I just had a great meeting with a 4th grade math teacher and the lab specialist at a local Catholic school in Mountain View, and I got some very interesting feedback: Negatives were NOT welcome in the fractions levels that we had created!
This was not a total surprise to me, as I have gathered that Common Core pushed the learning of negatives back several grades, and as a result negatives are taught fairly late in elementary math education. However, in Mathbreakers, students are exposed to negative numbers right away; indeed it is one of the core tenants of our game, because in order to reach zero you must match positive and negative numbers together.
In practice, students don't have any trouble understanding that the light numbers and dark numbers with a "-" sign behave differently; they are able to work their way through all of the challenges of the game just by experimentation. This, to our credit, was exactly our goal -- to expose the concept of negatives in an environment where they "just worked", so that by playing around in this environment you could master the use of these positive and negative integers.
But there's a huge problem: Students have a difficult time translating this ability into solving a worksheet or chalkboard problem.
Although they had been using 1 + -1 = 0 literally hundreds of times, they did not make the connection that they could solve exactly the same problem on the whiteboard, because it looks different and they didn't realize it was the same problem.
This is a difficult, but not insurmountable challenge for us. The obvious solution to me is to (ugh) add a pop-up quiz at various points, probably at the end of the level, which clearly shows a visual relationship between 1 + -1 = 0 and the game.
This is, perhaps surprisingly, a common problem in mathematics: Context. Many math learners will totally understand a concept on paper, but be unable to perform the exact same math in the real world. The reverse also happens; Keith Devlin has an excellent book that covers this with third world marketplaces where children bargain and sell goods in the streets. The children perform with 97%+ accuracy in the market, but when presented with exactly the same problems on paper, they could not get a passing grade!
Overcoming this disconnect is going to be a cornerstone of how we add value to the classroom. When the students can make a clear relationship between the game and a worksheet, then students who play Mathbreakers will be able to translate those skills to paper, to make the test-makers happy.
Stay tuned for an update -- we will be testing again at the same school in June, and I'll post the results to this blog.