I practiced and practiced, working quietly and mostly alone to line up columns neatly and check my work carefully. I learned the lessons well. But many of my classmates were not as lucky. They became math casualties who hopelessly struggled with numbers, learning to dislike rather than embrace math. Children need to deal with numbers in a variety of settings, not just as computations done in isolation.
Problem solving and number sense are integral to arithmetic.
When I think about teaching arithmetic, I picture a three-legged stool. Computation, problem solving, and number sense are the three legs that support the seat. Children must develop competence and confidence in each area. If they only become skillful in, say, computation, the stool will collapse, leaving in its wake students who are unsuccessful at and turned off to math. Teachers need to pay attention to each leg of the stool so that students develop a firm, well-balanced support for understanding in arithmetic.