算数・数学教育における「日常の文脈に即した問題」に関する研究 ―数学的シツエーションとの関連に着目して―

抄録

　　 As nature of mathematics activity, there are two aspects as “adopting mathematics onto daily life situation” and “creating mathematics from daily life situation”.  Even though many people believe that such connections are important, it is still difficult to make them in good use, because of the NOISES in real life situation.  In this paper, the “Mathematics Problem in Real Life Situation” was examined from the view point of “Mathematical Situation Theory” by Prof. Hirabayashi.

　　 First of all, “Social Open-ended Problem”, which has been presented by Shimada & Baba (2013), is examined as the typical example of “Mathematics Problem in Real Life Situation”.  Finding the major characteristics of it, “Open-Closed Continuum” theory by Dienes, Mathematical Modeling theory, explicit and implicit mathematics theory by Chevallard, are also examined to establish the framework of Mathematics activities with Open-Closed Continuum situation.

　　 By using this framework, a proposal for the lesson is presented, with the procedure of ①Socially Closed situation, ②Socially Open situation, ③Mathematically Open-Closed situation, and ④Socially Closed situation. (Fig.15)  Finally, some advantages for “Mathematics Problem in Real Life Situation” were concluded as follows:  1) Smooth connection between real world and mathematics world, 2) Supporting for students’ motivations for finding rules, 3) Making good use of the value of problem solving, and 4) Getting deeper understanding of mathematics contents.