Goodrow concludes that children in the mixed group almost always performed less well than children who had either a curriculum built on understanding number relationships or a curriculum built on learning procedures. This was particularly true on more difficult problems. Goodrow suggests that children in mixed programs may be confused about when to use a taught procedure and when to rely on one s own number sense. Seeking balance through mixed programs is dangerous because students can learn the steps in procedures much earlier than they can understand them. Frequently, these steps are forgotten, leading to the need to reteach the same procedures nearly every year of elementary school.
Most educators know that teaching procedures without understanding doesn t work.
However, the Massachusetts Mathematics Framework specifies that both must be taught in a particular window of time without allowing for the careful development of all the elements that go into competent problem-solving. A New Kind of Balance Several math curricula bring a different perspective to the idea of balanced instruction. These factors are integral to learning all kinds of mathematical content, but we will illustrate them within the area of whole number computation. If a fourth grade student solves the problem accurately by using this cumbersome procedure, she is not demonstrating computational fluency. She has not made use of the obvious relationship between the two numbers in the problem.