Teaching Children Algebra

[syrakusos]

In another thread, Roger Bissell said: "For instance, you wouldn't teach little children algebra, for that is far too abstract. You start with learning numbers, counting, adding and the rest of arithmetic, and then having them rise to the abstract level. Similarly, you wouldn't teach them the virtue of honesty or rationality first, but instead touch on lots of concrete situations and examples."

The following could have gone in the Parenting forum, or under Psychology. I chose this as the broadest application. I read Atlas and attended Basic Principles when I was 17. Ten years later, I was a new parent, armed with ideas on self-esteem and books on how to give your child a superior mind. One morning, I met her pre-school class and gave them a 30-minute session in the theory of relativity. One day, I went around the kitchen and labeled everything in Latin. She hated that, so she made up her own language and we used those words. It was a game. The ubiquity of altruism meant that twice, during presidential elections, she came home making pronouncements on why she was for the current Democratic candidates. These were statements of princple. ""No guns in space." (Age 4.) "People should be nice to each other." (Age 8).

David Kelley has an excellent lecture on the problem of induction. The human brain has the ability to form abstractions from minimal information. You can teach a child princples first and from them demonstrate concrete applications. In fact, we all learned many things this way to some extent. On the other hand, I can remember my mother trying to teach me the concept of "furniture" as a means to keep me from standing on the kitchen table. I was all up for naming things, but I never got the point of that exercise. (I think she kept me off the table with concrete applications of something fairly sensory. In any event, if you invite me over to your home, I promise not to stand on the kitchen table.) Anyway, what and how we learn is complicated. The huge holes in IOE were part of my motivation to learn to fly an airplane. I have had probably 20 flight instructors and written probably 20 articles about learning to fly. According to IOE -- and according to the behaviorists as well -- one learns to manage a low speed stall by doing several. I had done many, but my learning moment came while driving out in the country, looking up at a plane that was obviously training... and sure enough... seen from the ground, it was a different experience, entirely. Humor works like that, seeing the known from a new perspective. From Katmandu to Timbuktu to Kalamazoo, people are all very similar and yet each one very different.

In IOE, Ayn Rand remembered back to what was in her own head -- the only one she knew -- as she learned from infancy forward. Even if those memories are accurate -- as opposed to constructions after the fact -- it remains to be demonstrated that everyone's brain works like hers did. The classes that I am taking now open doors to research that suggest structures which impact the IOE, as for instance, the scans that show the formation of an INTENTION for an act not completed, before the subject can announce his "decision."

Our daughter had perhaps accidentally vocalized Dad-like or Mom-like sounds when, at one dinnertime, I served food hot from the stove to the table. She reached for her serving and my wife and I both reacted yelling "Whoa!" holding and reaching our hands out to protect her. Close call. Next day, the kid and I are in the backyard. I am carrying her around. Our place abutted a cemetary (quiet neighbors) and at the chain-link fence, she put her palm up to a barb not touching it, clearly indicating it, and said "Whoa" in a very serious and low tone of voice.

[BaalChatzaf]

I discovered empirically that a neat and effective way of teaching children is to ask questions. It is a variant of the midwife approach advocated by Socrates (or by Plato being the man behind Socrates). I have done this a lot with my grandchildren. With my own kids, I -told- them a lot, but I encouraged counter-arugument. With my grandchildren I -ask- questions a lot. Of course I tell them things, but I usually put the things I tell them in the form of an inquiry. Phrase like look at this, what do you think that is? Or look at what happened. Why do you suppose that happened. This invites output from the kids and makes them active participants in the discussion. It seem to work. It is less confrontational and it encourages their original, if often mistaken, contributions. Better to make a mistake than be silent for fear of being mistaken.

With my oldest grandson who is truly artistically talented, I noted his visual inclination and would often ask: what does this look like to you? I tried not to impose my interpretations of things on him before he had a chance to say something on his own. He is fifteen years old now and has a very sharp intellect. He is interested in many things in addition to his art work which is rather good for his age.

Ba'al Chatzaf