5 ms·

Gamifying Algebra

82 points by robinhouston 15y ago

oskarth 15y ago
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 15y ago
  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.
EvilTerran 15y ago
I'm reminded of Manufactoria ( http://pleasingfungus.com/Manufactoria/ http://pleasingfungus.com/Manufactoria/ ), which does a rather nice job of 'gamifying' a concept that's effectively Turing Machines.
6ren 15y ago
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 15y ago
  ... now I'm also reminded of Alligator Eggs ( http://worrydream.com/AlligatorEggs/ http://worrydream.com/AlligatorEggs/ ) - a symbol-free kinda-gamification of lambda calculus.
- deleted 15y ago
  [deleted]
sausagefeet 15y ago
Math Blaster needs to make a comeback!
AlexLegg 15y ago
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!
ranit8 15y ago
Can you still edit the post title? It's missing an important question mark.
SagelyGuru 15y ago
'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.
- srconstantin 15y ago
  I agree that difficulty is a good lesson; but it doesn't seem to be working for a lot of people in the US. Many students give up on math early. That might not be economically sustainable. I don't think math education is optimized to make the most of intuition and motivation, and I really don't think experimenting with improvements is harmful.
  - nocipher 15y ago
    I concur. Hard life lessons should not be taught in the context of learning a new skill. Those can wait until after a degree of proficiency has been attained lest we undermine their efforts completely.
- evincarofautumn 15y ago
  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.
albertsun 15y ago
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 15y ago
  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.
achllies 15y ago
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.
vessenes 15y ago
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 15y ago
  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.)
huherto 15y ago
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/ http://algebraexplorer.appspot.com/

82 points by robinhouston 15y ago

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 15y ago
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.

EvilTerran 15y ago

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

6ren 15y ago

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 15y ago
... now I'm also reminded of Alligator Eggs ( http://worrydream.com/AlligatorEggs/ http://worrydream.com/AlligatorEggs/ ) - a symbol-free kinda-gamification of lambda calculus.
deleted 15y ago
[deleted]

sausagefeet 15y ago

Math Blaster needs to make a comeback!

AlexLegg 15y ago

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!

ranit8 15y ago

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

SagelyGuru 15y ago

'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.

srconstantin 15y ago
I agree that difficulty is a good lesson; but it doesn't seem to be working for a lot of people in the US. Many students give up on math early. That might not be economically sustainable. I don't think math education is optimized to make the most of intuition and motivation, and I really don't think experimenting with improvements is harmful.
- nocipher 15y ago
  I concur. Hard life lessons should not be taught in the context of learning a new skill. Those can wait until after a degree of proficiency has been attained lest we undermine their efforts completely.
evincarofautumn 15y ago
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.

albertsun 15y ago

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 15y ago
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.

achllies 15y ago

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.

vessenes 15y ago

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 15y ago
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.)

huherto 15y ago

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/ http://algebraexplorer.appspot.com/