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 studentsunderstand and solve mathematical problems. The model is based on graph theory, a topic under discretemathematics. The types of problems to be modelled for BoS were determined by looking at densities of theproblems in the central placement examinations and exam preparation books. As a result, three types of problemswere selected; namely Mixture, Worker and Motion problems. In order to develop a common model for solutionof the three types of problems, a total of 1509 mixture, worker and movement problems were examined. Afterthe analysis, the problem types were taken together, and variable relations were determined, and a commongraph model was created. Since it is an algorithmic model, it allows solving problems both by paper and penciland computer. This study proves that different types of problems (with different scenarios, objects and objectrelations) can be solved using a single model. It is expected that the BoS developed in this study will offer twobenefits. It is hoped to both provide an algorithmic basis for computer-aided instructional materials, adaptivesystems and intelligent tutoring systems to be developed for problem solving and also help students to develop anew understanding of the problem-solving process. A common graph structure that can covers the entirety of aproblem can allow students to construct their own learning while solving the problem step by step.