Designing a web-based learning support system for flow-chart proving in school geometry

This is the final version of the article. Available from the publisher via the DOI in this record.As international research confirms, many secondary school students can find it difficult to construct mathematical proofs. In this article, we explain the pedagogical and technological underpinnings of a web-based learning support system for students who are just starting to tackle deductive proving in geometry. We show how the system was designed to enable students to access the study of proofs in geometry by tackling proof problems where they can ‘drag’ sides, angles and triangles from the figural diagram of the problem to on-screen cells within a flow-chart proof format. When doing so, the system automatically converts the figural elements to their symbolic form and identifies any of four kinds of errors in the learners’ proof attempts, providing relevant feedback on-screen. We use empirical examples from our pilot studies to illustrate how this combination of technological features and systematic feedback can support student understanding of the structure of proof and how to plan one. Finally, we point out some limitations to mathematical expression and the usage of the flow-chart format, and indicate the prospect of minimizing such limitations by adopting a learning progression for the introductory lessons concerning deductive proofs.This research is supported by the Daiwa Anglo-Japanese Foundation (No. 7599/8141) and the Grant-in-Aid for Scientific Research (No. 26590230, 15 K12375, 16H02068, 16H03057), Ministry of Education, Culture, Sports, Science, and Technology, Japan. Special thanks to Yoichi Murakami who programmed this web-based system