Brief Reports: Preservice Teachers' Misconceptions in Solving Verbal Problems in Multiplication and Division.

In recent years much has been written about children's and adolescents' misconceptions concerning the operations needed to solve multiplication and division word problems (e.g., Bell, 1982; Bell, Fischbein, & Greer, 1984; Bell, Swan, & Taylor, 1981; Brown, 1981; Vergnaud, 1983). Fischbein, Deri, Nello, and Marino (1985) argued that the arithmetical operations generally remain linked to implicit primitive behavioral models. They noted that the primitive models for multiplication and division may be viewed as the source of misconceptions such as "the divisor must be a whole number" or "multiplication always makes bigger and division always makes smaller." The purpose of our study was to explore whether preservice elementary teachers have the same misconceptions. If preservice teachers hold these misconceptions, they are not likely to recognize the related errors students make. In fact, their instruction might inadvertently contribute to perpetuating the misconceptions. We attempted to determine whether preservice teachers select the correct operation when they are presented with problems having data that conflict with the implicit rules of the primitive behavioral models of multiplication and division. As teacher educators, we were also interested in noting whether the preservice teachers would exhibit other misconceptions and the extent to which such misconceptions were similar to those previously noted among children.