

Gamifying Algebra  - robinhouston
http://terrytao.wordpress.com/2012/04/15/gamifying-algebra/

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SagelyGuru
_'My own son can get quite frustrated after performing a lengthy series of
computations to solve an algebra problem, only to be told that the answer was
wrong due to an arithmetic error; I am sure this experience is common to many
other schoolchildren'_

This frustration is largely due to the fact that such a useful lesson for life
is generally neglected, skimmed-over or outright deliberately denied in order
to satisfy the ideologues of 'modern education'.

Thus many people are way too much surprised that being right is what matters,
not the amount of effort it took to get there.

~~~
evincarofautumn
So are you opposed to teachers offering partial credit for problems that are
mechanically correct but have clerical or arithmetic errors?

For me, algebra is easy, but writing out steps is very difficult, and
sometimes I prefer to use a process other than the one taught in class. Should
the goal of math education be to solve problems or to learn processes?

In the real world, it’s solving problems that matters—I wouldn’t say “being
right”, necessarily—but it’s also important to be able to weigh different
potential solutions to find the best or most efficient. Programming is a
decent example of this—don’t go for the O(n²) algorithm when the O(n log n) is
just as easy to implement.

But even better, consider a startup. If you want to build an online store
application in 1995, and doing it in Lisp means you expend less effort than
your Lispless competitors to get to the same “right answer”, then you should
take the advantage. The amount of effort _does_ matter.

~~~
nocipher
_For me, algebra is easy, but writing out steps is very difficult, and
sometimes I prefer to use a process other than the one taught in class. Should
the goal of math education be to solve problems or to learn processes?_

That is a false dichotomy. The goal of math education is to "learn processes"
to "solve problems". You can't skip the processes and jump straight to
solving. Before you can pick a proper algorithm, you have to already know a
few -- that's the learning processes part in programming. This holds for any
skill you choose to learn; before you can do something well, you have to be
able to do it in the first place.

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6ren
Playing the demo game, I think the idea has merit. But I'm concerned that even
the presence of numbers is a turn off - that aspect certainly _looks_
unappealing.

Perhaps reverse the application of the initial observation, that many games
use maths, and start with a game without any figures, then, show the numbers
behind it, in phases. This would create a link between something kids already
grasp, and something new (numbers), which is a great way of learning. It would
give the experience of a deeper world being revealed. And if using the numbers
also made it easier to beat the game, it would give them a motivation; an
example of useful application; and a sense of mastery.

For the game designer, that initial version with no maths would also make it
clear whether the game was any fun in its own right. (It seems educational
aims often obscure this.)

~~~
EvilTerran
... now I'm also reminded of Alligator Eggs (
<http://worrydream.com/AlligatorEggs/> ) - a symbol-free kinda-gamification of
lambda calculus.

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oskarth
Idea for a simple mobile game, Gauss Jordan Golf:

\- Specify 18 (or a multiple thereof with minor number changes) equations of
varying difficulty.

\- Allow free choice of standard computer calculated operations, and a give-up
button once you reach, say, 5 strokes.

\- Keep a highscore.

Could be extended by viewing Gauss Jordan class of problems as a golf course
and adding other courses.

The emphasis on a low stroke count as well as removing the obstacle of
arithmetic makes the experience more like a game, just like Tao is suggesting.
This assumes a low stroke count is a good metric, as well as something
necessarily desirable - something that might not be true for all classes of
elementary mechanical problems.

~~~
srconstantin
I agree; the whole thing could be done with pictures rather than numbers. Lay
out an actual grid, with objects -- seven ladybugs in the third row, fourth
column, etc. When you subtract one row from another, you physically drag the
ladybugs from one row over the other row, and when they 'match' they
disappear. You can tap into physical intuition.

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AlexLegg
I'm not sure that gamifying algebra will make it any more desirable to kids. I
think that those who want to see it as a game already see it as a game in
their heads. I know I certainly did back in high school.

Still a cool idea though!

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EvilTerran
I'm reminded of Manufactoria ( <http://pleasingfungus.com/Manufactoria/> ),
which does a rather nice job of 'gamifying' a concept that's effectively
Turing Machines.

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albertsun
It seems that the main improvement here is not anything magical about
"gamification" but the idea of presenting students with progressively harder
algebra problems in which they get to try out new problem solving methods
gradually.

Unfortunately, this doesn't work in many classrooms because the teacher has to
manage too many different students learning at different rates and can't
tailor the lessons appropriately to all of them at once.

~~~
michaelf
I'd think that a huge benefit "gamification" is that it allows students to
learn at their own pace and without much teacher guidance. Kids figure out how
to play Portal and Civilization, for instance, without a teacher hovering over
them to tailor their lessons.

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vessenes
This is the wrong sort of of 'gamification'.

The part of gamification that works is dripping out little bursts of serotonin
based on intermittent reward schedules.

Farmville has proved you could addict people to successful algebra
manipulation, but it won't be in an interface like this, in fact, there isn't
a need for the cute dragons and fairies and stuff at all -- just levels,
achievements, cool rare rewards, sound and a little bling all around doing the
algebra problem correctly.

One thing I think the scratch demo does get right is the per-step nature of
solving these problems. I would imagine that you'd have a directed graph of
possible intermediate steps for solving and reward along the way for a harder
problem if you were serious about teaching algebra this way.

~~~
Estragon
You're kind of missing the point. Tao is under the impression that most
"gamified" math education software is based on rewards for solving entire
problems. He believes that rewarding smaller steps on the path to the solution
of more complex algebraic problems would be more effective. He's not trying to
suggest the specific rewards to use with his demo, only the reward schedule.

(I say "under the impression" because the first comment on his post implies
that games which break things down this way already exist. I don't actually
know the truth of it.)

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huherto
I had a similar idea after watching my kid staring at the blank paper. The
idea was to have an interactive white board where you could manipulate an
equation. The kid can try several things but the computer will only allow
those that are valid. I even made a very crud attempt to show the concept.
Please take a look at it. <http://algebraexplorer.appspot.com/>

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achllies
I absolutely love this concept. The game mechanics have the potential to make
the concepts extremely clear, though we might end up with a generation of
people who need "algebra calculators". I suppose that is why he suggest in
game points for doing things by hand.

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sausagefeet
Math Blaster needs to make a comeback!

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ranit8
Can you still edit the post title? It's missing an important question mark.

