> The problem I find is that students have a hard time making the connection > between the 'game' and the mathematical process involved. Any comments?
I've played a "red-negative/black-positive" card game on several occasions and have seen exactly what you have: the kids are very proficient at playing the game but don't immediately make the transition from the game context to the traditional symbolic context of negative and positive numbers.
Two thoughts arise here: first, we as teachers need to figure out what's happening well in the game that isn't happening at all outside the game. This is what the Standards mean by relating in-school math experiences to out-of-school math experiences, and the Standards *don't* claim that in-school math experiences are necessarily "right" or "better" or "more meaningful." On the contrary, we've got to adapt the in-school math to the point at which it makes sense to the students in terms of the out-of-school math, not the other way around. This is where traditional instruction falls apart.
Second (or actually zeroeth: this may precede the other), we need to clarify what we mean by "appropriate math practices." If we mean that we want kids to be able to work 35 sums of integers with 85% accuracy, then that's one thing; if we mean that we want kids to be able to explain, justify, and notate why one hand in the game would beat another hand, then that's something entirely different. The Standards would claim that if the kids spend enough time explaining and notating their thinking about the cards, then they'll be able (after some guidance) to work the written sums. And traditional instruction has spent years proving that the converse is not true: working all the sums in the world won't lead to an ability to explain the reasoning behind the sums.
Kreg A. Sherbine | To doubt everything or to believe Apollo Middle School | everything are two equally convenient Nashville, Tennessee | solutions; both dispense with the firstname.lastname@example.org | necessity of reflection. -H. Poincare