초록/요약

Objectives Based on the principle of mathematics education that students can learn mathematics best when they construct mathematical objects, relationships, and meanings by themselves, this study applied the activities of learners generating mathematical examples to examine the level and forms of mathematical abstraction and communication. Methods The process of generating mathematical examples that fit specific conditions on the fifth grade geometry area and refining them through interaction with others was qualitatively analyzed with multifaceted data such as activity output, video records, interviews, field notes. In addition, the quantitative frequency of mathematical abstraction and communication in the course of the class was mutually complemented. In the data analysis process, the content feasibility was verified and field applicability was checked through consultation and review by relevant experts, and the triangulation method was used to minimize bias and verify research results. Results Studies have shown that students have developed a comprehensive level of mathematical abstraction through activities of learners generating examples, representing and comparing mathematical examples in various ways, with sharing and discussing new strategies. These results confirmed that activities of learners generating mathematical examples that expand the scope of existing mathematical concepts promote flexible thinking and organization of new mathematical structures, and that the qualitative and quantitative improvement of mathematical communication is significantly related to flexible thinking and the organization of new mathematical structures. Conclusions In the course of these activities, it was found that mathematical abstraction and communication were closely related, and students were able to break down the typical example spaces, organize mathematical structures, expand mathematical abstraction and communication skills through flexible thinking. Furthermore, it was proposed to strategically analyze problem-solving and psychological mechanisms that students reveal in generating examples through follow-up studies to analyze capabilities and definitive factors other than mathematical abstraction and communication.