Jonathan Poritz is back! This makes me happy not only because it alleviates any guilt I feel over not live-blogging the Annette Gordon-Reed speech I’ll be attending later this morning, it means that everyone gets a different perspective on this whole MOOC thing. As I know less than nothing about teaching math, I was absolutely chomping at the bit to read the argument that follows:
So Jonathan (Rees) is allowing me to have another post in his blog, on a tangent from my previous guest post about the CopyrightX MOOC. My topic today is the old canard that MOOCs are more appropriate/effective/desirable/efficient for STEM classes than they are in the humanities and social sciences, because there are clear-cut right answers in STEM so these MOOCs can use computer grading to scale to great size.
There are so many problems with this point of view that it isn’t even wrong. (Well, OK, it is wrong. Let not the Internet trolls misinterpret.) Why this quackery infuriates me goes back to what I think education is about. Bear with me for a moment while I condemn all of current STEM education.
Let’s have a go at this in the particular case of mathematics, since it’s my field. People say there is a fair bit of memorization in mathematics. Do you remember learning the times tables? [I clearly remember Mrs. Sullivan at Littlebrook Elementary School saying that she particularly liked 7×7=49, because 49 only comes up in the times tables as that particular number times itself … “How stupid!,” I recall thinking, “that’s true of the square of any prime!” I was a math geek at a young age, I guess.]
Later one gets to algebra where, for example, students are taught these days to do multiplications like (a+b)*(c+d) by FOILing it out: “FOIL” stands for “firsts outers inners lasts”, so you get a*c+a*d+b*c+b*d. I learned this technique when I taught “College Algebra” (don’t be deceived by the title, the course content is what we used to call “high school algebra”) at my current institution and the students were confused when I said the words “distributive law of multiplication over addition” while doing a calculation like that at the board– one of them said “oh, you’re just FOILing it out.”
Then in pre-calc, you would have to memorize some trigonometric identities. In calculus, perhaps some formulae for derivatives or integrals of particular functions. In more advanced math classes, perhaps you would memorize a few useful power series, or the definition of a mathematical object called a vector space, or the detailed statement of the Fermat’s Little Theorem.
Along the way from memorizing tables of numbers in elementary school to definitions in college, you were probably taught some algorithms: rote procedures like computer programs or cooking recipes which take certain inputs and produce certain outputs. The pattern of numbers you write on the page to do multiplication of numbers with several digits is an algorithm, as is something like “bring the power down out front and subtract one from the power” to take the derivative of a power function, or “always put a +C at the end of an indefinite integral” (with an implied “or your teacher may take off a point from your solution”).
Nearly all students actually like following algorithms, in my experience as a teacher. Thinking is hard, after all, and isn’t it nice that someone has done all the thinking for you, and figured out if you just keep your brain comfortably in the off position but follow these particular steps you will magically arrive at the right answer, which you can put in a box at the bottom of the page and get full credit.
(I do think there is a large element of magical thinking in this attitude, in the sense of magic as pre-scientific and pre-modern. An authority figure told you what to do, and it is your job to perform that action without asking why. Not unlike a ritual invocation or public declaration of fealty to your feudal lord, or some other pre-modern formality.)
But modernism, when it works, is all about asking why and contesting arbitrary authority. So I might encourage a child today: by all means, memorize some of the times tables, it could be useful if you have to calculate a tip in a restaurant or want to know how many pecks of pickled peppers Peter Piper picked … but ask why, the answer might be interesting. [In fact, your teacher might concede that the symbols for the first ten numbers are arbitrary but that multi-digit numbers are an invention, there are other ways to do things like base two (good for computers), base 60 (which the Babylonians used, apparently … you can see why they gave us 360 degrees in a circle), or Roman numerals (terrible for all arithmetic, no wonder the Roman empire fell).]
Because of students’ — well, all human’s — laziness, it can be much more accepted by the students to learn the rote, algorithmic [pre-modern] mathematics. It’s a lot easier to teach, as well: nothing is ever new in the classroom or the textbook, you simply run through a description of the algorithm and ten examples in class. Approaching the material in this way as alienated factory workers tightening the same bolt every time means that the learning is mostly a matter of muscle memory, not higher critical thinking, so it requires a great deal of repetition.
Hence the piles of homework every day, graded on the sole criterion of whether the number in the box at the bottom of the page is correct or not. Likewise the proliferation of computerized instruction and homework systems for math in K-12 in the US.
Since it is so easy to teach, to flagellate the students with this kind of homework, and to assess, math fit wonderfully into the whole No School Left Unpunished system of George W. Bush, repackaged but not dismantled as the Race to the Top under Obama, with disastrous consequences: my students come out of the public schools in southern Colorado *hating* mathematics, thinking it is both abstract and rote, that there is nothing beautiful or intriguing or interesting there, merely piles of factoids and algorithms to memorize.
[Sadly, the same computerized systems are proliferating in colleges as well, although there are some other issues factoring into the situation: On my campus, contingent math faculty are paid a criminally low wage per class. As a consequence, they must teach way too many sections to make ends meet. Given a chance to lift the entire weight of homework grading off their shoulders by using a computerized system, who wouldn’t fall to the temptation? I do not fault them for this, nor can I, since I’ve used the same programs when teaching our College Algebra, so as not to rock the boat, and to have the time to do the other things required of me. Although I do fault professors who say that college algebra is a “drill and kill course”, so we shouldn’t fight to change it.]
When is he going to get to MOOCs, you cry. Here we go: I contend that we are doing a terrific disservice in how we teach math in K-12 by frequently taking the easy way out of teaching algorithms without thought. To some extent this is also happening in some courses at some universities. And this is exactly what those who suggest MOOCs can do “well” for STEM courses see as a great MOOC/STEM combination.
It is a mistake to teach math this way in K-12, which was easy to fall into because it seems cheaper and easier to assess (yay NCLB!). It is a mistake to teach math this way in colleges and universities, which was easy to fall into because of the economics of underpaid contingent faculty. When fans of the MOOC lifestyle talk about the ease of automatic grading of homework and quizzes for the eager masses in math classes, they are making a virtue out of the worst current trends in mathematics education.
Jonathan (Rees) has pointed out the profound flaws in the peer grading and peer evaluation used by MOOCs to attempt to accommodate all comers without imposing impossible burdens on the MOOC staff. Automated systems, in MOOC mathematics at least, seem to offer another cheap way to scale up to thousands of students without much taxing server space or bandwidth, while offering the illusion of the real classroom experience.
As Jonathan (Rees) has written:
So online educators of the world, let me propose a truce: Instead of arguing about whether online education is good or bad, let us simply agree that all students, online or otherwise, deserve access to a professor. Not a teaching assistant. A professor, someone with enough knowledge and experience to help every student overcome the inevitable stumbling blocks on the road to educational enlightenment.
Let me add a corollary to this proposed truce: students need that knowledgeable and experienced professor and not just a computer program. Just because a solution to a math or science problem can be judged correct or incorrect does not mean a student who gets on that green check or red X will be learning how to think like a mathematician or scientist. For real education, in STEM as well as humanities and social science, in person or on-line, students need the professorial access Jonathan (Rees) proposes.
I should point out that much of what I have criticized here in the context of mathematics instruction is true in all the rest of the STEM fields. Here’s one example: A colleague of mine who teaches an intro-level biology course on our campus says that a very large part of the content is plain facts which the students must cram into their heads. This may be correct, but I don’t see why a potential student in a disadvantaged geographic location who wanted to learn this material wouldn’t just read a book, preferably a free one on the ‘net, rather than signing up for a MOOC. For a course which also teaches students to think about biology, to put ideas together in new ways, surely automating homework is just as impossible as it would be in a creative writing MOOC.
This story of the felicitous synchronicity of STEM and MOOCs doesn’t hold water. All of Jonathan (Rees)’s critiques of peer grading and poor interactivity for the masses in a MOOC on social science or humanities are equally true in STEM fields, and to say that at least STEM work can be graded by a computer program is to believe that STEM fields could be done by robot: If you can write a program to grade homeworks and tests for a MOOC, then I bet I could write a program which would get perfect marks on all those assessments. I don’t want to teach, nor do I think my students should or do want to learn, material which could equally well be done by a few hundred lines of Java code. Teaching them that way only cheapens what we do when we do STEM or teach it well.