Trying to find math inside everything else

Posts tagged ‘dragonbox’

Intentions Change Approach (DragonBox 2 vs DragonBox 1)

So since I first had my students play DragonBox last year, We Want to Know came out with a sequel, DragonBox 2. They are now branded as 5+ and 12+, as the original DragonBox is intended to introduce the idea of algebra and solving equations to someone unfamiliar with it, while DragonBox 2 is meant to deepen the equation-solving toolbox of someone already familiar with solving equations, allowing them to deal with more complex equations.

I was trying to decide which one to use with my class this year. It seemed like DragonBox2 would be better at first glance, because I teach high schoolers: we have seen basic equations, and now we need to kick it up a notch. But I wound up going with DragonBox 1, saving the sequel for a handful of students who blazed through it and were advanced. I know I made the right choice because of situations like I tweeted about:

5-18

There were several students who could solve the first level (one of the hardest in the game), but not the second, which came later. This showed me that there was something about the structure of an equation that wasn’t getting through and that we needed to work on it.

In DragonBox 1, you only really have four abilities: you can combine inverses into 0, you can divide a card by itself to get 1, you can add a card from the deck to the game (one on each side), and you can attach a card from the deck to another (multiplication/division), as long as you do it to every card in the level. In DragonBox 2, you can do new things like flip a card from one side to the other, divide a night version by a day version (leaving negative 1), combine like terms, factor out common terms, and treat complex expressions as single units to multiply/divide by.

Those are all good things to do, and someone proficient in algebra should be able to do those things. But I backed away from using it in class because it lacked the why. At the end of the first DragonBox lesson, I compile the notes students took while playing to make a comprehensive list of rules and abilities you have in the game. The one student who played DragonBox2 insisted that, in the game, you can slide a card from one side to the other. No matter how much I pressed him, he didn’t see that the card wasn’t sliding over, it was flipping/inverting.

And that’s what I was afraid of by using DragonBox2. These tools are important, but they have to be earned by understanding them. DragonBox2 gives them to you by completing previous levels, not necessarily by understanding how. At the least, in DragonBox 1, because you are stuck with the basics, you have to grapple with where the solutions come from. They can’t magically appear.

So while DragonBox2 is rated as 12+, I wouldn’t give it to any student who didn’t already have a firm grasp on the concept of equality. Maybe post-Algebra 1. Or at least not until much later in the year.

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Dragonbox in the Classroom

Last week, my students spent 2 double periods playing Dragonbox, the iPad (and computer) game 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 summer.)

While one of my goals was teaching solving equations, it was not my only one, which is what I wanted to talk about here. (I’ll probably review the game itself later.) I told the students that I had forgotten to make a lesson, so we were just going to play a game on the iPad today. What I did want, though, was for them to home their ability to figure out how something works. To me, this is an even more important lesson to get than just solving equations.

To this end, I talked about how websites like GameFAQs has walkthroughs for all sorts of games, but one walkthroughs were all written by regular players, who sat down with a game right when they bought it, took notes on what they did, figured things out, and shared with others. So we were going to take that role. In their Interactive Notebooks, I told them to write down every thing they could do in the game. Whenever they came across a new rule, some new ability, or a new solution to a tough puzzle, write it down. Example: “Tap the green swirl to make it disappear.”

The surprising part was, they really did it, and quite well. Hey even discovered a lot of things about the game that I didn’t know, because I always played it “perfectly,” since I knew the rules of algebra. (Example: if you have a denominator under a green swirl (aka 0) and tap it, the while thing disappears. Or a green swirl won’t disappear if it is the only thing left on its side, which was fun to talk about later.)

At the end of my first double, with about 20 minutes left, I compiled all the notes they took using Novel Ideas Only (where all students stand and share things they have written, only sitting once everything they have written down is said, either by themselves or someone else), creating a master list of actions they could refer to next time.

The next class, they came in and immediately started playing. I must say, the entire time I used it, the kids were really into it, and most of them were really persistent. Some occasionally requested help, but my intervention was minimal. This time, I had this answer several questions after they had played some more, which really dove into the meat of the game. What does this card or action in the game represent in math? Why does a certain rule in the game happen that way?

One thing I really loved is how solid the game got them on how dividing something by itself won’t make it go away. It was a tactic many of them tried in several levels and it always got them stuck. I focused on the difference between “zeroing out” and “oneing out.”

We had one major downside, technology-wise, though. Each game had four save files, which worked out, because I had four sections. So one file per student. But there is nothing to stop a student in one class from playing on, or, even worse, DELETING, another student’s file. I e-mailed the company, and they said a solution would happen in a future update.

Today was the follow-up quiz, and they mostly did well. The things they stuck on was something that wasn’t well covered in the game: the distributive property. But we’ll work on that.