２次方程式を利用するよさを実感させる授業について ―協同的探究学習を用いた中学校数学の授業開発―

抄録

　　In mathematical activities practiced in junior high school mathematics, mathematical modeling is popular and their focuses tend to be on daily life.  In contrast there are few practical studies on structure-oriented mathematical activities in junior high school.  In fact, most of the mathematical objects dealt with in junior high school mathematics can be obtained by mathematizing real objects or phenomena.  Thus, application problems, in which mathematics are applied to real problems, are easy to use.  In such problems, students’ focuses might be on solving the problems rather than on developing mathematics.

　　On the other hand, we expect that not only just solving problems but also reconsidering their own solving processes can lead students to make new discoveries or to notice better solutions.  These are nothing but the mathematical activities within “mathematics world” written in the commentary to the curriculum guidelines: the processes in which students review their solving processes and results, and consider in integrated and developmental manners.

　　For this purpose, we adopt “collaborative inquiry learning”, which is a didactic method designed and proposed by Fujimura（2012）  to enhance “understanding academic ability”.  In collaborative inquiry learning, students are given a task first and tackle it, then are encouraged to review their own solving processes collaboratively with other students, where each of various solving methods is respected, and finally are given a second task and requested to select the solving method on their own.  In this manner, it is expected to develop understandings of concepts.  Therefore, if the teaching materials dealt with in the lessons are pure mathematical phenomena, lessons designed based on collaborative inquiry learning would be compatible with what is demanded as the learning processes within “mathematics world”.

　　In this paper, we propose lessons regarding the small unit of “applications of quadratic equations” in the 3^rd grade of junior high school.  In this small unit, daily life problems that can be solved using quadratic equations are usually dealt with and comparison with extra method other than quadratic equations is uncommon, and as the result it might be difficult for students to realize the advantages of using quadratic equations.  In the contrast, we adopt problems in “mathematics world” which can be solved various way and suggest practices in this small unit based on collaborative inquiry learning.  The aim of this practice is to make students to obtain the advantages of quadratic equations.  In this paper we verify the achievement of the above aim and show the effectiveness of collaborative inquiry learning in for this purpose and to obtain suggestions for future practice development.