DragonBox: Secretly teach algebra to your children
dragonboxapp.com
dragonboxapp.com
Thanks to the nice comments here. Very appreciated!
To add a bit to the discussion: we made 3 games so far, 2 versions of our algebra game and one about geometry (Euclidian geometry proof really).
We also co-organized Algebra Challenges with our research partner the University of Washington. As an example, one of those events, in Norway last year, gathered 36k students from ages 7 to 16. They solved almost 8 million equations in under a week.
We are not just app makers, we are more focused on providing tools and social innovations.
We would like to do coding one day, but first things first! Our next games are targeting younger kids and number sense.
Feel free to ask questions, or take contact!
Jerome, head-nerd @ WWTK :)
Advice: focus on the kids, test test test
We're currently based in Norway (with part of the team in France). We use the Norwegian price in NOK as basis.
We used to have these nice per-country-almost-rounded-prices, like 4.99$ etc. But the latest European laws affected the Play Store and caused a price change. We didn't really bother trying to round them properly again.
Is the current price really too odd ? ;)
I am downloading lightbot right now. Will test with kids during the week-end :)
More seriously, we would like to cover all the big ideas in math. And statistics is one of them. It's in the big plan.
I've occasionally asked if she has played any more DragonBox, but she is continually uninterested. I'm not sure how to encourage her to make more progress at this point.
Some three years ago when a Wired article about this was submitted[0] I wrote an extended comment[1] expressing some concerns about this. The Wired article has since gone missing, but the HN discussion remains.
Let me say from the get-go that anything that helps get over the barrier for playing with, experimenting with, and generally messing about with algebra type stuff is a Good Thing(tm). I'm really pleased to see this here and doing well.
There is a comment here[2] that gives an instance of exactly the sort of thing I'm worried about. Kids could play the game for a bit, decide they've had enough, and then move on. The question is: will the things they've done in playing the game have a positive effect?
I can envisaged the possibility that kids that have played DragonBox and then moved on with get introduced to "proper" algebra later and not even bother trying too hard, because they'll think "I've done this, I don't care any more."
So let me say that I think it's important that these things exist, and I think it's great that they are being developed, and I really want them to succeed in their own right. But having said that, I'd be reluctant to herald games like this as the future of teaching math.
I'll finish here by quoting the last paragraph of my previous lengthy reply[1]:
... 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
manipulation from any sense of meaning, but I look
forward with interest to see if it can be used in a
meaningful way.
My goal is not that he literally walks away knowing algebra. My goal is that his brain gets primed with the patterns he'll need to learn algebra. Even if he never consciously puts the two things together, it can only help to have pre-burned neural pathways for the sorts of otherwise counter-intuitive manipulations that algebra calls for.
My feeling is that the exact opposite of what you fear will happen; children with prior exposure will find algebra simply easier, and in so finding it easier are far more likely to engage, even with the shit school curricula for algebra we have.
Contrast this to something like Kerbal Space Program. This is a game about shooting rockets to other planets. In playing KSP, I've learned a bunch about orbital mechanics, which is the quite obvious result. If you were making an edutainment game to teach about how to work with orbital mechanics, it would look like KSP.
But the secret thing that the game has done is make me revisit calculus. You have a rocket that has a certain force at sea level, a certain force in the upper atmosphere, you have a mass that is a full tank of fuel, and a mass that is an empty tank of fuel. You have aerodynamic drag that changes with the density of the atmosphere.
It gives you some information, and you can go and get mods which give you more information (and expose you to more of the math, but at your own request). Or you can do what I did and take experimental data and build your own model.
But when I'm doing this it's not to balance an equation. It's because I want to get a rocket to the Mun, it's because I want to build the cheapest ship that can take space tourists up and down to fund my space empire. It's because I want to build a base on a distant planet. It's just that in order to do that, I learn me some calculus, and some orbital mechanics, and some other things until I can break some of it down in my head, until I'm talking about thrust to weight ratios, delta v, specific impulse etc. like they're no big deal.
A game like dragonbox falls into the edutainment trap. It's a game about balancing an equation on either side of a playfield. It's too abstract. It's just doing math problems with pictures.
It's like all the different typing tutors that we were given in computer class when I was growing up. Even the most gamified ones like mario teaches typing, or later typing of the dead, were still typing tutors.
But what really improved my typing speed more than any typing tutor out there was when I started playing Everquest online, and later World of Warcraft. Because in those games, before voice comms were common place, you had to be able to communicate reasonably effectively, but quickly, and in the middle of doing other things.
I wasn't typing to get points typing. I was typing on the way to do things that I enjoyed. Nobody would sponsor a World of Warcraft class to teach typing, first of all it wouldn't necessarily be effective, how much you type depends on the individual, plus it wouldn't be particularly fast, and it would be impossible to test on.
But we don't learn things well by learning them fast and then dropping them. We learn things well by being engaged in them and repeating them frequently over a long period of time. KSP will do good things for my calculus, because there's a lot of space to cover in that game and it's fun to explore space. A game like dragonbox is not interesting enough to say a year after finishing the challenges "Ah man, I really want to pick that up again and play through it again." it doesn't engage your imagination, it doesn't give you any context except "Solve this disguised math problem and get a gold star"
edit: All that said, I'm still happy the program exists, and I hope it does well. I do think it takes the wrong approach, and I do think that edutainment in general really misses the mark, as does the current "gamification" trends we're seeing around other places. That said, I don't think it would do harm, and it will definitely expose kids to algebra in a way that could definitely help them.
I guess my point is more that sometimes the better way to teach is to do it more indirectly. If another game that was really interesting on its own merits allowed you to excel by figuring out algebra, that game is a more organic way of learning, and it also makes the subject matter more meaningful. It's also incredibly hard to measure or predict it's efficacy, so you can't really sell it to parents as a way to teach algebra any more than you could sell WoW to parents as a typing tutor.
I wonder if there's not some way to skip a lot of the tedium of algebraic manipulation that is forced upon students, such that students can learn how to use algebra as a tool to solve problems, rather than as an interesting written dance where each step is shown that they must perform for points. These sorts of games may make the tedium go by quicker, and there is something to be said that understanding can come through rote, but once a student grasps the meaning of these things, I think we should immediately encourage that student to avoid as much tedium as possible and move on to higher subjects instead of more and more worksheets testing knowledge of process rather than knowledge of usefulness.
I occasionally link back to this text (ignoring the controversial remarks on violent video games): http://www.theodoregray.com/BrainRot/ In short, if you think of the brain as a limited resource, then all these numerical and analytical methods that were needed before computers have a cost -- one which our intelligent ancestors paid for out of necessity, and it's foolish to suppose these things don't require significant amounts of brainpower or cognitive resources. Is this cost still worth it for most of them, is the amount of brainpower in fact trivial despite our ancestors' struggles, were they just stupider back then? Do our children have enough resources that they can learn all they knew, at least until the final exam, and then all we've found out about higher levels of math and about automated computation this last generation? I don't think so.
More recently I think I've identified what it is, and I included a little rant about it in my blog post about the birthday problem[0].
In particular, you've said:
> I wonder if there's not some way
> to skip a lot of the tedium of
> algebraic manipulation that is
> forced upon students,
But more than that, sometimes it's the hours of practice in algebra (or similar) that means that when something turns up in disguise then you still recognise it, and still know how to torture the equations to twist them into the standard form.
It's really hard to explain. Sometime I'll have another go at it, try to put into words the meta-intuition I've developed over the past 40 years. In the meantime, the side-box with the rant is the best I've managed.
[0] http://www.solipsys.co.uk/new/TheBirthdayParadox.html#toc_na...
To me it feels like purely rote learning. Children learn mechanical rules to manipulate things but (at least up to level 3) I'm not sure they're getting any understanding of what those manipulations actually mean.
HN seemed to really like a math teaching app that ended up being used in Malawi.
https://news.ycombinator.com/item?id=8280961
I got downvotes for suggesting it was expensive https://news.ycombinator.com/item?id=8282644
And I got an upvote for finding the research (not linked in the submission and for pointing out that the expensive app provided limited learning - "counting to ten" isn't somethig I want to pay $24 for.
I think there was a study done [1] that showed that love and security and the availability of parents and family mixed with a certain degree of freedom were more crucial to success later in life than skills such as math. It allowed children to explore the world on their own, but if anything bad happened they could always rely on parents to be there for them. To tell them things would be fine, or to put a band-aid on their wounds. This allows children to develop trust in others, self-confidence and a positive outlook in life. While at the same time motivating them to explore the world.
However, another very important thing was allowing the kids to join in when the family (or other kids) were solving a problem. This could be anything from helping with cooking, fixing something in the house or collecting firewood. I assume the benefit of this was not only practice of problem-solving and social skills, but also allowing them to develop a sense of self-worth.
(The problem is, I guess, that our modern world is solving all our problems for us. We don't repair, we replace. We buy solutions for things that we'd had better dealt with ourselves. And so forth. And that we put so much emphasis on self-reliance, which seems to be a good thing but in reality has serious disadvantages. I believe this is one of the big (root-) problems of our modern civilisation that nobody seems to be talking about, but I might be wrong.)
Furthermore, the ability to work on a specific problem _with others_ is a different from being able to do maths alone. It teaches all the right things in life.
So I guess the point is: If you want your kid to succeed, be there for and allow it to take part in life the way he or she choses to (all within reasonable limits of course, you still need raise your kids to be decent etc.), especially with others.
[1] wish I had a link.. :/
But! As a parent, there are times when you need to distract the kids for a few minutes. My main goal during those distraction times would be that they are distracted sufficiently, and enjoy themselves. If they happen to also "learn Algebra", well I don't really have a problem with that. So I see this as something that is probably worth having on a tablet instead of the completely made-up-off-the-top-of-my-head Disney Princess Tea Party App.
True that may be, but the blurb on the "DragonBox Algebra 5+" product on the linked page says:
"It’s perfect for giving your child a head start in mathematics and algebra. "
.... love and security and the availability of parents
and family mixed with a certain degree of freedom were
more crucial to success later in life than skills such
as math.
I can imagine having some visual blocks and wires to get a wanted output image, and then gradually it could use symbols or function names instead of the pictures, or you could even go deeper into the blocks to get down to more lower level instructions...
Like Blueprints in UE4 : https://docs.unrealengine.com/latest/INT/Engine/Blueprints/G...
http://appinventor.mit.edu/explore/designer-blocks.html
https://blockly-games.appspot.com/ (transitions to JavaScript)
https://www.makewonder.com/ (physical robots)
It's not intended at all as a programming education product but I think that's what's so great about it.
I can't recommend it enough to help explain programming concepts, and as a brain teaser for my colleagues.
As a father of two young boys, I don't think that "tools are from the 20th century" is the reason that it's easier for young kids. It's more about touching and pointing being more intuitive than typing and using a mouse. Kids will adapt to whatever tools they are given. The fact that most of us these days will put kids in front of a touch-enabled device before a keyboard doesn't mean that the keyboard is any less useful or important. It's still going to be a while before touch-and-gesture will be a better tool than typing for writing code.
https://itunes.apple.com/us/app/kodable/id577673067?mt=8
Kodable. It's free but more importantly, it teaches kids about loops and sequencing commands - things you do on a day to day basis while programming (unless you're a functional programmer haha).
Got Robot Turtles for the kids (4 and 7) and they got bored pretty quickly since there's only so much you can do (move, turn, shoot).
Take a look at this video: https://www.youtube.com/watch?v=oLA-fde2eR0
That is the typical response to the game... My own boys were solving equations within a few hours... This is clearly how math should be taught...
Edit: Found it!
http://www.forbes.com/sites/jordanshapiro/2013/07/01/it-only...
[1] http://trimensional.com/blog/2011/05/23/trimensional-is-1-in...
Not sure whether it's connected but he now says he likes maths at school :-)
It's so awesome to see their eyes open up at these things. My younger daughter has been going on for days about powers of two. She doesn't know how to multiply, but exponentiaton just tickles her. I showed her some of Vi Hart's videos, and now she's in love with hexaflexagons.
It's so wonderful to see the beauty of math, and moreso when a child is discovering it.
Haven't had as much luck with educational apps now that my kids are post pre-school, so I'm very glad to see the recommendations for Dragonbox.
We (SO and I) have a newborn, and I often use my computer or phone around him. We think it might be detrimental to his development if he used electronics as much as I do, but I am not a good example to him.
Our strategy for balance is to (1) provide a lot of alternative means for engagement like outdoor activities, excursions, and interesting physical toys; and (2) provide many useful learning apps like this one that will harness healthy, natural interest in electronics with added developmental and educational benefits.
Growing up, I always sought out electronics and gadgets, from Gameboy, to Palm Pilot, to iPhone. But I think we are well past the tipping point where moderation is easier than excess with mobile devices. Adding more of the "good" stuff, we hope, will crowd out too much of the "bad" stuff.
I agree, wasting time on shooters probably isn't a good idea, but there are very good story driven games (monkey island type of games) or strategy games (sim city etc) that kids could get inspired by.
There is wisdom to be had in learning first hand why a bad thing is bad, rather than just being told it is forbidden.
If people believed that, drug law would have a three-strike policy. So you see why I'm skeptical when people say what you just said.
Maybe you really believe what you said but don't fool yourself into thinking you live in a society that does too, because we don't.
> There is wisdom to be had in learning first hand why a bad thing is bad, rather than just being told it is forbidden.
"a bad thing" is a variable. It's generic enough that it allows for both "playing video games all day" (which is a bad thing) and racist drug laws (which are also in the same category of bad things).
That's why I said people that say that usually don't believe it, as you've just shown. When it comes time to test that hypothesis by filling in the "a bad thing" blank, then you want to change the rules and say "well not EVERY bad thing, racist laws aren't bad in the same way playing games all day is".
If that's the case, then just don't say silly generalizations like "there is wisdom in learning why bad is bad"; instead, think before you say something, so we can have constructive conversations, and not conversations where your side is always backtracking and changing the meaning of basic things such as "a bad thing".
Because when you say "there is wisdom in learning why bad is bad" you make it sound like there is an underlying principle you believe in, but when I come in and test if you really have that belief, then it becomes clear you just wanted to make it sound like you had a principle behind it, but really you just winged it and pretended there was a principle, and when confronted about it, instead of admitting and saying "I shouldn't have phrased it as if I thought it's a principle", you want to argue with me how there really are two different categories called "a bad thing" where "playing games all day" and "racist drug laws" can't co-exist because you said so, without providing a reason.
The context of our conversation was video games. No koan, maxim or quote contains the unquestionable logical truth in all applications.
Ultimately your video game restriction might not even matter. If the kid goes through any kind of teenage rebellion from your strict rules, that will be a "bad" wisdom gaining experience itself. The only real choice you might be making is whether to deal with confrontation in small doses or in one major flame out.
The thought process was that it's hard for me to _know_ why drugs are bad other than what I've been told and other outside knowledge sources (anecdotes, wikipedia pages, etc). However, wasting time on videogames is something I do often, so I can draw from my own experience in what is "too much" and what the deleterious effects are. It's a much more valuable lesson, because I know exactly what my situation is instead of trying to place myself in a hypothetical.
On the other hand, for truly educational content, like Khan Academy, they have unlimited access.
The bad things about these kinds of rules, around this age, is that it provides strong incentive for kids to learn to lie and hide things from you.