算数教育における子どものインフォーマルな表現に焦点を当てた授業に関する考察 ―小学校第４学年「おはじきゲーム」の授業実践を通した主体的・対話的で深い学びの実現―

抄録

　　 The purpose of this study was to clarify whether or not a class designed by normatively using the “framework for capturing expressions that occur in math and arithmetic classes,” which has been used as a descriptive model in previous studies, can realize children’s proactive, interactive and authentic learning.  In this study, we considered that proactive, interactive and authentic learning is realized if the class develops from informal to formal representations.  The lesson aimed to utilize division with remainder and the way of change, and assumed expression while taking into consideration the domain and grade level, and treated a game of “OHAJIKI-Game” as a context for expressing informal representations.  As a result of teaching the game to 4th grade elementary school students, we confirmed the development from informal representations to preformal and formal representations.  This suggests that this lesson realized proactive, interactive and authentic learning.  Furthermore, in the discussion of the class, we discussed the proposed improvements to the class design and the effectiveness of the class design using a framework for capturing informal representations.