Hi! Who out there in math-teacher-twitter-blog-land has played DragonBox yet? It’s an iPhone/iPad app that teaches the rules of algebraic manipulation through an intriguing, almost context-less, rule-based environment. You can download it for $2.99 or read about it on GeekDad over at Wired here: http://www.wired.com/geekdad/2012/06/dragonbox/

I’m asking because I’m really intrigued!

First of all, I want to play in the environment (I want to invent a subtraction operation, introduce the distributive property, play with addition of fractions, etc.). What breaks? What becomes less clear/mathematically sound? What is improved?

Second of all, I am really surprised by the total lack of context, especially that there’s no support to think of why we’re isolating the box and why we have to do the same think to each side sometimes and each group other times. Every context I try to associate in my head is confusing/incomplete when we get to higher levels. But clearly there are reasons we add to both sides and divide/multiply every group by the same thing, all about preserving equality. What does equality mean in this game?

I’d love it if you would play the game (with your kids, I hope) and tell me what you think! Is the lack of context a plus? What happens as kids play? What would a “sandbox” area look like?

I only played it a little just now, and while I think it is an improvement over most of what is out there, I still have a few criticisms.

First is that the rules still feel arbitrary. We’re told what they are, and that we have to follow them, because, well, they’re the rules. Doesn’t seem like an improvement in that department.

Second, I don’t like the way they quickly turned images of cartoon monsters into “c” or “a”, and the “box” into an “x”, without any explanation. Like the students won’t notice? It just seems too soon to shoehorn algebra into the game.

I do like that when you “add” a monster to its “nighttime” version, they don’t disappear immediately, but turn into a “vortex” (representing zero) which must then be removed.

This is just my initial reaction after a few minutes of play. Will keep playing!

One way I can tell the rules feel arbitrary is that I am really experienced at manipulating equations and I’m good at making sure they stay equivalent. I can almost feel it when I make a mathematical manipulation that “breaks” equivalence. But on this game I’m constantly losing points because I forget to do the same thing on both sides. It’s an arbitrary rule that isn’t becoming 2nd nature even after playing all 100 challenges 3 times each (and some more than that!).

I wonder if I had a back-story about what I’m trying to do and why I do the same thing to each side/group, if I could hold onto the need to do it.

I wonder if it would help me create that back-story and understand the world if the box opened, revealing whether what I had on one side matched what was in the isolated box on the other side.

I wonder if it would help even more if the game then “stepped back” through from the isolated box, with content displayed, to the original starting space, showing the inverse operations being applied to everything.

I love the vortex too, and how it really makes the idea of zero-pairs more concrete. Have you tried to make one side equal zero? When you do, the zero vortex disappears and comes right back up — zero is a number, not the absence of number!

I don’t mind the variables and numbers if kids don’t mind them, which I think will depend on the kid, their familiarity with and enjoyment of Algebra, their willingness to be taught Algebra through a game vs. just enjoying the game, etc.

A colleague and I have just spent a half hour with this app and will be recommending it for purchase for our Year 7 and 8 Maths classes. It introduces algebra in a fun and creative way and quite quickly proceeds to higher levels of difficulty. I agree with both writers above, that the rules seem arbitrary, but I think kids will adapt easily to this – more so than making them “write -3 on both sides” of an equation on paper.

It is much better than some of the apps which are just tablet versions of textbook problems – boring! I look forward to trying this out with my Year 7 students when we start algebra in term 4.

Thanks for sharing Max!

I should give credit for finding the app to Dr. Borenson of Hands-On Equations (http://www.borenson.com/). The Hands-On Equations materials use the balance metaphor that Matt talks about below… that’s how I learned the basics of Algebra manipulation and I’d say I got a pretty strong sense of equivalence and doing the same thing to both sides through the balance metaphor.

I’m thinking that a better metaphor–one that has actually been employed in print for decades, and for good reason–would be a balance. Even though younger students might not have had experience working with an actual balance, it’s just about the simplest physics concept there is: If these two things balance, then they weigh the same (or have the same mass, whatever). So you’re given two dishes of weights, with an object of unknown weight on one dish, and the two dishes balance, and you need to determine the weight of the unknown object using a series of “actions.” One thing technology would allow you to do that the “real world” couldn’t is employ “negative” weights.

Of course, I’m sure that a) there already exist such apps somewhere, as I’ve really only just started looking into math ed apps, and b) the use of numbers right off the bat would violate someone’s idea of being “context-free.” I do think it’s a better analogy, though, with a clearer goal.

I searched Math Tools (http://mathforum.org/mathtools/) and found an Algebra Pan Balance from the National Library of Virtual Manipulatives, which has a nice representation of “negative weight” — helium balloons!

Here’s the link to the applet: http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html?open=instructions&hidepanel=true&from=category_g_3_t_2.html

What DragonBox seems to have that the pan balance doesn’t (which to me is an argument for using both at some point in a kid’s development) is:

- an intuitive way to think about rational expressions.

- a way to make 0 and 1 visible and show their algebraic meaning as identity elements in the “put in the same area” and “link with a dot” operations (aka add and multiply).

- more of a focus on operations, inverse operations, and using inverse operations or inverse elements to make identities.

- no emphasis on the value of x, all the emphasis is on the logic & relationships

What the pan balance has that DragonBox doesn’t:

- a clear metaphor for equivalence

- non-arbitrary feedback when equivalence is broken (the balance tips, it’s not just “wait, you can’t do anything ’til you do it to both sides”)

What both have that paper and pencil don’t:

- immediate feedback

- internal fading scaffolding

- physical/kinesthetic experience to connect to the concept

- fun!

hi, well most of my colleagues pushed to use the balance metaphor. I categorically refused to use any metaphor because i experience that it shows often rapidly limits to understanding, especially in advanced maths. meaning here that the sooner we help children see the abstract manipulation of objects, the better it is. That said, my youngest kid asked why he has to balance the equation. To me, it means i have a design problem. It doesn t question the power of directly manipulate objects. With the right design, children will just accept this balancing act without problems, as in any other game. Rules are rules. They are tricky when not symmetrical, because more difficult to remember. Of course, this is only my subjective view on the subject.

Hi Jean Baptiste,

I’m so glad you found this conversation — I was about to email you to invite you to chime in. I have a lot of colleagues who are against metaphors in math, and a lot who believe math is based, cognitively, on metaphors because all language is. I found the lack of metaphor refreshing in this game.

I still wonder, is there any way to help players like me understand that the “you must do the same to both sides/all groups” has to with the mathematical concept of equivalence? Is there a way to reveal that the box is

equivalentto the stuff it chomps at the end?By the way, my girlfriend who doesn’t think of herself as a math person played through all 5 levels eagerly last night and at the end said, “wait! I was doing math all along? How? No way!” I think that’s a good thing!

Max

The final comment that Max made is a key to DragonBox´s future success. Here at last is a game that Kids can enjoy playing without immediately realizing that they are developing an understanding of how to solve algebraic equations. Angry Birds or Maths? Kids would choose Angry Birds everytime. But with Angry Birds or DragonBox – then there is certainly a chance that DragonBox (Maths) has a chance. When the UK Media is currently reporting that “The number of 14 year olds with a poor grasp of maths has doubled since the mid-70´s with many children failing to understand key concepts such as algebra and ratios.” (The Telegraph, 21 June 2012), I believe that We Want To Know and Jean-Baptiste offers a long awaited solution to this crisis.

[...] designed to teach solving linear equations, which I think it does quite well. (I agree with many of Max Ray’s opinions when he writes about it here. Which makes sense, as Max first showed me the game this past [...]

Hi Max,

Thanks for mentioning the Hands-On Equations app for teaching kids algebra. I posted this article (link below) showing the learning that takes place in the three lessons of this free app, enabling any 8-year old to solve an equation such as 4x+5=2x+13 in three lessons.

http://edudemic.com/2012/12/a-free-interactive-ipad-app-to-teach-algebra/

I have also looked at Dragonbox in depth and did a review of it for Macupdate. Here is the link:

http://www.macupdate.com/app/mac/45006/dragonbox%2B

In short, I wish to say that I too was quite impressed initially with the “algebra” hidden in the Dragonbox app. After careful analysis my conclusion is that without coaching by a parent or a teacher it is quite unlikely that the child will learn much algebra from this app, although the child may indeed learn the rules of the Dragonbox universe. My review noted above and the comments below will shed light on my thinking.

First I note that none of the comments in this string noted the mathematical violations inherent in Dragonbox. For example, if Dragonbox is supposed to model how algebra works, shouldn’t multiplication be commutative? Whereas you can move the one-card unto the x-card to indicate multiplication by 1, you cannot do the reverse. What kind of algebra or mathematics is the child learning here?

Likewise, shouldn’t addition be commutative? In Dragonbox you can place the zero-card unto another card to indicate addition, but you cannot do the reverse. One wonders why the designers did not allow a card to be added to the zero-card so as to be consistent with the principle that a + 0 = 0 + a? Again, what kind of mathematics is the child learning here, assuming he is analyzing the meaning of his movements with the cards?

I have a number of other observations in a similar vain. I will conclude with this one: Example 13 of Level II provides an answer of x= (-a)/(-u). If the app represents the world of basic algebra, the answer should be simplified to x = a/u, but it cannot be. Is the child learning that it is fine to leave an answer in the form of (-a)/(-u)?

I do not by any means wish to discourage anyone from getting and playing with Dragonbox. I agree that it is a fun app. I am simply making the claim, which I believe I can substantiate (as evidenced by my comments above and by the review noted above), that without coaching by an experienced teacher of mathematics, it is questionable what algebra the child is learning or the quality of that learning.

FYI we have just released our new game DragonBox 12+, based on the same concept but taking it much deeper. It takes difficult subjects like signs, parenthesis, factoring…. a must have to teach algebra in middle/high school level.

I find this an extremely interesting discussion. Before learning of DragonBox, I embarked on my own goal of teaching algebra through a fun “Angry Birds” type game. As Matt and Max have discussed, a balance truely captures algebra as it shows how changing one side affects the other and how each item has a value. For reasons like this, I adpoted that metaphor for my game, including good graphics, a basic but fun story, and multiple levels where the player is egged on to solve the puzzle, all while learning algebra.

If you’re interested, you can get the game here for $2: http://algebalance.com/appStoreBadge.png

Sorry, I meant: https://itunes.apple.com/us/app/algebalance/id662409244?ls=1&mt=8