The typical structure of equations influences how we learn the meaning of the equal sign. Previous studies have shown that as students gain experience with addition problems, they actually performâ€¦ (More)

How should we think about the nature of our knowledge of mathematical concepts, and the mechanisms we use to learn and use these concepts when we do mathematics? Here we describe a perspective on theâ€¦ (More)

In math education the goal is for children not only to master the materials and problems presented, but to understand underlying principles and properties that can be applied broadly to new problemsâ€¦ (More)