I have a thirteen-year-old daughter who is now learning the basics of chemistry, algebra and physics. I teach students statistics, and often have them use SAS for data analysis. I’m in the middle of using javascript for a much larger scale application than I have created with it in the past.

I get irritated by the frequent use of  the phrase “STEM education” for science, technology, engineering and mathematics, as if there is no difference among organic chemistry, javascript and calculus, but in this case I really did see a common thread.

Existing mathematics (and statistics and science) education programs are too limited. They either focus ONLY on drill and practice, not progressing past the first stage, or they try to skip the first stage or two entirely, an overreaction that while having the laudable goal of teaching “higher order thinking skills” often leaves students frustrated and discouraged as they do not have the basis for the tasks required. Part of the problem comes from, I think, having subjects taught by people who were not experts themselves.

Let me give two examples, one horrid and one good.

It’s common for middle school teachers to give students assignments that are supposed to be “relevant”, for example, “Make up your own periodic table”. They did not, however, come up with a new way of arranging elements. No, they did a periodic table of football players or TV shows. I suggested to The Spoiled One that perhaps she could do Disney channel shows and have those that had a character move from one show to another be in one group, just like elements that lose an electron are in one group. Similarly, those shows that shared a character, like if Miley Cyrus also did appearances on The Suite Life could be a different group, like those elements that shared an electron. I was out of town at the time –  (if you follow this blog, you know that my children contend most stories of their childhood begin this way) – but when the project was due, the world’s most spoiled thirteen-year-old turned in something she drew with a pencil on a piece of paper and got a 50% on it. When I quizzed the rocket scientist about how this happened he answered unrepentantly,

“I didn’t make her put any effort into it because she said it was stupid and I agreed.”

While I did not have this precise conversation with the school –  Seriously… What. The. Fuck – you want a kid to learn about the periodic table, covalent and ionic bonding – you teach them that,  NOT relate it to stupid  TV shows we’d just as soon she not watch any way. We spent many hours going over with her the idea of electron shells, what happens when a shell is not full, the number of electrons in each shell. You want a kid to know that NaCl is sodium chloride? You explain that Na is the symbol for sodium and Cl is the symbol for chlorine and you put the two together and you get sodium chloride. There’s actually some really interesting stuff you can throw in there about how it’s kind of weird that when you combine these two elements you get something that really isn’t very similar to either one individually. You want to get kids interested in chemistry? Do experiments. Few things are more motivating to the average eighth-grader than the possibility (however slim) that they might get to see the school blow up with the teachers in it.

I’ve been a teacher. I started out, like most people, as a not particularly good teacher, and then, with years of experience, I got better. I recognized that all of that stuff, like the periodic table the electron shells, multiplication tables, how to read an ANOVA table, you need to learn that. Even if you don’t get it at first, if you ” … focus on the superficial and your knowledge is poorly organized” – you still learn that p-values, df, sums of squares should be in there. At first, you don’t know what df stands for and when you find it is degrees of freedom that doesn’t really tell you much. After a while, you vaguely start to get it. It’s frustrating, it really is, going through those motions you don’t really understand – but there isn’t any alternative.

Let me go on to a different example. I wanted to use javascript to write an extremely complex application. So I needed to learn javascript better. I read a couple of books. I did a bunch of codecademy exercises, watched some videos. I wrote small programs that did bits and pieces of what I wanted. Then, I took someone else’s program that was pretty complicated. Not thousands of lines of code but hundreds. I went through and typed in their whole program line by line trying to figure out what each part did as I copied it. After I got it to run, I made some changes just for my own amusement. Then I did the same with a few other programs.

After a while, I could see where those “master programmers” had made mistakes. I’d notice they’d left a semi-colon off the end of a statement, left out the period, typing Mathrandom instead of Math.random or used a semi-colon when calling a function instead of a comma. In short, I got better at understanding the superficial – how the syntax has to look. At the same time, though, I started to see how the logic worked.  To see how one could use a loop inside a function to draw a deck of cards, for example. In the end, I had a game that worked. Then I changed it to be a different game, more like what I had in mind. I’m not as expert as I’d like to be in javascript yet, but I’m getting there.

Yes, in this process, I drew a lot of connections to other programs I had written in other languages. What I did not do is draw a parallel with the time we got lost and went driving around Miami trying to find somewhere it was legal to make a u-turn. (Let me just say that Florida has commitment issues. If you are going south they think you should just keep going and if you change your mind and want to go north, forget it.)

What I also did not do is one mindless fill-in-the blank or multiple-choice exercise after another ad infinitum. I didn’t memorize rules until I could pass some arbitrary test at 100% accuracy. Although I did start with that, I didn’t finish with it. In fact, I did the very minimal amount until I could move on to the imitating experts and making it my own.

If you want to learn programming, statistics, chemistry then DO that. Don’t just read about how to do it and for the love of God, don’t do something else, like stupid charts of TV shows or biographies of women mathematicians and pretend you’re doing STEM education.