> - playing games such as _Dragon Box_ (which teaches the principles of math and esp. algebra)
One of my kids got pretty damn good at Dragon Box in like... first grade, I think it was?
As far as I can tell this has had (years later) no effect on actually being able to understand algebra any better. The connection's not there. I can see why, too—doing it myself, it was sometimes hard for me to figure out how the various patterns of actions in the game connected to the mechanics of solving algebra problems, and that's with my already understanding that part pretty well. Even when it gets a little more explicit about which symbols are connected to what, later on, what actual mathematical operation or set of scribbles on paper does "drag this little box onto that other little box so it disappears" translate to?
My conclusion is it was good at making me feel like my kid was learning something, but not a great use of time for actually learning that. I think she got a ton more out of the couple times I sat down with her for five minutes to show her how something worked on paper, than hours and hours of Dragon Math.
This goes for other games that are supposed to teach place value and such, but make it really abstract and "fun". Maybe it's just my kids, but even when you point out that what they were doing perfectly well in the game is the same thing they're supposed to do on this worksheet for school, the presentation and mechanics are so different from "drag these colored blobs around" that the value the game provided was practically none. It didn't confer understanding, it taught a very specific kind of pattern recognition just for the game that the kids have trouble generalizing, same as Dragon Math.