A General Analytical Model for Problem Solving Teaching: BoS

Abstract

In this study, a general analytical model called Bag of Solution (BOS) was developed to help students understand and solve mathematical problems. The model is based on graph theory, a topic under discrete mathematics. The types of problems to be modelled for BoS were determined by looking at densities of the problems in the central placement examinations and exam preparation books. As a result, three types of problems were selected; namely Mixture, Worker and Motion problems. In order to develop a common model for solution of the three types of problems, a total of 1509 mixture, worker and movement problems were examined. After the analysis, the problem types were taken together, and variable relations were determined, and a common graph model was created. Since it is an algorithmic model, it allows solving problems both by paper and pencil and computer. This study proves that different types of problems (with different scenarios, objects and object relations) can be solved using a single model. It is expected that the BoS developed in this study will offer two benefits. It is hoped to both provide an algorithmic basis for computer-aided instructional materials, adaptive systems and intelligent tutoring systems to be developed for problem solving and also help students to develop a new understanding of the problem-solving process. A common graph structure that can covers the entirety of a problem can allow students to construct their own learning while solving the problem step by step.