Inducing PI

At Z's school, they were taught how to measure the circumference of cylinders. They do this by marking a point on the circumference and then rolling the cylinder along a straight line until the marked point touches down again. Then, they take the flat side and measure the diameters off against the same line. They've done this for a whole lot of circles. Every time they do that, they see that it takes about 3 diameter-lengths to cover the length of the circumference. Now, they're dividing the circumference by the diameter and finding that all the numbers are approximately 3.14. Finally, they had a lesson in the meaning of PI.

Hasty Generalization

After they've learnt words and sentences, kids go on to reason. They start forming knowledge of the form "All A is B", i.e. principles. For the first few years, they have a tendency toward hasty generalization. For instance, a kid who has never seen a male elementary teacher can easily conclude: "All elementary teachers are female".

I've encountered many examples of this in my son. Often, individual examples come as a surprise to me -- a reminder of how little he knows about the world.

When he was about 6 we were talking about the ryhme, "Rain rain go away", and he commented that it sometimes works! Presumably he'd been experimenting! I realized that if a kid sang that song a few times when it rained, and it stopped raining even once, he might draw the conclusion that "it sometimes works", even if he's not sure exactly when: could it be the volume, the tone, getting the words just right?

When my son was really small I used to think to myself that small kids are so much like little animals, only much less self-sufficient. Around 6 and 7, one gets a glimpse of how primitive men must think. It's only a glimpse, because our kids are provided with so many true facts now, that they believe the right things. However, in an instance like this "rain, go away" example, one sees a little sliver of hasty generalization.

From Journaling to Planning

In Z's school, elementary kids fill up a few lines in a journal near the end of the day. It's a list of things they did that day. Now, in 3rd grade, Z decided that he will make a list in his journal in the morning -- the plan of things he was going to do that day. Then, at the end of the day, he checks it off, scratches out what he didn't, and adds in any extras.

The thing I find interesting is that he was not asked to do this. From what he says, he did not see any other kid doing it. I would not be too certain of this type of self-reported fact; nevertheless, there is no requirement or push for him to continue to do it. So, what I find interesting is that he must "get" something from it. Probably he gets something similar to what an adult would get: a sense of control over his activities for the day.