Diagramming Mathematical Proofs Based on Logical Structures for Learners

Abstract

This study aims to help learners read mathematical proofs. Mathematical proofs consist of propositions and are logically structured. The structure is based on inferences, i.e., a proposition as consequence is derived from propositions as premises. However, the structure is not always represented explicitly in proofs written in natural language, which prevents learners from understanding the proofs. Therefore, we develop a system that allows mathematics teachers or content providers to create diagrams illustrating logical structures of proofs based on natural deduction to provide learners a visual aid that improves their understanding. The diagrams created by our system display natural deduction and arrange additional information (e.g., symbol definitions or explanation to assist understanding) as comments. Further, the system has a function to add buttons to show/hide parts of the proof based on individual learners' requirements. Further, we introduce the basic components of a diagram and the method to create it. © Springer International Publishing Switzerland 2014.