Division Word Problems Research Articles

Children's Solution Strategies for Equivalent Set Multiplication and Division Word Problems

Children's Solution Strategies for Equivalent Set Multiplication and Division Word Problems

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 operations needed to solve 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 arithmetical operations generally remain linked to implicit primitive behavioral models. They noted that primitive models for and division may be viewed as 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 same misconceptions. If preservice teachers hold these misconceptions, they are not likely to recognize related errors students make. In fact, their instruction might inadvertently contribute to perpetuating misconceptions. We attempted to determine whether preservice teachers select correct operation when they are presented with problems having data that conflict with implicit rules of primitive behavioral models of and division. As teacher educators, we were also interested in noting whether preservice teachers would exhibit other misconceptions and extent to which such misconceptions were similar to those previously noted among children.

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 amd division word problems (e.g., Bell, 1982; Bell, Fischbein, & Greer, 1984; Bell, Swan, & Taylor, 1981; Brown, 1981; Yergnaud, 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 reachers 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 perpetulating the misconceptions.

The Role of Implicit Models in Solving Verbal Problems in Multiplication and Division

Arithmetical operations were assumed to remain attached to primitive behavioral models that influence tacitly the choice of an operation even after the learner has had solid formal-algorithmic training. The model for multiplication was conjectured to be repeated addition, and two primitive models (partitive and quotative) were seen as linked to division. A total of 623 pupils enrolled in 13 Italian schools (Grades 5, 7, and 9) were asked to choose the operation needed to solve 26 multiplication and division word problems. Violations by the numerical data of the constraints imposed by the assumed tacit models (for instance, when the operator was a decimal number) constituted particular sources of difficulty at all three grade levels. The findings seemed to confirm the impact of the repeated addition model on multiplication and of the partitive model on division. The quotative division model influenced the pupils' choices only at the ninth-grade level.

Children's Mathematics Learning: The Struggle to Link Form and Understanding

Children's Mathematics Learning: The Struggle to Link Form and Understanding