In order to learn, a certain amount of work needs to happen. Rote memorization allows students to be able to quickly complete basic types of questions, and to recall information that aids more complex types of analysis or questions. Work helps to establish structure. The main problem with asking students to work at problems is that, well, it is work. Work in most students minds is a rigid process, and doesn’t really allow for creativity or flexibility.
But when it comes down to learning, nothing beats play.
Minds at play… don’t color inside the lines. There has been a great deal of research about “gamification” of education. One of the best things that our technology has given us is vast quantities of feedback. And instant feedback is the kind of thing that lets students make games out of math. And of course, making any kind of practice fun is fantastic news for any teacher.
On a side note, I just told my students that they “leveled up” in their math.
They were amused.