Evoking Cognitive Conflict to Explore Preservice Teachers' Thinking about Division

This study investigated conflict teaching as a means of probing the misconception held by many preservice elementary teachers that in a division problem the quotient must be less than the dividend. Individual interviews were held with 21 preservice teachers who were able to correctly compute quotients for division problems with decimal divisors less than one, but who agreed with an explicit statement that the quotient must be less than the dividend and who selected operations to solve word problems that reflected this misconception. The interviews illustrated how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding of the division algorithm support their misconception. The authors also noted preservice teachers' lack of access to the measurement interpretation of division and their willingness to change procedural rules to preserve their misconception.