Investigating Preservice Teachers’ Determination and Representation of Proportional and Nonproportional Relationships in Terms of Problem Contexts

Abstract

This study investigated 46 preservice middle school mathematics teachers’ solution strategies and determination and representation of proportional and nonproportional relationships in terms of problem contexts. The preservice teachers were given a paper-pencil test with two mathematical tasks (Bicycle and Candle). The preservice teachers’ responses were analyzed using a content analysis method. Based on the analysis, semi-structured interviews were conducted with eight preservice teachers. The findings indicated that the preservice teachers’ solution strategies and determination and representation of relationships were affected by the problem contexts. The preservice teachers were better at determining and representing inversely proportional relationship than directly proportional relationship, which was quite opposite of the findings usually cited in the literature. Determining and representing nonproportional relationship appeared to be the most challenging task for them. Problems that required in-depth examinations elicited the use of more sophisticated solution strategies and helped the preservice teachers to avoid using rote computations.