Research Into Practice: Misconceptions about Multiplication and Division

M ultiply your options—divide and conquer— these and many other everyday expressions imply that multiplication always makes larger and division always makes smaller. In fact, these two ideas are so self-evident and so pervasive in many people's thinking that they are among the most notorious misconceptions about mathematics. Misconceptions or naive conceptions are commonly held ideas or beliefs that are contrary to what is fonnally acknowledged to be correct. Mathematics educators study misconceptions because if we can understand how students are apt to see mathematical ideas, we may be better prepared to offer instructional experiences that help them develop accepted conceptions. The two misconceptions just described have been the subject of many research investigations (see, e.g., Bell, Fischbein, and Greer [1984]; Fischbein, Deri, Nello, and Marino [1985); Greer [1987)).