Structuring mathematical knowledge and skills by means of knowledge graphs

Abstract

The aim of the study reported on in this paper was to develop, test and improve a cognitive tool which could help students structure their mathematical knowledge and skills. Mathematics teaching as an auxiliary subject in the context of secondary or tertiary education courses in other disciplines pays too little attention to the structure of the mathematical concepts presented. For the students, therefore, the network of relationships between these concepts does not become a part of their mathematical knowledge and skills, and is consequently not fully available for purposes of reasoning, proving, mathematicizing and solving problems. Knowledge graphs (KGs) can be used by students as a tool to visualize this structure of the concepts and the relations between them. The learning activity of structuring one's mathematical knowledge and skills can be supported by a model, the Mathematical Knowledge Graph Model (MKGM), which serves as a pre-structured heuristic framework. The elements of this model include a central concept, special cases of this concept, operations or actions on the concept, areas of application and properties of the concepts and operations. The present paper reports on a trial among five students of the Open University of the Netherlands (OUNL), who constructed a KG in accordance with the MKGM model. The paper focuses on the graphs produced by the students, their appreciation of the structuring activity and the relation between their graphs and test results.