LeftoverPi

I would like to do a series of posts on "Lockhart's Lament". Keith Devlin reposted the Lament on his "Devlin's Angle" column in March 2008. (The direct link to the pdf was

http://www.maa.org/devlin/LockhartsLament.pdf

in case the column is less permanent.)

Lockhart's Lament is a hefty (in blogger terms) 25-page screed about mathematics education. It covers a lot of ground and makes a lot of claims. It's way too much to respond to in a blog post, so I'm going to break it up and take it a piece at a time.

The first thing that Lockhart does is to present an absolutely beautiful analogy describing what music education might look like if our educational system ever really got its hands on it.

Continue reading "Some thoughts on the leading analogies in Lockhart's Lament" »

[This is part 2 of a two part series, parts 1 and 1a may also be of interest.]

So, one thing that kind of cooled off the passion about the Math Wars (see part 1 for an introduction the Math Wars and my brief participation therein) for me was the fact that I planned on home schooling. I thought, "Well, I know how I am going to present math to my kids, and that's the most important issue for me right now, anyway." And so I went to teacher supply stores and bought fun counter things and pattern blocks and base 10 fries and all sorts of stuff. I was giddy. What fun these things will be to use! And my kids will totally "get it"--no half-formed ideas or things they don't really understand because they just learned by rote, etc, etc, etc.

Guess how that turned out?

Continue reading "How I became an enemy combatant in the Math Wars, Part 2: Wrong War" »

Woohoo! Talk about your old "todo" items. For a looong time now I've wanted to add some kind of animation to the noollabs to make it clear that they are able to propel themselves through the air. Originally they were going to have jet propulsion, and the things on either side of their body were supposed to be the intake/exhaust for that. I tried to do an animation of one filling with air, and pushing that air out one side. It was...pathetically bad. I thought about having little puffs of steam coming out, and I guess that's still a viable option (viable meaning one that I can do with my limited artistic skills). However, for the time being, I've settled on a very poor animation of a propeller.

You can see it in action in the noollabs game:

http://www.leftoverpi.com/play/balloons.

(I did not add it to the introductory part, which becomes more and more amusingly-out-of-date with each enhancement. You have to get to the game itself to see it working.)

The impetus for this wasn't really checking the todo item off as much as it was getting a step closer to removing the placeholder introductory part entirely, and replacing it with gameplay that teaches you what that text was. But that's a topic for another day.

So, in my last post I mentioned that I started seeing the plight of the anti-reformists in the Math Wars side, and in a recent conversation with my brother he asked me what I saw in their side. Below I have included excerpts from my conversation with him and some expansion on the ideas.

Continue reading "How I became an enemy combatant in the Math Wars, Part 1a, A Brief Digression on the Futility of Force" »

I don't actually know when the Math Wars started. You might say that the first battles were with the New Math back in the 60's when I was still an accident waiting to happen (just kidding, Mom!). I don't really know what the "New Math" was, but I have some sense that there was an attempt to get kids to understand the concepts of math rather than just learning rote algorithms. So, rather than saying to the kids "just follow this procedure, and you'll get the right answer", you talk to them about the base ten number system, explain the concept of regrouping, etc when you teach subtraction.

Which sounds like a good idea--we want kids to understand, not just robotically replicate. The devil was in the details of course.

Continue reading "How I became an enemy combatant in the Math Wars, Part 1, Introduction to the Math Wars" »

So, the game of life now has a better explosion. Took more time to do this than any of the other features, but my son's gleeful giggle upon seeing it made it worth it.

First I just set it up to send all the currently "on" squares radially outward (actually I think it was/is a little more complex than that--they go out in such a way that everything gets to the outside at the same time). I had to struggle with it for quite a while until I figured out that Director was doing something weird when you called "mod" against floating point numbers. Anyway, when I finally got it all worked out, the explosion was disappointingly mundane. So I added a couple of rings around the center so there's always something to explode, and voila! giggles.

Updated the Conway's Game of Life game to let you nuke all the current cells and start over. This was requested by my kids shortly after they started playing with it.

For the forseeable future (1.5 weeks is usually about how long that lasts for me), I'm going to work exclusively on things my kids are interested in. That means I'm only going to be adding features they request or that their usage shows a strong need for. This "nuke button" is an example.

The funny thing about the nuke button is that when my wife saw it, she said "you should have some kind of explosion show on the screen". I said something like "maybe if the kids ask for it". My new focus was already saving me work!

But it was practically the first thing Jacob said when he saw the button. So it looks like I can't win.

Specifically, it's Conway's Game of Life. Even (or especially) if you don't know what that is, go to this url:

http://www.leftoverpi.com/play/life/

draw a little picture by clicking on the white canvas. Click the play button and watch it go.

It's amazingly complex--in fact, complex enough that you could build a computer out of it!--and equally mesmerizing.

You can read more about it here:

Conway's Game of Life [Wikipedia].

All for now, hopefully I'll get time to update this later.

So, once upon a time I was thinking about the statement that 2 is the only even prime. People observe this from time to time and think "Wow, that's weird--of all the primes, only 2 is even". Well, it doesn't take too much to realize that it's not really weird at all. One way of describing "evenness" is to say "any multiple of 2". There can't be any multiple of 2 in the primes (except 2), because it would be 2x[something], and therefore not a prime.

But why is it that people think it's weird?

Continue reading "Threevenness and other neologisms" »

So yesterday I was talking to a friend of mine about an alternative funding model I call "Nurture Capital". The basic idea is that some ideas that might normally take form as a non-profit organization might be able to be run at a profit. It would be different from a normal for-profit business in the sense that the profit wouldn't be the main motivation, but rather a means to keep the enterprise running. The main motivation would be whatever cause the business was designed to further.

Continue reading "Nurture Capital (tm) :)" »

A new feature has been added to Stretcher to give you more room to play with the fractals. You click the diagonal arrow to make the interface elements move out, and click it again to make them come back when you need them again.

Perhaps I should make it default to being "out", and have a toolbox icon or something to let people know that there are more controls available.

I would like to make the effect a little more smooth, with the stuff sliding out to the edge, and then perhaps having the mouse entering that area make them automatically slide back into place. All in good time, I suppose :). I should take a look at my todo list for that project and see what's missing.

Anyway, enjoy!

This was exciting to me, because it's the first time I have seen Benezet's experiment mentioned on the web. I've been carrying around a copy of his paper (not because of my fanatical devotion, but because it's still in my laptop bag from when I put it there to read on the plane to OSCON) and referring to it every so often, but now I can actually point to it on the intarwebs!

Apparently someone at this place in the UK that does really cool computer science research read about Benezet and loved it, and created the "Benezet Centre":

http://www.inference.phy.cam.ac.uk/sanjoy/benezet/

One of the best things about this is that now I can link to the three articles instead of depending on my paper copy to always be handy.

Oh, I guess you're wondering what Benezet did, eh? He quit teaching formal arithmetic to kids who were too young to care. Instead, he had teachers make up questions that might stimulate some mathematical thinking, develop concepts of scale and ratio, etc. By the end of sixth grade these kids were far, far beyond their traditionally-"educated" peers.

I've read that he got fired for this, but I don't have the background on that, I'll check it out and update. Benezet is one of the people I cite for proof to my assertion in an earlier post that mathematics instruction in school is worse than a waste of time. It's nice to see him getting attention from other folks.

I am pretty sure I referenced the "oodometer" in an earlier post. I had read someone talking about a little counting gadget (press the button and it adds one to the count, like a car's mechanical odometer registering another mile) and how they were surprised at how much interest it generated in their kids.

I figured I could bang one of those out in software in pretty short order, so I did, and then presented it to my son (maybe five years old at the time? Not sure exactly) to see what his reaction was.

Continue reading "A cute little mini-app with some cute history" »

I was doing some screen capture of Stretcher to show off its many cool features, and realized partway through editing that nobody would want to sit and watch all of it. So I started trying to pick out the cool stuff and release it separately.

Here's the first from that:

The writer of originality, unless dead, is always shocking, scandalous; novelty disturbs and repels.

Simone de Beauvoir

Of course, that doesn't necessarily mean that shocking, scandalous, disturbing, or repellent ideas are all original :). Nor that the original is worthwhile. But it's a good thing to keep in mind. A lot of what I'm talking about is kind of hard to swallow, but I think when we look back at it later people will wonder why we ever saw it differently.

And here's another from the same person--this really just says it all:

I wish that every human life might be pure transparent freedom.