The written and oral justifications of mathematical claims of middle school pre-service teachers

Teaching meaningful and productive mathematical argument in school requires teachers who are comfortable with diverse forms of mathematical justification. This study examines the written and oral justifications of pre-service middle school teachers (PSTs) in a single classroom, focusing on the types of justifications they use during the patterns unit of a required mathematics class. Toulmin's argument framework (1958), in conjunction with a coding scheme for classifying justification types, was used to investigate this question. The PSTs relied heavily on inductive justifications, including the use of counterexamples and applying inductive justifications at multiple levels when solving complex problems. When they used non-inductive justifications, the PSTs tended to support those justifications with inductive evidence. Taken together, these exploratory results suggest that PSTs have a deep understanding of inductive processes, raising questions about ways to leverage this knowledge to promote more diverse use of justifications in mathematics classrooms.