How do I help children use the symbolism of mathematics to describe their thinking?
When I am planning new experiences for children, I use those five process standards as my guidelines. I say, “Am I providing kids the opportunity to problem solve, reason/give proof, communicate, connect, and represent?” But there is another thing I think about, and this has been the biggest change for me in the last five to ten years. Teachers often say to me, “Children are supposed to understand, but is it okay to tell them something? How do I teach it?” One criticism that I frequently hear is that in reform math teaching there is no direct instruction. But, of course, there is direct instruction. I make the distinction this way: I ask myself when teaching something new, “Where is the source of the knowledge for the child-inside or outside?” Mathematical concepts and skills rely on logical structures and learning them calls for making sense of these structures, so the source of learning is internal. But social conventions are also part of learning math, and the source for learning th
