The purpose of this study is to investigate the recognition of The purpose of this study was to investigate the perception of mathematical justification and the practice of performing justification in middle school gifted students. Through this, we tried to understand the characteristics of the mathematical justification of gifted students. Furthermore, it is trying to get implications for mathematical justification education. In this study, the following research questions were established. First, the recognition of the role of mathematical justification and the type of justification favored by gifted students were investigated. And, in the practice of justification, the types of justification revealed in the process of directly solving the questions in the algebraic and geometric domains were investigated. I did. Finally, we tried to analyze the characteristics of gifted students in the performance of mathematical justification.
In order to solve such research problems, a questionnaire and an analysis frame were developed to analyze the justification activities of middle school students by reviewing the literature on the recognition and type of mathematical justification. After that, a survey was conducted on 17 gifted students in the 1st and 2nd grades of middle school, and the following conclusions were obtained.
First, it was found that the subjects of this study had a relatively broad understanding of the meaning of mathematical justification. They recognized not only the role of justification as proof and communication, but also of a wide range of justifications such as logical systematization, mathematical discovery, and intellectual challenge.
Second, gifted students were found to have a high ratio of deductive justification in their preferred justification type. In the practice of actual justification, the types of justification in algebraic and geometric domains were investigated differently. In the algebraic domain, it was expected that deductive justification would be possible, but in actual justification, there were many cases listing empirical evidence as much as the frequency of deductive justification. And in the geometric domain, students were expected to be able to do deductive justification, and most of the answers that completed justification performed deductive justification. However, the empirical justification seen in algebraic questions was hardly found in geometrical questions, and there were many cases of non-response responses.
Third, gifted students often expressed dissatisfaction when the level of justification they actually performed was lower than the expected level of justification. In other words, it was expected that deductive justification could be possible, but when empirical justification was not completed or justification was not completed, they expressed regret for failing to justify deductively using mathematical letters and symbols.
Fourth, looking at the distinguishing features in the mathematical justification of gifted students who participated in this study, there were many cases of formal and deductive justification using algebraic characters even in the first and second grades of middle school. However, through the fact that there are several students who complete deductive justification with verbal expressions, it can be seen that there are individual differences among gifted students. In the case of substituting numbers in order to obtain conviction even after succeeding in deductive justification, there have been cases where the development from inductive to deductive justification has occurred. In addition, when justification was developed, there were cases where the abundant mathematical background knowledge was used improvised.
The following implications were derived from the above research results.
First, it is necessary for teachers to create a variety of instructional environments where they can experience the nature and various functions of mathematical justification, and for this, secure enough time for mathematical justification to provide gifted students.
Second, teachers need to instruct gifted students to recognize useful aspects of inductive justification and to develop into deductive reasoning through the process of inductive reasoning, rather than emphasizing only the deductive aspect in the justification guidance.
Third, it is necessary to provide sufficient experience to express mathematical ideas using algebraic letters and symbols, so that gifted students can develop algebraic translation skills. It is also desirable to recognize that a simple case in geometric items can be an opportunity for deductive justification.
In the 2015 curriculum, it is mentioned to present a justification method appropriate to the student''s level in order to improve mathematical reasoning ability and thinking habits. Based on the conclusions of this study, follow-up studies on teaching and learning are needed to draw out the interest and interest of gifted students.