Monday, August 31, 2009
Friday, August 21, 2009
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?
Monday, August 17, 2009
Sunday, August 16, 2009
W also painted a wooden puzzle (a paint your own sort of project) that he had gotten for Christmas from Auntie Chris. He chose two of his favorite colors, blue and green, and had a great time painting, it turned out very ocean-like. Then he wanted to make it an alphabet puzzle (which was a great idea because otherwise even I would have a hard time putting that puzzle together) so I wrote the letters for him and he finished it by writing his own name on the bottom pieces using the "gold dust" as he calls my gold colored craft pen.
Friday, August 14, 2009
Austrian theory can be expressed in plain English (though occasional graphs can help illustrate concepts), and I believe it is appropriate for high school aged students and perhaps even advanced junior-high students. In particular, I would recommend Gene Callahan's book Economics for Real People as an effective and breezy introduction to economics. Another good choice would be Henry Hazlitt's Economics in One Lesson. One or both of these books could serve as the basis for a first course in economics for homeschoolers.
However, some good news from Bob Murphy, an Austrian economist, is that the Mises Institute is moving forward on a project for him to create a high school course geared especially for homeschoolers. Read about it here. While I am a little concerned about the result being "too mainstream" I have no doubt that this will be a worthwhile course and a boon for homeschoolers.
Wednesday, August 5, 2009
The solution which I am urging, is to eradicate the fatal disconnection of subjects which kills the vitality of our modern curriculum. There is only one subject-matter for education, and that is Life in all its manifestations. Instead of this single unity, we offer children -- Algebra, from which nothing follows; Geometry, from which nothing follows; Science, from which nothing follows; History, from which nothing follows; a Couple of Languages, never mastered; and lastly, most dreary of all, Literature, represented by plays of Shakespeare, with philological notes and short analyses of plot and character to be in substance committed to memory. Can such a list be said to represent Life, as it is known in the midst of the living of it?
Alfred North Whitehead has many great insights in his essay The Aims of Education. Here is one:
I appeal to you, as practical teachers. With good discipline, it is always possible to pump into the minds of a class a certain quantity of inert knowledge. You take a text-book and make them learn it. So far, so good. The child then knows how to solve a quadratic equation. But what is the point of teaching a child to solve a quadratic equation? There is a traditional answer to this question. It runs thus: The mind is an instrument, you first sharpen it, and then use it; the acquisition of the power of solving a quadratic equation is part of the process of sharpening the mind. Now there is just enough truth in this answer to have made it live through the ages. But for all its half-truth, it embodies a radical error which bids fair to stifle the genius of the modern world. I do not know who was first responsible for this analogy of the mind to a dead instrument. For aught I know, it may have been one of the seven wise men of Greece, or a committee of the whole lot of them. Whoever was the originator, there can be no doubt of the authority which it has acquired by the continuous approval bestowed upon it by eminent persons. But whatever its weight of authority, whatever the high approval which it can quote, I have no hesitation in denouncing it as one of the most fatal, erroneous, and dangerous conceptions ever introduced into the theory of education. The mind is never passive; it is a perpetual activity, delicate, receptive, responsive to stimulus. You cannot postpone its life until you have sharpened it. Whatever interest attaches to your subject-matter must be evoked here and now; whatever powers you are strengthening in the pupil, must be exercised here and now; whatever possibilities of mental life your teaching should impart, must be exhibited here and now. That is the golden rule of education, and a very difficult rule to follow.
Saturday, August 1, 2009
- blog updates or thoughts on blogging (meta)
- ideas for tools, techniques, or projects to use in the homeschool (schoolidea)
- reviews of books (bookreview)
- planning or discussion of curriculums (curriculum)
- reasons to prefer homeschooling to other forms of schooling (whyhomeschool)
- philosophical thoughts on education and learning (armchairphilosophy)