2018 Volume 24 Issue 1 Pages 99-120
New Course of Study guidelines have been made public, and a “talent and ability” based curriculum will finally be enforced. The most pressing issues today are to identify the talents and abilities to be fostered through math education in the coming “talent and ability” based curriculum, to develop learning and teaching methods based on the curriculum, and to promote the improvement of lessons. In this research, we focus, therefore, on critical thinking as a talent and ability to be nurtured through math education and one of the “21st century abilities” (Katsuno et al., 2013). The objectives of this research are the following: first, to position critical thinking as a thinking method for solving problems and clarifying the characteristics of math education; and second, to develop lessons using various problems from “combinatorics” as materials for fostering and strengthening the efficacy of critical thinking and the critical thinking abilities of children as a result of completing the lessons.
The results of this research indicate the following findings. For the first objective, critical thinking in a broad sense is shown to have an important effect on the process of solving problems in social contexts. In terms of the characteristics of judgment standards, we can identify personal or social value judgments as well as mathematical judgments. For the second objective, we focus on “socially open-ended problems”, as described by Baba (2009), aimed at developing experimental lessons for nurturing critical thinking in a broad sense. In our prepared lesson, we find that students perform critical thinking and make alternative choices through compound-eye analysis based on their own social value judgments for developing “better” opponent matching in league competitions without accepting on faith the “ideal” opponent matching in league competitions completed by using mathematical induction.
A future issue is to develop a method for evaluating critical thinking as described above. Other issues include how to develop general-purpose critical thinking in the contexts of math education and investigating the characteristics of critical thinking as fostered in math education. Further studies will be required to clarify these issues.
