Archive for the 'Bad Math Education' category

Everyone should program, or Programming is Hard? Both!

Oct 05 2012 Published by under Bad Math Education, Programming

I saw something on twitter a couple of days ago, and I promised to write this blog post about it. As usual, I'm behind on all the stuff I want to do, so it took longer to write than I'd originally planned.

My professional specialty is understanding how people write programs. Programming languages, development environment, code management tools, code collaboration tools, etc., that's my bread and butter.

So, naturally, this ticked me off.

The article starts off by, essentially, arguing that most of the programming tutorials on the web stink. I don't entirely agree with that, but to me, it's not important enough to argue about. But here's where things go off the rails:

But that's only half the problem. Victor thinks that programming itself is broken. It's often said that in order to code well, you have to be able to "think like a computer." To Victor, this is absurdly backwards-- and it's the real reason why programming is seen as fundamentally "hard." Computers are human tools: why can't we control them on our terms, using techniques that come naturally to all of us?

And... boom! My head explodes.

For some reason, so many people have this bizzare idea that programming is this really easy thing that programmers just make difficult out of spite or elitism or clueless or something, I'm not sure what. And as long as I've been in the field, there's been a constant drumbeat from people to say that it's all easy, that programmers just want to make it difficult by forcing you to think like a machine. That what we really need to do is just humanize programming, and it will all be easy and everyone will do it and the world will turn into a perfect computing utopia.

First, the whole "think like a machine" think is a verbal shorthand that attempts to make programming as we do it sound awful. It's not just hard to program, but those damned engineers are claiming that you need to dehumanize yourself to do it!

To be a programmer, you don't need to think like a machine. But you need to understand how machines work. To program successfully, you do need to understand how machines work - because what you're really doing is building a machine!

When you're writing a program, on a theoretical level, what you're doing is designing a machine that performs some mechanical task. That's really what a program is: it's a description of a machine. And what a programming language is, at heart, is a specialized notation for describing a particular kind of machine.

No one will go to an automotive engineer, and tell him that there's something wrong with the way transmissions are designed, because they make you understand how gears work. But that's pretty much exactly the argument that Victor is making.

How hard is it to program? That all depends on what you're tring to do. Here's the thing: The complexity of the machine that you need to build is what determines the complexity of the program. If you're trying to build a really complex machine, then a program describing it is going to be really complex.

Period. There is no way around that. That is the fundamental nature of programming.

In the usual argument, one thing that I constantly see is something along the lines of "programming isn't plumbing: everyone should be able to do it". And my response to that is: of course so. Just like everyone should be able to do their own plumbing.

That sounds like an amazingly stupid thing to say. Especially coming from me: the one time I tried to fix my broken kitchen sink, I did over a thousand dollars worth of damage.

But: plumbing isn't just one thing. It's lots of related but different things:

  • There are people who design plumbing systems for managing water distribution and waste disposal for an entire city. That's one aspect of plubing. And that's an incredibly complicated thing to do, and I don't care how smart you are: you're not going to be able to do it well without learning a whole lot about how plumbing works.
  • Then there are people who design the plumbing for a single house. That's plumbing, too. That's still hard, and requires a lot of specialized knowledge, most of which is pretty different from the city designer.
  • There are people who don't design plumbing, but are able to build the full plumbing system for a house from scratch using plans drawn by a designer. Once again, that's still plumbing. But it's yet another set of knowledge and skills.
  • There are people who can come into a house when something isn't working, and without ever seeing the design, and figure out what's wrong, and fix it. (There's a guy in my basement right now, fixing a drainage problem that left my house without hot water, again! He needed to do a lot of work to learn how to do that, and there's no way that I could do it myself.) That's yet another set of skills and knowledge - and it's still plumbing.
  • There are non-professional people who can fix leaky pipes, and replace damaged bits. With a bit of work, almost anyone can learn to do it. Still plumbing. But definitely: everyone really should be able to do at least some of this.

  • And there are people like me who can use a plumbing snake and a plunger when the toilet clogs. That's still plumbing, but it requires no experience and no training, and absolutely everyone should be able to do it, without question.

All of those things involve plumbing, but they require vastly different amounts and kinds of training and experience.

Programming is exactly the same. There are different kinds of programming, which require different kinds of skills and knowledge. The tools and training methods that we use are vastly different for those different kinds of programming - so different that for many of them, people don't even realize that they are programming. Almost everyone who uses computers does do some amount of programming:

  • When someone puts together a presentation in powerpoint, with things that move around, appear, and disappear on your command: that is programming.
  • When someone puts formula into a spreadsheet: that is programming.
  • When someone builds a website - even a simple one - and use either a set of tools, or CSS and HTML to put the site together: that is programming.
  • When someone writes a macro in Word or Excel: that is programming.
  • When someone sets up an autoresponder to answer their email while they're on vacation: that is programming.

People like Victor completely disregard those things as programming, and then gripe about how all programming is supercomplexmagicalsymbolic gobbledygook. Most people do write programs without knowing about it, precisely because they're doing it with tools that present the programming task as something that's so natural to them that they don't even recognize that they are programming.

But on the other hand, the idea that you should be able to program without understanding the machine you're using or the machine that you're building: that's also pretty silly.

When you get beyond the surface, and start to get to doing more complex tasks, programming - like any skill - gets a lot harder. You can't be a plumber without understanding how pipe connections work, what the properties of the different pipe materials are, and how things flow through them. You can't be a programmer without understanding something about the machine. The more complicated the kind of programming task you want to do, the more you need to understand.

Someone who does Powerpoint presentations doesn't need to know very much about the computer. Someone who wants to write spreadsheet macros needs to understand something about how the computer processes numbers, what happens to errors in calculations that use floating point, etc. Someone who wants to build an application like Word needs to know a whole lot about how a single computer works, including details like how the computer displays things to people. Someone who wants to build Google doesn't need to know how computers render text clearly on the screen, but they do need to know how computers work, and also how networks and communications work.

To be clear, I don't think that Victor is being dishonest. But the way that he presents things often does come off as dishonest, which makes it all the worse. To give one demonstration, he presents a comparison of how we teach programming to cooking. In it, he talks about how we'd teach people to make a soufflee. He shows a picture of raw ingredients on one side, and a fully baked soufflee on the other, and says, essentially: "This is how we teach people to program. We give them the raw ingredients, and say fool around with them until you get the soufflee."

The thing is: that's exactly how we really teach people to cook - taken far out of context. If we want them to be able to prepare exactly one recipe, then we give them complete, detailed, step-by-step instructions. But once they know the basics, we don't do that anymore. We encourage them to start fooling around. "Yeah, that soufflee is great. But what would happen if I steeped some cardamom in the cream? What if I left out the vanilla? Would it turn out as good? Would that be better?" In fact, if you never do that experimentation, you'll probably never learn to make a truly great soufflee! Because the ingredients are never exactly the same, and the way that it turns out is going to depend on the vagaries of your oven, the weather, the particular batch of eggs that you're using, the amount of gluten in the flour, etc.

To write complicated programs is complicated. To write programs that manipulate symbolic data, you need to understand how the data symbolizes things. To write a computer that manipulates numbers, you need to understand how the numbers work, and how the computer represents them. To build a machine, you need to understand the machine that you're building. It's that simple.

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Argh, argh, argh!!!!

Oct 06 2010 Published by under Bad Math, Bad Math Education

Via FailBlog:

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Stupid Grading Tricks

May 20 2008 Published by under Bad Math Education

A bunch of people have been mailing me links to an article from USA today
about schools and grading systems. I think that most of the people who've
been sending it to me want me to flame it as a silly idea; but I'm not going to do that. Instead, I'm going to focus on an issue of presentation. What they're talking about could be a good idea, or it could be a bad idea - but because the
way that they present it leaves out crucial information, it's not possible to meaningfully judge the soundness of the concept.

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Idiot Math Professors, Fractions, and the Fun of Math

Feb 01 2008 Published by under Bad Math Education

A bunch of people have been sending me links to a USA Today article about a math professor who wants to change math education. Specifically, he wants to stop teaching fractions, and de-emphasize manual computation like multiplication and long division.

Frankly, reading about it, I'm pissed off by both sides of the argument.

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Dirty Rotten Infinite Sets and the Foundations of Math

Oct 15 2007 Published by under Bad Math Education

Today we've got a bit of a treat. I've been holding off on this for a while, because I wanted to do it justice. This isn't the typical wankish crackpottery, but rather a deep and interesting bit of crackpottery. A reader sent me a link to a website of a mathematics professor, N. J. Wildberger, at the University of New South Wales, which contains a long, elegant screed against the evils of set theory, titled "Set Theory: Should You Believe?"

It's an interesting article - and I don't mean that sarcastically. It's over the top, to the point of extreme silliness in places, but the basic idea of it is not entirely unreasonable. Back at the beginnings of set theory, when Cantor was first establishing his ideas, there was a lot of opposition to it. In
my opinion, the most interesting and credible critics of set theory were the constructivists. Put briefly, constructivists believe that all valid math is based on constructing things. If something exists, you
can show a concrete instance of it. If you can describe it, but you can't build it, then
it's just an artifact of logic.

Some of that opposition continues to this day, and it's not just the domain of nuts. There are
serious mathematicians who've questioned the meaningfulness of some of the artifacts of modern
set-theory based mathematics. Just to give one prominent example, Greg Chaitin has given lectures in which he discusses the idea that the real numbers aren't real: they're just logical artifacts which can never actually occur in the real world, and rationals are the only real real numbers. (I don't think that Greg really believes that - just that he thinks it's an interesting idea to consider. He's far
too entranced with set theory. But he clearly considers it valid enough to be worth thinking about
and talking about.)

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Innumerate School Administrators

May 16 2007 Published by under Bad Math Education

Have you ever wondered about the real reason why math education in our schools is so awful? Why despite the best efforts of large numbers of parents, the schools seem to be incapable of figuring out why they're so dreadfully bad at recognizing the difference between a halfway decent math curriculum and a trendy piece of garbage?

Read below the fold for a perfect example of why. The short version: the people who are involved in running education in America consider it perfectly acceptable to be idiots when it comes to math.

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