

DragonBox: Algebra beats Angry birds - aymeric
http://www.wired.com/geekdad/2012/06/dragonbox/all/

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jessriedel
Does anyone have any evidence, anecdotal or otherwise, that gamification is
good for teaching STEM ideas in the long term? I am wary of rewarding the
brain with in-game loot for memorizing the rules of algebra rather than with
the deep satisfaction that comes with understanding. Obviously, this latter
type of reward cannot be as consistently provided and requires a certain
maturity (maybe), but ultimately I think it's what drives most insightful
people.

Here's a good example of what bothers me:

>As the game progresses, you’ll start seeing cards that are above and below
each other, with a bar in the middle — and you’ll learn to cancel these out by
dragging one onto the other, which then turns into a one-dot. And you’ll learn
that a one-dot vanishes when you drag it onto a card it’s attached to (with a
little grey dot between them). These, of course, are fractions —
multiplication and division — but you don’t need to know that to play the
game, either.

That last sentence is especially telling.

To me, gamification is suited for making necessary but painful tasks fun (e.g.
cleaning your desk, tagging media, memorizing facts), but not for deep
learning (e.g. algebra, quantum mechanics, object-oriented programming). But
maybe, at 26, I'm just not with the times.

EDIT: I think ColinWright is getting at the same worry, and his comment is
more fleshed out <http://news.ycombinator.com/item?id=4106567>

~~~
ezyang
Brett Victor writes:

 _When most people speak of Math, what they have in mind is more its mechanism
than its essence. This "Math" consists of assigning meaning to a set of
symbols, blindly shuffling around these symbols according to arcane rules, and
then interpreting a meaning from the shuffled result. The process is not
unlike casting lots._

 _This mechanism of math evolved for a reason: it was the most efficient means
of modeling quantitative systems given the constraints of pencil and paper.
Unfortunately, most people are not comfortable with bundling up meaning into
abstract symbols and making them dance. Thus, the power of math beyond
arithmetic is generally reserved for a clergy of scientists and engineers
(many of whom struggle with symbolic abstractions more than they'll actually
admit)._

I think gamification is a great way to teach symbol manipulation, and I think
(contrary to Bret) that symbol manipulation is a prerequisite for deeper STEM
ideas.

I do also believe that harder mathematical problems can also be gamified, but
this process is much less well understood, and you'll probably want a few
theorem prover experts around if you attempt a system like that.

~~~
jessriedel
> I think (contrary to Bret) that symbol manipulation is a prerequisite for
> deeper STEM ideas.

Can you elaborate on this further? I tend to disagree, but I don't know if I
have all that much to say to back it up.

I mean, sure, there's just no good way to understand shear forces without
being able to manipulate matrices (so I agree with dbaupp's sibling comment),
but that doesn't mean you want to learn the rules of matrix algebra as if they
were arbitrary rules enforced by the stick and carrots in a game.

~~~
ezyang
In the case of mathematics, there is a fundamental sense in which _the symbols
and their manipulations are what you're studying._ Think of it as if you were
an archeologist: the symbols are the artifact of study. It's only half of the
picture: you must(!) come up with a different way of intuitively understanding
it--but at the end of the day if you really want to precisely say what it is
you're talking about, it's symbols.

~~~
jessriedel
OK, I think I see what you're getting at. But we could devise a AltDragonBox
game with a completely different set of arbitrary rules. (Possibly even rules
that are inconsistent.) And as far as game play goes, AltDragonBox would work
just as well. But there's a reason that the rules of algebra are what they
are. And if you can't distinguish between DragonBox and AltDragonBox, I don't
think you're learning what you need to learn.

Here's another way to look at it: we all know people who could ace their high
school math tests because they had memorized the rules of manipulation but
_weren't_ good at math--as evidenced by their poor performance in college and
failure to succeed in future STEM classes. If "the symbols and their
manipulations are what you're studying" (which, I agree, there is some truth
to), then what _is_ it exactly that these people were lacking?

~~~
dxbydt
> there's a reason that the rules of algebra are what they are

But which algebra, and which rules ? There are infinitely many algebras ( eg.
Algebra over the field of reals, Banach Algebra, relational algebra, boolean
algebra, sigma algebra etc. ) The "rules" are really constructs you decide
that apply to the elements of the space that conform to your algebra. So for
example the reals are a field that have ordering, so you can talk about less
than and greater than, but the complex numbers don't have an imposed order and
you'd have to first define a norm to map them onto the reals. The AltDragonBox
with its own inconsistent arbitrary rules will still have some algebraic
encoding. Whether that's useful to you is debatable. Like in my algebra I
could overload plus to mean multiply and square root to mean divide by 7 and
add -3 and then try to figure out what exponentiation works out to. It would
be interesting...maybe not useful, but its still an algebra. Maybe you won't
have closure...the elements may not end up in a field or even in a
semigroup...its a nice make-believe algebra.

~~~
jessriedel
Yes, that's a very impressive display of all the math you must surely know,
but its completely misses the point. The rules of elementary algebra really
_are_ special, and it has to do with their correspondance to real things in
real life. There's a reason mathematicians don't just enumerate all possible
algebras and study them one by one.

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ColinWright
I was going to add this as an edit to my earlier comment, but I'm on a crappy
connection, and was too late. Let me expand on my comment.

I think this is a brilliant idea, and it seems to be well executed. I don't
have the necessary hardware to run it, so I haven't played with it, but it
looks to be a wonderful game based on algebraic manipulations. I, along with
everyone else, expect and hope that it will engage players and allow them to
learn the rules and skills of such manipulations.

And probably that's a good thing. Let me try to explain the underlying reasons
for my sense of unease, as best I understand them.

Firstly, I am concerned that this will merely enhance the sense that math is
simply arbitrary manipulations with neither meaning nor motivation. Many of
the kids I tutor can do the manipulation, but don't get the point, and never
connect it with reality.

Next, some of the kids I tutor can't do the manipulations without making
stupid errors, and I can't help but feel that even after practising with this,
they will still make stupid errors. Link that to the apparent meaninglessness,
and there's a recipe for frustration.

Thirdly, this doesn't help to connect the creation of equations with the
physical problem to be solved, and it doesn't help interpret any final answer.
These are the steps that the kids I deal with simply can't do.

Finally, as someone commented, this isn't intended to be the whole and entire
course, and it's supposed to be just one tool to help one stage, and to be
built on and leveraged by the teachers. I've lost count of the number of
wonderful tools and ideas that I've seen whither and die because the teachers
can't make use of them. In some cases the teachers don't really understand
them, but I would hope that fate would be avoided by this.

So in summary, I think this is a wonderful tool, and it has the potential to
be a fantastic aid to learning. I am deeply uneasy about the further divorcing
of algebraic manipluation from any sense of meaning, but I look forward with
interest to see if it can be used in a meaningful way.

~~~
pacala
You keep using this word, "meaning". What does it mean? ;)

~~~
loboman
In a programming language, you have syntax and semantics. Syntax tells you
what you can write and how; for example what is a valid program. Semantics
tells you what a program evaluates to, and maps your programs to another
domain.

Here you have the same thing. In math you have syntax, and semantics. The
other domain from semantics might be abstract, or it can be purely mechanical,
but it can also be connected to reality. If your operations map to nothing
that makes sense to you, the operations are just mechanical; you solve
equations in some way because you know it's right but you don't understand
why. If your operations map to other domains that you understand (also if they
are abstract domains in your imagination), you can understand why the
operations work like they do, and you know why you have to solve them the way
you do it.

Maybe the equations don't have a specific meaning per se; but if they don't
have any meaning for you, there is no way you understand what you are doing
when you solve them.

~~~
pacala
A programming language semantics is a set of mutually recursive equations
describing how a well formed program manipulates values. The equations
themselves are as mechanical as the they can possibly be.

~~~
loboman
The recursive equations are the means by which you obtain a mapping from one
domain to the other (eg. from the programming symbols to the program values).
For equations there are many ways in which you can give meaning to each
equation in the same way, such that the mechanical process makes sense.

For example:

a x = b (text) --> x is unknown, it is the right one if f(x) = a x equals
f'(x) = b; both functions are programs you can compute and play with

from there you go mechanically to:

x = b/a (text) --> x is unknown, it is the right one if f(x) = x equals f'(x)
= b/a

while in the first step it was hard to tell much about x, now we can see that
it is trivial to guess which is the right x; x must be b/a

This is the first mapping from the domain of symbols to another domain that I
could think of. There must be more natural mappings that can be used like
this.

~~~
pacala
Check out abstract interpretation and Galois connections. These require a
different kind of mechanical manipulations than simple algebra. I wonder if
there is a gamification to be found in this direction.

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patio11
I lack words to describe how awesome this game is, both from a pedagogical
perspective and from "It's genuinely fun to play."

My fiancee has just ordered me to take a bath as a clever way to get me away
from the iPad _because she wants to do algebra, by herself_.

~~~
solutionyogi
You are the master of the words and if _you_ are failing to find words it
means that I HAVE to get this game. Thanks.

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ph0rque
I have an idea similar to this that would secretly teach circuits:

The game would be a water-tube building game. Voltage would represent the
height drop that causes the water to flow, current would be, well... current,
resistance could be marked by notches in the tube section, etc. Each scenario
would involve building a water maze to reach a specific objective.

Gradually, different tube sections would be replaced by circuit schematics,
until at the end of the game, you would be designing straight-up circuits.

Feel free to build this, just let me know when it's available :).

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ColinWright
I have a deep unease about this. It's brilliant that the kids learn the
manipulations (although it's unclear if they'll be able to follow the rules
when not enforced by the app) but it's detached. It's unconnected, and there's
no sense that it's actually potentially useful.

It will be fascinating to see where it goes, but I'm worried about how it will
translate into actual solving of problems, which is what algebra is about. Too
many people think algebra is about mindless manipulation, and this seems to
reinforce that.

Yet to be seen. Interesting times.

~~~
Dn_Ab
I remember you said once that rote practice and drilling of arithmetic helped
even higher math. I agree. How is drilling mental math any less mechanical
than the unconscious familiarization/ingraining of algebraic concepts of this
app? In both cases there is an intangible benefit beyond the process.

For the brain, prior meeting in a simpler guise is useful in reducing friction
when incorporating new concepts. I imagine it like starting off with good
weights when doing a search with no global.

~~~
ColinWright

      * How is drilling mental math any less mechanical
        than the unconscious familiarization/ingraining
        of algebraic concepts of this app?
    

There is a difference in that with mental arithmetic you have, or can have, a
direct connection with an underlying reality. This seems to be entirely
divorced from any reality, and the rules can, if you don't already know what's
going on, appear completely arbitrary.

I can picture asking an adept "why do you put the same thing on each side?"
And getting the answer - "Cos that's just how it works."

~~~
VSerge
It -is- how it works. In algebra at least.

~~~
ColinWright
Yes, it is how it works, but it's not _just_ how it works. There are reasons
for the rules, and underlying models for the rules. It's not arbitrary, it has
evolved over centuries to have purpose.

It's not "just" how it works. When you have the equals sign between two
expressions you are saying that instantiation of the variables must result in
quantities that are the same. When you modify one side then you must make the
same modification on the other side in order to retain that property. there
are _reasons_ for things to be the way they are.

It's not "just" how it works.

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DannoHung
Very cool. This actually intensely reminds me of Ed Yang's logitext sequent
calculus tutorial:
[http://logitext.ezyang.scripts.mit.edu/logitext.fcgi/tutoria...](http://logitext.ezyang.scripts.mit.edu/logitext.fcgi/tutorial)

You don't have to know the rules of the sequent calculus, you can just click
around, but the theorem prover will ensure that you can't break them. Then, by
fucking around and reading through the tutorial, you can pretty much learn how
it works.

I think that things like this are the _right_ way to start designing
interactive education. Create a play space, enforce the rules, provide lessons
that act as hints and tips for understanding how the rules work.

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fallous
This is brilliant. You're teaching the mechanics of algebra but initially
ignoring "this is math" which lets players avoid the mental barriers they may
have erected about that particular subject.

Being able to "do" first makes explaining the "why" later much easier and more
interesting.

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patrickk
When I saw the title, I thought "would it not make more sense to use
trigonometry to beat Angry Birds?"

<http://news.ycombinator.com/item?id=1043491>

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SpencerAiello
Who's trying to prove the Goldbach conjecture before they learn the rules of
algebra? Most kids in middle to high school math classes aren't worried about
their "mathematical maturity" or about having powerful insight. Rather, this
obviously shows that the rules of algebra can be applied to other sets of
symbols, and that letters and numbers are simply a subset of a much larger
set. How is that not a powerful notion? If you're bothered by this, then go
back and read Herstein, or any other intro to group theory. Seriously, this is
a great way to get kids actively thinking about the rules of manipulation of
symbols.

The seeds of abstraction must be planted before you can play with more lofty
ideas. If games aren't a good way to enjoy mathematics, then you have missed
the point of a lot of math.

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carb
Very innovative, I love seeing educational apps that make the player think and
solve puzzles instead of just repeatedly showing them rules to memorize.

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jbhkb1
Hi, as the guy behind the game concept, I am thrilled to read all these
comments and discussions. For those interested I can explain how I thought of
this game and which goals we try to reach with it. First of all, the game is a
direct translation of my view of math. Abstract objects, relations between
them, and playing around with it. Obviously there is no One mathematics. Each
of us we have our own subjective understanding of it. Secondly, I have three
kids, and I want the best for them. Mathematics can be used to understand
better our world and can give access to better decisions. The earlier, the
better. That means I d like them to learn K-12 math as soon as they can get
it. And they could get everything now, if we had the right tools. Just to say
that I make sure that the games we create transfer to useful knowledge. I am
not here to sell another game, I am here to make children learn. Third, first
we teach how to solve equations and then, how to set up equations. 4\. Our
goal is to make players think and learn. For example, players have to figure
out themselves how to solve an equation with x in denominator. I think we are
the only ressource that let a kid find out that by herself. School has no time
to let kids spend time on high level thinking... 5\. most importantly, this
game is about discovery learning. Trial and error. The only reason there are
texts, is that parents feel unease with textless discovery games. Children and
parents learn completely differently. So imagine what a teacher does to our
poor kids (i am myself a teacher, so i try to replace myself...). She cant
test her teaching as we tested our game... how can you be better without
feedbacks? 6\. no teacher will be able to beat this game. Because of
feedbacks, discovery mechanisms, beautiful symbols, tests etc.. players solve
200 equations in 1,5 hours without any prerequisite... and explanations. This
game avoid many pitfalls that communication with words create when explaining
algebra. Teaching algebra from arithmetic, concrete to abstract is to my mind
crazy. It s an unecessary step. This game is the result of a thinking process
where I sat as a big hairy goal to teach K-12 math in less than 20 hours. It
is obvious that to do that, we have to think very differently. For example
none has noticed that the equation is set up in two dimensions. The game seems
simple and obvious and it is easy to start discussing the effect of it. It was
pretty complex to make it that simple.... Make complex things simple without
oversimplifying, that s the point to discuss to progress in learning science.
That s what the game is about. And i hope it inspires many to work with it.

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ph0rque
I just bought this for my 5-year-old daughter. She mastered the first level
(or chapter, as the game calls levels) in about an hour, with minimal input
for me (I just read the minimal instructions at the beginning).

I am really excited about this game, and others like it.

As someone from the former Soviet Union where we started learning rudimentary
algebra in first grade, I remember variables being explained as a box that you
have to figure out what is in it by putting everything else on the other side
of the equals sign. This game literally takes this concept and gamifies it.

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jacoblyles
I studied pre-Algebra in the 6th grade - about 12 years old. The author's
child is learning the same things from Dragon Box at 5 years old. That gives
kids nowadays a 7-year jump on the standard American public school curriculum.
It's amazing to think of how much more kids will be able to learn and
accomplish with their lives with iPad based learning tools.

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creamyhorror
This is awesome, I'm going to buy this for my little brother.

I can imagine expanding upon this concept to get kids to solve word problems.
Present a simple word problem, give the player some variables/cards and
operators to pick from, and let her arrange them into a suitable equation or
three. Award points for reaching states like a fully isolated variable, which
is basically the solution.

Maybe specific guided processes could be created for different varieties of
problems, e.g. distance-time problems, simultaneous equations, algebra applied
to geometry, combinatorics...each type of problem could be broken up into sub-
components which the player first arranges into the right combination, and
then returns to the original algebraic solving process as the final step.

Hmm. If my current startup idea doesn't work out, I might have to look into
venturing into education. I always liked tutoring anyway.

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delinka
I convinced my mother to purchase the iOS version for all her grandchildren
... and then I played it. There was a distinct change in my behavior when
there was a distinct change in the cards - they go from colorful bugs with
different backgrounds to different symbols in black on white backgrounds.
That's when I had to concentrate on what was actually on the screen and think
about what moves to make.

I have yet to see what the younger ones do with it, but my 13yo found it
somewhat interesting until he had to _think_ \- that made it less of a game
for him and he became less interested.

My anecdotal experience with this game suggests that the same people who would
excel at math (with a trait for "why is this wrong? let's try something else;
let's dig deeper") will also excel at this game. Those that don't want to
_think_ are going to give up when the game changes.

~~~
SudarshanP
This is not a solution for those don't want to think. But many who would
gladly think if they cared will now find the transition to algebraic symbol
manipulation lot less painful. Kids have their own set of "wants"... In most
situations they have no clue how math is a path to satisfy such a want.

I once came across a thread on the scratch website where a student was saying
he wanted to figure out how to use trig functions because the guys using trig
functions wrote much better games. He(she) was complaining that all the
explanations on the web made no sense to him(her). These kinds of tools
together can ease the path for those who want to think, but never end up
paying enough attention to math due to unnecessary hurdles that prevent
exposure to deeper ideas. It is not a silver bullet, but definitely a nice
tool in the hands of a teacher who wants to stimulate thinking and a student
who wants to think.

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jswanson
Great idea, look forward to playing this with my daughter.

But, from the article: "the flip side to that in the case of DragonBox is that
you don’t learn the reasons for the rules. My kids (particularly my five-year-
old) have no idea why, when you drag a card below another one, you have to
drag it below all the other cards on the screen."

Games like this still have a place, but knowing the reasons and the why of
things is still incredibly important.

