If you walk into almost any elementary/primary school mathematics classroom, you should find kids using “Manipulatives.” These are physical objects—like Base 10 Blocks, Cuisenaire Rods, or Tangrams—that allow kids to explore math concepts in physical, three dimensional ways. Now, DragonBox Numbers, a new digital app from We Want To Know raises the standard not only for mathematics manipulatives, but also for learning games.
For years now, all the research has shown that students learn math best with manipulatives. The National Council of Supervisors of Mathematics says that “in order to develop every student’s mathematical proficiency, leaders and teachers must systematically integrate the use of concrete and virtual manipulatives into classroom instruction at all grade levels.”
Although most of us think of math as “numbers.” Our numbers—the Hindu-Arabic numeral system—is really just a kind of code. The numbers themselves are just symbols that represent an abstract philosophical conception of the human experience in the world. That’s all mathematics is: a complex and extremely useful language through which we organize and categorize our experience. The hard part of math is not using the code, but rather learning to think about your world in mathematical terms, learning to understand what the numbers actually mean, learning to speak “math” fluently. Mathematicians and educators refer to this kind of understanding as “number sense.”
Starting math education only with Hindu-Arabic numerals just teaches kids to follow directions—they are taught to memorize a symbolic code and use it according to a set of rules that must seem completely arbitrary to them, seeing how as there’s no way for them to know that those rules are grounded in physical reality. Which is why any kid who isn’t driven by obedience alone will eventually ask, “why do I need to know this?” Starting with manipulatives, on the other hand, can teach children “number sense.”
All good (and many bad) elementary/primary school teachers understand just how essential manipulatives are to learning math and number sense. They also understand that at some point, parents (most of whom have very highly developed number sense themselves, but still understand very little about it) will inevitably walk into conferences demanding that their children stop playing so much and start receiving a “rigorous” mathematics education.
The word “rigor” literally has to do with hostility, severity, or harsh inflexibility. Check out the Oxford English Dictionary and you’ll discover that the word has more to do with obedience—in both its negative and its positive connotations—than it has to do with the sort of accuracy and thoroughness with which we associate it in the context of education. I suspect most parents would prefer accuracy and meticulous precision over the “stiffness” or “cold shivers” that are implied by a fastidious definition of the word “rigor.” And to anyone who argues that our current usage is adequate because we all understand what the word means, I’d say: you’re hardly being rigorous with your use of language.
Let’s forget rigor; the word is an obstacle to developing pedagogy and improving education for the next generation. Anyway, what we really want is graduates who have sophisticated number sense and thorough mathematical thinking/comprehension. In fact, that’s precisely what matters now that computers do most mathematical procedures. The necessary skill these days is not solving equations, but rather, understanding math well enough to know how to translate real world experiences into complex calculations that can be assigned to the machines. This kind of learning requires manipulatives, which turn real-world mathematical concepts into flexible playful experiences.
The world’s wealthiest students already have brightly colored math manipulatives; they’ve been using them for decades. Some even use LEGO bricks, which also work well. LEGO Education actually sells some fantastic “MoreToMath” products that come with all the bricks you need, plus a comprehensive curriculum. But these things are rarely within the financial means of underprivileged schools. Luckily there are now free digital versions of almost all the world’s great math manipulatives. This site from Houghton Mifflin Harcourt School Publishers offers tons of digital manipulatives. But these are just basic virtual versions of the classics. They are visually boring. And knowing what to do with them still requires a great teacher.
DragonBox Numbers could change all that. It shows us how perfect a digital manipulative really can be—not only in the classroom with teachers, but also for kids at home alone. Numbers involves a world full of animated sprites, called “Nooms,” that behave according to the rules of simple arithmetic. The app is from We Want To Know, a Norwegian developer that makes some of the best educational apps. I regularly recommend their original app DragonBox Algebra, both to parents of kids struggling through 8th grade algebra, and to anyone who wants to understand the power of learning through digital play. DragonBox Elements, the company’s take on teaching Euclidean geometric proofs, was addictive for both adults and older kids. Now with Numbers, they prove that they can also create games for the early childhood education space.
DragonBox Numbers is the first thing you should download on a tablet if you have kids 4-8 years old. Think of it as a math sandbox, or a digital arithmetic playground. It takes the notion of a virtual manipulative to whole new interactive level, doing things blocks never could. Numbers combines the benefits of classic manipulatives with the quality art design and sophisticated production values of commercial game design. There are whimsical characters, great sound effects, and first-rate animations.
If you were in Norway, where Jean-Baptiste Huynh (creator of all the DragonBox games) is based, your children would probably already be playing. Fifteen percent of Norwegian first graders are already using DragonBox Numbers at home. It also spent a month as Norway’s top grossing app in all categories (even beating out Minecraft).
Last month, to understand Numbers first-hand, I visited Jean-Baptiste Huynh in Oslo. He took me on a trip to his children’s school. There, we spent time in a first grade classroom where he projected DragonBox Numbers onto the large projector screen. He playfully asked the kids to guess what would happen as he reached tens, hundreds, thousands. The kids were learning the logic of number placement—an ordinary lesson in base 10 that involved interactive digital animations that could be manipulated in real time. They were doing it through engagement with silly characters. They guessed. They played. They laughed. They worked together. It felt like I was in the classroom of the future.
When the lesson was over, they each picked up their own tablets and played with Numbers independently. Well, it was hardly independent. Within seconds they were self-organized into small groups, sharing tips and tricks and discoveries. Discoveries not only about the game, but also about numbers and arithmetic.
Afterwards, Jean-Baptiste and I took the ferry together across the Fjord to central Oslo. He told me he was concerned about inefficiency. He knew that most of the kids comprehended the lesson, but there were certainly some who missed it. He suspected they might learn number sense faster if they were each playing by themselves. Certainly a digital adaptive game engine could be much more personalized to each individual student’s level of comprehension than a single teacher at the front of the room ever could be. But part of a teacher’s challenge always involves balancing the real need for content retention with the real need for classroom socialization. We discussed, argued and debated for the rest of the day, trying to imagine what school could and should look like in a world where children can learn so easily learn through digital play.
The thing about Hindu-Arabic numerals is that they are just the symbols we use to express mathematical concepts. Just like we can easily switch from Roman Numerals to Arabic numerals, we can also do math with animated “Nooms.” We need only to make sure they behave according to the laws of numeracy. Math is not just about obedience to the rules of the numbers, but ultimately about how we best share our mathematical experience with others. First we need to have the kinds of meaningful and playful experiences that are worth sharing. DragonBox Numbers provides precisely that kind of rigorous learning through digital play.
