Abstract
This study attempts to describe characteristics of graph thinking in solving a mathematical problem. Three students at the 10th grade of senior-high schools were involved as the subject. The data was collected from the result of an optimization problem task (OPT), video recording, interviews, and field notes. The results showed two major characteristics of graph thinking were found in solving the problem. First, students used the concept of graph theory to create a problem modelling. They were able to represent the information given in the problem in the form of graph. Second, students also used the concept of graph theory to create a problem modelling and search algorithm. The problem modelling was created as the students interpreted the problem by making connection between the objects in the form of an adjacency matrix and connectivity. In devising a plan, the students referred to the problem modelling to develop search algorithms. However, the algorithms were not entirely efficient. Some of them required the students to initially describe all answer possibilities. The algorithms constructed by the students referred to sequential and conditional algorithms. This study argues that graph-thinking skill can be developed through a learning process which involves students in the solving of open-ended problem to stimulate ideas of problem solving. By developing graph thinking ability, students will be able to analyse and reason information, express mathematical ideas, and have flexibility in solving a problem. These skills are urgently needed in the 21st century where rapid and continuous changes occur.
Highlights
Thinking is an important activity in human life
The students who have never been exposed to the optimization problem were assigned to do the optimization problem which was generally solved through the concepts of graph theory
The results of this study elaborated the characteristics of graph thinking in solving the Optimization Problem Task (OPT) shown by three students divided into two groups
Summary
Thinking is an important activity in human life. People cannot be separated from thinking activities. People are able to gain meanings or understanding about everything they face in life. Thinking refers to information processing which involves mental activities such as judgement, abstraction, reasoning, imagination, and problem solving (Solso et al, 2005). Mathematics learning at school is acknowledged as a means of clear, critical, creative, systematic, and logical thinking activities. Once mathematics is considered as a means of thinking, it no longer functions as a product that must be given to students. The product of mathematical thinking comes as a result of thinking process in learning mathematics. When students encounter mathematical problems, they will be likely to carry out mathematical thinking activities in providing ideas or solutions
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