Developing an Interactive Computer Support System to Facilitate Teacher Learning of Proof-related Instruction in Mathematics

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Besides a central concept in Mathematics, proof is regarded as an essential component of Mathematics Education, but is still an alien concept in most classrooms. Thus, teachers face difficulties in supporting students and tackling their multiple misconceptions, but have limited chances to practise. Headway in addressing this educational problem can be made with the use of Computer Science know-how to develop a computer system that will enable teachers to teach proof to virtual students before real ones, similarly to how flight simulators help pilots prepare for real flights. Seeking a framework for the design of a both educationally valuable and technologically feasible computer support system, this study uses Lakatos' approach to proving, which productively uses examples and counterexamples to make and refine conjectures. The design of virtual students requires a reliable student model. Using data collection and artificial intelligence techniques, a manually constructed and an automatically generated student model will be built, respectively, and then combined into an integrated model. Six teachers will teach proof to either real (control group) or virtual students (experimental group). Qualitative data will be collected through observations and interviews. Besides contributing to teachers' learning of proof-related instruction and thus, indirectly, to students' learning of proof, this study may open new pathways to student modelling and computer-assisted teacher training.