The Posing of Division Problems by Preservice Elementary School Teachers: Conceptual Knowledge and Contextual Connections.

Previous research has suggested that many elementary school teachers have a firmer understanding of addition and subtraction concepts than they have of more complex topics in elementary mathematics, such as division. In this study, (n=24) prospective elementary teachers' understanding of aspects of division involving remainders was explored by examining the problems they posed. The teachers' responses revealed a clear preference for posing problems associated with real world contexts, suggesting that the term "story problem" had that particular meaning for this group. Although the vast majority of problems were situated in contexts, the problems and solutions frequently did not represent a solid connection between the mathematical and situational aspects of the problem. About two-thirds of the subjects spontaneously posed problems and proposed solutions that reflected their understanding of the relationship between the given computation and at least one member of its family of associated computations. For 20 posed problems, almost all of which were partitive division situations, subjects failed to specify the need for equal-sized groups or the number of items per group in the division situation being posed. The findings were that, although some aspects of division, such as its connection to different types of problem situations and its relationship to multiplication, were fairly well understood by most of the subjects in this study, limited or flawed understanding was also noted in many different areas. The document contains examples of the question sheets used in the study and examples of posed problems. (Contains 14 references.) (MKR)