Application of Graph Theory in an Intelligent Tutoring System for Solving Mathematical Word Problems

Abstract

This study is aimed to construct a model to transform word "motion problems" in to an algorithmic form in order to be processed by an intelligent tutoring system (ITS). First; categorizing the characteristics of motion problems, second; suggesting a model for the categories were carried out. In order to solve all categories of the problems, graph theory including backward and forward chaining techniques of artificial intelligence were utilized. The study outlines the adoption of graph theory in to the motion problems and put forth some evidence that the model solves almost all of the motion problems. In conclusion, the recommended model can be suggested to be used in educational software in the problem solving context.

Identification of Graph Thinking in Solving Mathematical Problems Naturally

“…Problem solving holds an essential role in mathematical thinking, and some literature argues that graph theory, a branch of mathematics, is widely used to solve problems in everyday life (Dafik et al, 2020;Medová et al, 2019;Nabiyev et al, 2016). Graph theory is able to represent a complex problem into the easier one to understand and to solve.…”

“…The application of graph theory in various fields in daily activities has been widely investigated, and the focuses include computer science (Cvetković & Simić, 2011;Singh & Vandana, 2014), health (Mears & Pollard, 2016;Vecchio et al, 2017), transportation (Lanjewar et al, 2015Nelson et al, 2019), geology model (Phillips et al, 2015), banking (Lin et al, 2011), architecture design (Poyias & Tuosto, 2015;Zboinska, 2015), regional planning (Foltête et al, 2014), biology (Gao et al, 2018;Garroway et al, 2008), and the electrical system (Benchouia et al, 2014;Šarga et al, 2012). In addition, several studies investigated the use of graph theory in learning process in class (Asghari et al, 2012;Medová et al, 2019;Nabiyev et al, 2016;Uyangör, 2019). Asghari et al (2012) in their study show that graph theory allows students to think creatively, construct a collection of ideas, and use graph representations in solving problems.…”

“…in his study pinpoints that integrating graph theory in the process of learning mathematics can improve students' achievement in the stages of mathematical thinking. Besides,Nabiyev et al (2016) also underpinned that the use of both artificial intelligence technique and graph theory is able to encourage students to solve complex word problems easily in the problem-solving process. Meanwhile, the study conducted byMedová et al (2019) identifies errors related to graph algorithms and compare them based on the types of error.…”