Prospective Middle School Mathematics Teachers' Awareness of Students' Errors regarding the Use of Letters in Algebra and Algebraic Operations

This study investigated the predictive power and awareness among prospective middle school mathematics teachers (PSTs) of student common errors in using letter variables, particularly in terms of student ways of thinking. This study was conducted in a methods course I offered in the Elementary Mathematics Education Program of a public university. The participants of this research included four junior prospective middle school mathematics teachers, who were selected among 44 prospective mathematics teachers enrolled in the methods course. During the research process, PSTs first predicted student common errors and incorrect responses, and then they compared these with the students' actual incorrect answers. The data sources for this study consist of individual interviews of four PSTs about their predictions of student errors and thinking behaviors, as well as before and after interviews regarding their self-evaluations. The findings of the study showed that while the PSTs were aware of some of the most common errors of the students, the scope of their awareness of various errors that students could make was low. This study suggests that mathematics educators should design a learning environment to improve PSTs' awareness of student errors and broaden the band of error types deemed common in mathematics education.