SUPPORTING STUDENTS TO OVERCOME CIRCULAR ARGUMENTS IN SECONDARY SCHOOL MATHEMATICS: THE USE OF THE FLOWCHART PROOF LEARNING PLATFORM

The extent to which students are competent in identifying circular arguments in mathematical proofs remains an open question, as does how it might be possible to enhance their competency. In this paper we report on a study of learners encountering logical circularity while tackling geometry proof problems using a web-based proof learning support environment. The selected episodes presented in the paper illustrate how learners who have just started learning to construct mathematical proofs make various mistakes, including using circular arguments. Using the feedback supplied by the web-based proof learning support environment, and with suitable guidance from the teacher on the structural aspects of a proof, learners can start bridging the gap in their logic and thereby begin to overcome circular arguments in mathematical proofs.