추론 유형에 따른 고등학교 수학 문제 분석 연구

Abstract

Recently, mathematical reasoning has been considered as one of the most important mathematical thinking abilities to be established in school mathematics. This study is to investigate the mathematical problems on the content of 'Set and Statement' and 'Sequences' in high school according to the four types of reasoning, namely Making Conjectures, Investigating Conjectures, Developing Arguments, and Evaluating Arguments. Those types of reasoning were reconstructed based on Johnson's six types of reasoning suggested in 2010. The content is dealt with in 'Mathematics II' textbook developed and published according to the mathematics curriculum revised in 2009. The subject of this study is nine types of textbooks and mathematical problems in the textbook are consisted of as two parts of 'general problem' and 'evaluation problem'. Finally, the results of this study can be summarized as follow: First, it is stated that students be establishing a logical justification activity, the highest reasoning activity through dealing with the 'Developing Arguments' type of problems affluently in both 'Set and Statement' and 'Sequence' chapters of Mathematics Ⅱ textbook. Second, it is mentioned that students have a chance to investigate conjectures and develop logical arguments in 'Set and Statement' chapter of Mathematics Ⅱ textbook. In particular, whereas they have a chance to investigate conjectures and also develop arguments in 'Statement', the 'Set' chapter is given only an opportunity of developing arguments. Third, students are offered on an opportunity of reasoning that can make conjectures and develop logical arguments in 'Sequences' chapter of Mathematics Ⅱ textbook. Fourth, Mathematics Ⅱ textbook are geared to do activities that could evaluate arguments while dealing with the problems relevant to 'mathematical process' included in 'general problem'.