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

证明是数学教育的重要组成部分，但在大多数课堂上仍然是一个陌生的概念。因此，教师在支持学生和解决他们的多种误解方面面临困难，但实践的机会有限。解决这个教育问题的进展可以通过使用计算机科学知识来开发一个计算机系统，使教师能够在真实的学生之前向虚拟学生教授证明，类似于飞行模拟器如何帮助飞行员为真实的飞行做准备。寻求一个框架，设计一个既有教育价值和技术上可行的计算机支持系统，本研究使用Lakatos的方法来证明，它富有成效地使用的例子和反例，使和完善的示意图。虚拟学生的设计需要一个可靠的学生模型。利用数据收集和人工智能技术，将分别建立一个手动构建和一个自动生成的学生模型，然后组合成一个集成模型。六名教师将向真实的（控制组）或虚拟学生（实验组）教授证明。将通过观察和访谈收集定性数据。除了有助于教师的学习证明相关的指令，从而间接地，学生的学习证明，这项研究可能会开辟新的途径，学生建模和计算机辅助教师培训。

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.