Paradigmatic Example (#1) of Education Fail

[Jacobus]

From my family's homeschool blog:

http://littlemenhomeschool.blogspot.com/2009/08/paradigmatic-example-1-of-education.html

I am going to post a series of personal examples that I believe serve as particularly good exemplifications of failure modes of the standard education system. After I have posted these, I will provide more general analysis and discussion, culminating in what I hope will be suggestions of how these can be avoided.

Here is my first example:

I was taking a college graduate-level course in computation and automata theory. This was one of my favorite courses because it managed to combine computer science, mathematics, linguistics, and even some philosophy in a coherent, interesting manner. The general idea of the course was to define a computational engine (e.g. a finite-state machine) and investigate what sort of problems the engine could solve, and with what efficiency. Even the most powerful machine with theoretically infinite memory (a Turing machine) turns out to have well-defined limits of what types of problems it can be guaranteed to solve.

Now, this class required us to write proofs and in so doing exercise some degree of creativity. The problems were not mere restatements of earlier theorems or problems, and their solution usually required thinking really, really hard and then having an "a-ha!" moment. I found these to be stimulating, often fun, and ultimately satisfying.

During a class, one student raised her hand and asked the professor something like "How are we supposed to know how to solve these problems?" After a little discussion of what she meant, it was obvious that she was not interested in the details of any particular problem; what she was after was a general algorithm for solving all of the problems we were given! I cannot think of a greater insult to the professor and his beloved subject. To him, each problem was intrinsically valuable. Each problem had its own reason for being, its own lesson waiting to be unlocked by just the right stroke of inspiration on the student's behalf. But to her, each problem was merely an exercise: at best, an exemplification of some general principle that should have been already given, and at worst, something that just needed to be completed to get course credit.

I cannot overly blame her though. This was, after all, presumably what everyone in the room was used to in math and science classes: start off with being given a set of general rules, then apply them to specific examples in a mechanistic fashion. The solution is produced in the most efficient manner, and with the least amount of thinking. Just figure out where to "plug in" the numbers and turn the crank. Education as the execution of algorithms.

The professor chided her and said "This isn't high school." Justice was served.

But that made me think: why does even high school have to be high school?

[Kat Kanning]

Proofs in geometry were my favorite part of math, but sounds like it wasn't as complex as what you're talking about.

[Pat K]

Some how I don't think the professor really helped any thing
here.

Perhaps he, also is to used to a plugged in response.