In today’s comics, there is this Non Sequitur one:

Comics, to me, are interesting regardless of whether a particular one is funny, since they reveal a lot about the community and the society in which they appear. Usually, comics make an explicit point, but whether they do or not, they operate in a background of shared assumptions about what does *not* need to be said.

So what does this comic strip reveal about widely-held attitudes about math? For one, there is no need to explain *why* the kid is frustrated in the first panel. The one-word title on the book says enough. It’s math! It also needs no explanation why Danae needs to come up with a *new* system to make math fun – because we all know and appreciate that the old system isn’t. This is so obvious that when a comic strip intends to portray somebody as a real geek, all they have to do is show that those kids do like math, like Jason in the Foxtrot comics.

What other attitudes about math does it reveal? On the surface, the strip talks about using math to prove that you are right. But what is meant by “proving”? Somehow, it doesn’t sound like the intent is to carefully lay out your ideas so that somebody else will be convinced, see it for themselves, and say “I see it now! Of course!” Somehow, it doesn’t sound like Danae now sees math as an activity aimed at shared understanding, or a shared appreciation of ideas. That’s *not* in the background of shared assumptions – however much I would like it to be, it isn’t yet. Far from it. Danae’s notion of proving herself right seems to be more akin to invoking a powerful spell that smites the other person dead. The notion of math as an activity of invoking mysterious incantations that – if done just right – *kills* argument: the notion of mathematicians as a priesthood with math teachers as the nuns, making you repeat incomprehensible magic spells like Quod Erat Demonstrandum! Except that they aren’t ever even half as much fun as the magic and the spells in the Harry Potter books.

Math as magic invocations is a common attitude in school, too. The magic invocations are important because the teacher says so, and the only way the child knows if she’s doing the invocations right is because the teachers says so. Some kids seem to have the knack, and others don’t, and that’s just the way it is. School essentially continues with the kids who have the knack. In secondary schools, kids meet many teachers – successful adults in a position of authority – who are *not* their math teachers, and who will tell them straight up that math wasn’t for them, either. If a vast majority of kids comes out of school, having survived school, thinking that they don’t have the knack to do magic math invocations right, we shouldn’t be too surprised. The structure of the school experience helps perpetuate it.

I came across this while searching for ways to make math fun. (Incidentally, I just came up with a fun math game for children).

I agree that math is not taught well by most math teachers. I had a few outstanding math teachers when I was growing up, and they did make math fun. In one case, the teacher had races with the children to see who was the fastest at doing multiplication. We spent about 2 minutes a day on this contest, and about 6 boys really enjoyed it.

Anyway, keeping math fun, especially for young people, is more important than making sure they learn everything right the first time.

William,

Thanks for your comment. I think “making math fun” is only part of the answer. We never talk about “making ice cream fun”. And that’s because we don’t need to! Ice cream IS fun. Everybody already knows that. I think ultimately the challenge is to have children experience that math, as math, is fun in its own right. But what we learn along the way isn’t necessarily mathematics, we learn some activity that people call math but that consists of drudgery work with no discernible meaning, and judged by an authority who knows the answers, the RIGHT ANSWERS, but won’t tell us what they are. There is a quote in the “about” page that sums this up very nicely.

In this blog, by the way, I have no intention to point blame at particular teachers (even though there is probably at least a handful out there who well deserve it). I think the issue lies much deeper than that: it is a deeply rooted and interlocking system of assumptions and expectations that passes itself on from generation to generation.

If children came home day after day telling their parents how much fun they had in math class and how excited they all were, even the girls, even the poor kids, the minority kids, and even the kid who can’t tie his own shoe laces, then watch how fast the parents would get up in arms, complaining that whatever they are doing it couldn’t possibly be REAL math. And it isn’t just the parents either. It’s the older brothers and everybody else who is a survivor of the current system, in whatever way they survived.

William,

I saw your game. It’s an interesting one. Depending on the grade level, there might be an opening to look with the kids of how the sheets are put together, and how the whole thing works. There are binary versions based on the same principle that might be more approachable that way, i.e. more open to discovery.

You’re right. I got the idea from the more popular binary version of the game. But since I didn’t “invent” that one, I came up with this on instead.

It has the advantage of requiring only 4 pages for numbers between 0 and 80, as opposed to 5 pages for 0-63, as in the case of the binary. It also has the advantage that all of the numbers are displayed in sequence, letting users find their numbers more quickly. (The binary version of the game only displays half the numbers, which is confusing to young children.)

At an introductory level, both are good for getting students to have fun while adding numbers in their head…which doesn’t require knowledge of it being binary or ternary.

Regarding teaching math, this is my philosophy: First show them how, in a fun way. Then show them why.

Most math teachers do the opposite. For example, teaching about limits and using limits to define derivatives. I would teach the mechanics of derivatives first, showing some applications, and then teach the theory behind them. This is, according to my wife, a teaching method called “advance organizer”, a teaching method that doesn’t have much support in educational research. (Never mind that educational research is usually flawed for a number of reasons that I won’t go into here).

This method is akin to teaching a student to use a hammer before teaching them how to make one.

P.S. My wife hates icecream:) She prefers to eat hot peppers.

William,

for sure, most kids learn from the specific to the general. best wishes with your game.

Hail Senor Speelpenning,

I loved this short article! You have written a manifest piece of synchronicity; for just on this past Wednesday (27th) I was asking my professor what the (x) and (y) axis on the Cartesian co-ordinate system represent in reality. Of course he answered that (x) and (y) are variables, and that I should know the definition of variables. Oh the frustration! I then asked him why all math has always been taught to me as a set of “incantations.” That word is the only word I possess that seems to capture the observation, and it truly is a fascinating observation.

Just for closure: I learned that the (x, y, z) axis represent the three directions of our three dimensional universe (and that every real place is a compromise of three directions) from a philosophy student. Fascinating.

R. Maldonado

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