Abstract
In the most general sense, mathematical thinking can be defined as using mathematical techniques, concepts, and methods, directly or indirectly, in the problem-solving process. In this study, efforts were made to include the Graph Theory of mathematics, which is found abundantly in physics, chemistry, computer networks, economics, administrative science, data communication, transportation planning, engineering, and similar areas of daily life, into the mathematics instruction process. Because suitable problems are selected in graph theory, the mathematical thinking skills of the students can be developed. A fundamental, qualitative research approach was adopted in this study, in which the mathematical thinking processes of 12th-grade students were examined. Two girls and two boys with average and high mathematics success who were in the 12th grade of a public school in Balikesir in the 2018-2019 Academic School year constituted the working group of the research. The data in the study were collected with the two worksheets the researchers prepared, the clinical interviews held during the application, and through unstructured observations. The results obtained by analyzing the data in the process of mathematics teaching in which graph theory included are: When students solved the problems they faced and when they ascend top steps of mathematical thinking, they showed a better performance when compared to the other studies. Because, in the steps of privatization, generalization and assumption, only 1 of the total 8 responses given by the students is empty. At the stage of proof which is the final stage of mathematical thinking, the students have achieved a success rate of 75% despite they did not have a lesson about making proofs. This situation was interpreted as the visual model of problems selected from graph theory and attracting the attention of the questions as stated by the students. The results of this study show that, in the process of mathematics teaching, especially if teachers provide enough diversity students by using different fields of mathematics, they can increase the performances of students in mathematical thinking stages.
Highlights
In our age, to say “education, instruction” means to know how to think and research and how to teach these to younger generations [1]
With the typical case sampling method, the study was conducted by choosing a typical public secondary school in central Balıkesir in this research, where the mathematical thinking processes of students was examined in instruction carried out based on the graph theory
Taking mathematics report card grades as a criterion in previous years, students with average and high levels of success were chosen. The reason for this is that it became the idea that rich data would be unable to be collected from students with low levels of success because mathematical thinking includes the characteristics of attaining new knowledge or concepts with estimation, generalizing, conjecturing and testing, abstraction, reasoning, and proving [26]
Summary
To say “education, instruction” means to know how to think and research and how to teach these to younger generations [1]. When general goals of the Mathematics Curriculum that were renewed in our country in recent years (2013, 2017, 2018) are examined in this context, it is vocalized that there is a greater need than normal for individuals who value mathematics, whose strength of mathematical-thinking has developed, and who can use mathematics in modelling and problem-solving in the world of today, which encounters new problems that previous generations didn’t as a result of developments in technology. Instruction programs aim to develop the problem-solving skills of students by looking at problems from different perspectives, to earn mathematical thinking and application skills, to accurately, effectively, and beneficially use mathematics, to develop a perspective on whether a problem they encounter in life is a problem for them and reach a certain level of knowledge, and more [3].
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