Thursday, February 15, 2018

Latent Knowledge and Maps of Knowledge

Bryan Caplan’s latest book, The Case Against Education, is very engrossing. Also depressing. The most depressing piece of the book is the section that describes just how much we forget. When tested even months after the final exam, people seem to have lost most of what they learned.

I’m skeptical. I’ll start by describing my experience with the actuarial exams. These are four-hour exams that people typically spend four or five months studying for. (The pass rate is something like 50% for a good sitting.) There is a broad syllabus covering, say, 15 to 25 papers or textbook chapters. I would be able to work my way through the entire syllabus maybe four or five times in my 4+ months of study.

On the first pass through, it literally feels like you learn nothing at all. You read over the paper and an associated study guide, look at some practice problems, and go “Huh?” Almost nothing sticks. It’s hard to conceive of any test that would pick up the meager knowledge-gain of this first pass-through. Maybe you could vaguely detect that students pick up a concept or two on this first pass. Thoroughly confused, you move on to the next paper, and so on until you’ve done a first pass for everything in the syllabus.

On the second pass, you think, “Oh, this looks mildly familiar. But I don’t remember what the hell any of this is about.” But something magical happens. You say, “I understand it now.” You do a little bit better on some of the practice problems. Then you move on to the next paper, for which you find yourself having a similar “Ah ha” experience.

So plainly it isn’t possible that I learned nothing at all on the first pass-through. I would have loved to skip straight to the “Ah ha” of the second pass. I would have paid a fortune to skip that painful, humbling, slogging first pass. But plainly I had to go through this step. Clearly I was learning something that allowed the second pass to be more profitable.

I think much of what we learn and then forget is like this. I couldn’t necessarily pass any of my college or grad school physics exams. But I can pick it up again if I ever need to. More to the point, I can pick it up quickly and easily without a first slogging pass through it. I wonder how important this “latent knowledge-building” truly is. I’ve learned subject matter that I had never studied in school, so it might not be all that important after all. Surely someone has studied this concept. I wonder if Caplan came across any research on it? It seems like some critics of his book have brought it up, but I’m not sure Caplan has referred to research exploring/debunking this latent knowledge theory of education.

In addition to this latent knowledge, maybe we retain "maps of knowledge" after we forget the bulk of the subject matter. I may not remember how to do all varieties of calculus problems, but I know whether some problem I come across calls for an integration or a Lagrange multiplier. I can look up the appropriate textbook chapter. (BTW, I may have that rare one job in ten thousand that ever calls for these things, and then only rarely, and even then I use a computer to do it for me after setting up the problem.) It probably helps to "know your way around a topic." Then again, to Caplan's recent Econtalk exchange with Russ Roberts, you could probably design a test for this. "Which technique is most appropriate for this problem..." "Which textbook would you reach for if presented with this problem..."

None of this impugns Caplan's overall thesis. I still think we're all over-schooled, we forget too much, and we waste time on silly or useless topics. Caplan's guess that education is 80% signalling is probably a good estimate. Those actuarial exams I mentioned? 90% useless. It's just another long vetting process. "Can you pass these exams? (Stamps forehead with "Grade A".) Awesome, you get to be an actuary! Can you pass these exams, too? (Stamps forehead with "Grade AA".) Cool, you get an even better job as an actuary!" Or maybe I'm wrong and the latent knowledge and knowledge maps are really important. I just get the strong sense that most of the official actuarial
 syllabus is rarely or never used.

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