Today's quote comes from Share & Compare: A Teacher's Story About Helping Children Become Problem Solvers in Mathematics. Maybe it will make a bit more sense after reading this thought.
"Children's problem-solving accomplishments can sometimes be characterized as 'unconscious competence.' They can solve problems and communicate their solutions using drawings and manipulatives, but they seem unaware of the thought processes taking place."
Larry Buschman, Share & Compare 17
These quotes challenge my way of thinking and operating as a math teacher. To me, they're saying that it's not all about the solution, and drawings and manipulatives aren't even the most sought after goal in a child's mathematics instruction. A mathematician's ability to communicate about their problem solving strategies is proof that something worthwhile is going on. I've been taking steps in the right direction. I've added "How do you know?" to my math conversations. I've been more aware of expecting my kids to teach their strategies to the class as well as informally with partners. Yet in spite of the positive changes I'm making, there are levels of communicating about math that my kids have yet to experience. Just finding the answer and showing the work isn't enough. The math talk that kids engage in is where it's at.