operations).
Manipulatives May Not Be Enough
Joanie’s second grade class covered a review of recognizing numbers, addition, subtraction, and even some multiplication. They worked a lot with concrete manipulatives and Joanie was doing well at the end of the year. But her third grade teacher complained that Joanie didn’t know anything about numbers.
Concrete experiences-manipulatives-have been used for many years in teaching math (Stern, 1971). However, like Joanie, many children and adults have often experienced success with manipulatives, but failure in the world of computation (NCTM, 1989; Moore, 1990; Papert, 1993). They have what has often been described as “application problems.”
Joanie’s second grade class had spent a lot of time with manipulatives. Some of the children moving on to third grade