I expect I'm too late to the party for this comment to be noticed, but I thought I'd add something.
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.
I just downloaded this for my soon-to-be seven-year-old, to experiment. ($5 for a shot at making math easier is a no-brainer bet... if he takes one look and rejects it, well, $5.)
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.
I hope that happens - I really do. We need kids not to be afraid of just playing with stuff, including abstract stuff like manipulating and rearranging equations. I see too many kids paralysed when faced with a problem, unwilling or unable to do anything because they are scared that what they do will be wrong. They don't know the right thing to do, so they don't do anything. There's a chance that games like DragonBox will help fix that. I'm just aware that there are other ways that it will play out for some kids, because not all kids are the same.
I'd be interested to see the results of any research into Dragonbox.
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.
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.
Edutainment is always iffy business. The problem with this is it is trying to make a game out of doing algebra. In the end the only point of this is doing algebra.
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.
There's a related thought I have with this whole idea, and it's that these types of tools mainly end up used for "circus math". Math that once may have been useful, just as slide rules were useful, but in modern times have much less direct value and seem mainly to be for show. When you're revisiting calculus in order to accomplish some goal, are you doing everything by hand or are you leveraging software like Maple, Octave, Wolfram Alpha, Python, Julia, or a plain TI-89? Do you derive or memorize or keep a handy table of integration/derivative formulas? Do you ever do integration by parts and show all your work? Where there are nth order DEs, Laplace Transforms can be very useful (and lead to the tremendously useful Fourier Transform), but do you do partial fractions by hand so you can get an expression to something you can easily invert by inspection (with a handy table reference maybe)?
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.
This is a point of view that I'm hearing a lot now, mostly from technically capable people who know that computer algebra systems exist and are more reliable than doing everything by hand. And there is merit in the argument, but I've always felt uncomfortable about it, as if something was missing.
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,
I'd like to compare this with the idea of missing all the tedium of practising the cross-court forehand drive in table tennis. And the answer in that case is no, not if you want to be a top flight player. You need your body to recognise the shot automatically and play it without thinking, so your brain is released to do the higher-order stuff necessary to work on the problem, not the detail.
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.
i totally agree with you, let s engage the imagination of kids, let s create situations where kids want to learn by necessity and own interest and drive! deeper learning!
that said, once you are motivated to learn, you still need tools to get fluency and learn conceptual stuff rapidly. Although i love that you make me think about what i m doing, i m still convinced we need specific tools. We need both approaches i think!
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]:
[0] https://news.ycombinator.com/item?id=4105397[1] https://news.ycombinator.com/item?id=4106567
[2] https://news.ycombinator.com/item?id=9472466