초등학교 수학 교과서에 나타난 수학적 추론 양상 탐색

Abstract

The purpose of this study was to explore how mathematical reasoning, one of the most important topics in school mathematics, is implemented in elementary school mathematics textbook. To this end, this study analyzed the type of reasoning, level of cognitive demands, and structural characteristics of mathematical reasoning tasks provided in the elementary school mathematics textbooks. As a result of this study, it was revealed that the mathematics textbooks had the strength of providing sufficient tasks dealing with pattern recognition type, but were deficient in providing tasks dealing with multiple types of mathematical reasoning, such as making a conjecture, investigating a conjecture, developing a justification, finding a counterexample, and evaluating an argument. Regarding the level of cognitive demands of mathematical reasoning tasks, the mathematics textbooks provided sufficient tasks of procedures with connections, but insufficiently provided tasks of doing mathematics requiring complex thinking. In relation with the structural characteristics of mathematical reasoning, the mathematical reasoning tasks in the mathematics textbooks embodied only the aspects of pattern recognition-making a conjecture and pattern recognition-developing a justification, but were insufficient in embodying the structural flow of mathematical reasoning. In addition, this study suggested that elementary school mathematics textbooks need to provide a wealth of tasks dealing with multiple types of mathematical reasoning, tasks of doing mathematics, and tasks reflecting the structural characteristics of mathematical reasoning.