According to the TIMSS, elementary school students in Japan are internationally highly ranked in arithmetic problem solving. However, it is reported that the percentage of students who like learning mathematics and students who appreciate the value of learning mathematics are extremely low. The major focus of this study is to develop classes to appreciate the beauty of arithmetic and to verify the effectiveness of these classes in an elementary school, on the basis of actual circumstances of Japanese children as mentioned above.
The beauty of arithmetic has the following properties in the Course of Study in arithmetic: usefulness, conciseness, generality, accuracy, efficiency, development, and the beauty. To help pupils appreciate them, the course study (part 1) suggested that “the self-assessment activities to transform mathematical ways of viewing and thinking and to value the beauty of arithmetic are important.” So self-assessment activities using OPP was taken in as the way in detail. Although a number of studies on the development of metacognitive ability using OPP have been made in actual teaching, the question here is the process of learning, which sets the selfassessment activities using OPP, which helps pupils appreciate the beauty of arithmetic.
To begin with, on the basis of previous studies, the structural elements on the self-assessment activities using OPP to appreciate the beauty of arithmetic can be classified into four components: the setting of a situation to give the title, the setting of a situation to design an essential question, the setting of a situation to writing the learning records, and the self-assessment at the end of a class. Then, a questionnaire was carried out it to clarify the actual situation of elementary school children regarding the appreciation of the beauty of arithmetic. Next, a teaching material and a teaching process were developed which considered the process that children appreciate the beauty of the arithmetic. As a result, it has been clarified that the setting of the selfassessment activities using OPP is valid in classes appreciating the beauty of arithmetic.
