A Learning Support System for Mathematics with Visualization of Errors in Symbolic Expression by mapping to Graphical Expression

Abstract

It is difficult for mathematics learners to solve problems that require describing solution procedures. This issue was revealed in the PISA and TIMSS tests. This issue is possibly caused by a lack of understanding of the relation between symbolic and graphical representations in mathematics. This work proposes a learning support system that realizes understanding of the relation between both types of expression. This paper describes the development of our system and reports on its effectiveness and considerations. We realize a function that converts symbolic expressions entered by learners to graphical representations, and a function for manipulating the converted graphic. The conversion function visualizes an input symbolic expression as a graphic. If the symbolic expression contains an error, the function visualizes the error so that learners can become aware of it. This is “learning from errors” by error visualization. The function also realizes learner operations related to the visualized graphic. The operation range is limited by constraints in the symbolic sentence input by the learner. Through their operations, learners deepen their understanding of how the symbolic sentence influences the graphic and clarify their understanding of the relation between the symbolic expression and its graphical representation. An experimental test verified that the proposed system using this method is effective in mathematical learning and facilitates learner understanding of the contents of symbolic sentences.