A General Analytical Model for Problem Solving Teaching: BoS

Year 2019, , 476 - 500, 10.09.2019

Ali Kürşat Erümit , Vasif Nabiyev , Temel Kösa , Mehmet Kokoç , Ayşegül Aksoy

https://doi.org/10.16949/turkbilmat.486084

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.

Keywords

Graph theory, problem modeling, problem solving, bag of solution

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