Determining the validity of mathematical statements in a third-level analysis course

Our study is based on data collected from interviews with seven students from a second-year Analysis course in University College Dublin. During the interviews, students were given statements about concepts from Analysis and were asked to say whether the statements were “True” or “False” and to verify their answers. One aim of the study was to determine whether the students took a semantic or syntactic approach when determining the validity of the statements, and to observe whether they could switch flexibly between approaches if necessary. Our work is based on the studies of Alcock and Weber where they explore in detail the notions of semantic and syntactic approaches to proving.