Examining the middle school preservice mathematics teachers’ verbal- algebraic representation transformations and errors

The purpose of this study is to investigate the errors and types of errors that middle school prospective mathematics teachers reveal in the transformation of verbal and symbolic representations. In order to examine these transformations of prospective teachers, a test including 12 different open-ended questions was administered to 69 prospective teachers. Results revealed that prospective teachers made various mistakes in their transformations and interpretation of symbols. The prospective teachers’ mistakes in algebraic-symbolic representation transformation were classified as multiple definitions, changing the meaning (a. establishing an equation and b. writing arithmetic expression) and arbitrary error. While generating verbal representation, prospective teachers made three different types of errors, namely missing meaning, changing meaning and wrong meaning. Moreover, the results showed that about half of the prospective teachers did not know the meaning of the symbols contained in the algebraic expression written for a verbal representation. The results of the research provide important suggestions for the development of programs and course contents, as they provide insight into the information to be provided to prospective teachers in mathematics teacher training programs.