A Study on the Power to Express Mathematically the Process of Thinking in High School Mathematics Lesson

Abstract

　　In the current Course of Study for high school mathematics, upbringing of the mathematical power of expression is made much of. From national and international scholastic ability investigations, it is well known that there is a problem for Japanese children in speaking one’s thought with showing reasons definitely. Therefore, in this paper, the author focused on power to describe one’s thought with showing reasons definitely, namely power to express mathematically the process of thinking in order to suggest some means to overcome the identified problem. First, based on the review of previous studies, the power to express mathematically the process of thinking is classified into five elements; “Use of the mathematical expression”, “Being conscious of unconsciousness”, “Visualization of the consciousness”, “Clarification of reasons and the logic”, and “Sophistication of the expression”. And the author proposes the structure of these five elements. Second, based on the structure, six guiding principles are extracted for three stages of “Expression to promote thinking”, “Clarification of reasons and the logic”, and “Sophistication of the expression” in reference to previous studies on meta-recognition and explanation. Finally some teaching methods are proposed under each of six guiding principles for improving students’ power to express mathematically the process of thinking in high school mathematics lesson.