Elementary School Teachers and Mathematics

This isn’t an original observation, but the previous post reminded me how annoying it is that elementary school teachers are among the worst candidates to introduce children to math.

There are exceptions, but by and large the people who are drawn to the career of teaching elementary school are people who are not mathematically inclined. They often don’t like math, don’t understand math, and have chosen a career that doesn’t require them to. So these people can’t help but give children the impression that math is excruciating, and incomprehensible.


Always Solving Problems

The Toilet Paper Question post below, and this page about traffic that it reminded a reader of, got me to think about something I’ve been wondering about.

Why is it that some people always seem to be trying to figure out the best way to do things while others don’t?

It seems to me that making sense of the world and what we’re doing is what we did as children all the time. So, I’d think the natural thing to do is to analyze what we do and try to understand its nature and how we can optimize our activity (whatever it is, and whatever we’re trying to optimize for). So I don’t think we need to explain why some people (like me) do this, but why other people don’t.

I remember an incident that happened to me when I was in the 3rd Grade. I was thinking about how the diagonal path across a square was shorter than going around the corner. I asked my teacher how much longer the diagonal of a square was than the side (I hadn’t heard of Pythagoras yet). She was annoyed by the question because I was supposed to be working on some worksheet (which I’d finished). Her first answer amazed me:

I don’t know…twice as long?
No, it’s shorter than that.
Oh right. It’s one and a half times as long.
No, it’s shorter than that too (I’d done a quick measurement with a ruler before asking)
[Angry] Go back to your desk. You should be working on [whatever I’d finished].

I went back to my desk, confused. I knew that I didn’t learn much in school, but I thought that teachers were supposed to know a lot of things and should at least be able to help you figure out what they don’t know. But this teacher (who, as I recall, was better than most) not only didn’t help me learn, but actively discouraged me from learning.

I can only imagine how many kids who were less stubborn than I was would come away from that experience learning that spontaneous curiosity is bad and gets you into trouble. And whenever you think of a question that you don’t absolutely need to answer right away, ignore it.


By the way, neither of my parents knew the answer either, but I got it from my uncle (an engineer) a month later. I got to learn about exponentiation and square roots, too. Cool

I’ve Been Outed

I created this blog a few days ago without being sure whether or not I wanted to announce its existence to anybody; I wasn’t sure I’d post enough quantity or quality to make it interesting to others, and I hadn’t settled on the look I wanted, either. I also thought I’d keep it anonymous, at least initially; I thought I’d at least try to maintain the privacy of myself and people I might write about. But those options are gone now. Somebody at The World (I’m guessing Sarah) has discovered this blog and identified me as the author in this post. I guess that she just assumed that because I put a page on the World Wide Web, I wanted other people to read it. Sheesh!

Damn You Sarah Fitz-Claridge!

Well, it’s probably for the best. Now, I’ll have to change the entry describing myself, and push myself to post more frequently.

But, if you don’t like anything you find here, then you should

Blame Sarah!

The Toilet Paper Question

You’re using a reasonably well-maintained public restroom and there are two rolls of toilet paper available for use, with differing amounts of paper left on each roll. Which one should you use: the roll with more paper, or the roll with less paper?

Of course, if you’re a selfish bastard then it doesn’t matter as long as there’s enough for you. But, is there any good reason that a decent person with concern for his fellow restroom user should choose one roll over the other? The answer is yes, and it’s pretty obvious if you think about it. Unfortunately, it seems that very few people have thought about it.

You should choose the roll with less paper on it.

Why? Because that way, if most people followed this rule, one of the rolls will empty faster and be available for replacement with a full roll when the maintenance person next checks. That will make it less likely that some unfortunate soul will be stranded with two empty rolls.

The world would be more pleasant if everyone followed this simple rule, but it’s clear that they don’t because I often see two rolls with roughly the same low amount of paper left. This is one of many cases where a misguided egalitarian tendency (“I think I’ll use the roll with more paper because then they’ll be more equal…”) leads to unintended bad consequences.

UPDATE: An anonymous reader entered this comment:

A valid point, from an altruistic perspective. However, call me a “selfish bastard,” but I always choose the roll with more paper. Why? More paper means fewer people have used it before, which in turn means that there is a lower probability that someone has contaminated the roll. So from a strictly personal standpoint, it may make more sense to use the full roll for hygienic reasons.

This is my response:

This is invalid. Only a brand new roll will be more hygienic (if the maintenance person who installed it is cleaner than the average user). But, after that they’re equal. The inward-facing side of the paper is still as clean as the machine that rolled it. And only one circumference (plus a little) of a non-new roll may have been touched by others regardless of how much paper is left. I guess the edge may have been handled a bit more, but I suspect this difference is negligible. In fact, the smaller surface area of the roll with less paper probably more than compensates for any extra handling. So, be nice. OK? I don’t think there’s a real cost in this case.

UPDATE 2: Here is a nice design that implements my solution.

Who is this “Reasonable Man”?

Hi. My name is Gil Milbauer. I’m a guy who strives to be reasonable (opinions vary as to how successful I have been). This quest has, thusfar, led me to be politically libertarian, epistemologically critical rationalist (Popperian), theologically atheist, parentally respectful, and temperamentally INTJ. I’m also  told that I have a pretty good sense of humor. I have a lot of opinions, but I’m not sure how frequently I’ll manage to post them here.

We’ll see.