Studied were the misconceptions that preservice elementary teachers have about multiplication and division. Results indicated that they are influenced by the same primitive models as students; the most common errors made by both groups are quite similar. (MNS)

Argues that intuitive and computational knowledge can be combined by focusing more explicitly on referential and quantitative meanings in division of fractions problems. Recommends teaching mathematics as problem solving, communication, reasoning, and connections to help students overcome misunderstandings and connect their intuitive knowledge…

Investigated was the use of cognitive conflict to probe the misconceptions held by preservice elementary teachers that in a division problem the quotient must be less than the dividend. Explains how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding support their misconceptions.…

Argues that consideration should be given to whether teaching solubility product calculations is at all useful. Claims that experienced teachers seriously misunderstand and misuse solubility product calculations. (DDR)