本稿では，教師の「数学することを知る」の枠組みを開発し，教師2 名を対象にしたケーススタディからの検証により，その有効性と妥当性を明らかにすることを目的とする。まず，先行研究をもとに「数学することを知る」を「絶対的固定的な見方・考え方」と「可謬的可変的な見方・考え方」に整理し，授業の「構想時」と「実践時」において特徴が表出されると想定して枠組みを開発した。次に，枠組みをもとに特定した因子を用いて，小学校教師，中学校数学教師の2 名のアンケートや授業実践の分析を行い，枠組みを検証した。その結果，構想時は「可謬的可変的な見方・考え方」であっても，実践時は「絶対的固定的な見方・考え方」となる傾向があり，教師の特徴を捉えるのに有効であることが見えた。また，教師が「可謬的可変的な見方・考え方」へと変容していく様相から，観点「数学することを知る」の基準は，「十分知っている：想定外受容」，「知っている：想定内受容」と解釈するに至った。

本研究は，発展的思考・態度の育成を視点とする授業評価ルーブリックの観点「授業展開を知る」に着目し，その基準解釈を明瞭にし，学習者の意思が働いて自律的に発展的に考える学習が展開できるよう，教師の支援の判断根拠を提案することを目的とする。教師の支援を，認知的支援及びメタ認知的支援を視点にしてⅠ，Ⅱ，Ⅲの3 つの支援レベルに整理し，小4「何百何十÷何十で余りのある除法」の授業実践を分析した。その結果，学習者の意思が働き，自律的に発展的に考える学習を促す発展型授業が可能な教師の支援について，「問題解決の状況を適正に判断して，適正支援が行えること」「教師の支援力量は3つの支援レベルに整理できること」の知見を得た。そして，基準の「十分知っている」とは安定的に適正支援ができること，「知っている」は部分的に適正支援ができること，の解釈に至った。

After studying at Tokyo Senmon Gakkō, Ōdō Tanaka (1867–1932) stayed in the US for more than eight years from 1889, and taught philosophy at Waseda University for more than 30 years. At the University of Chicago, Tanaka was supervised by John Dewey (1859–1952) and trained also by William James (1842–1910, the author of Pragmatism) and George Santayana (1863–1952). Tanaka naturally became a pragmatist. Tanaka, like James and Dewey, praised utilitarianism highly, and therefore he paid attention to the development of utilitarianism, political economy, and economics.

In the early twentieth century, several scholars became interested in Sontoku Ninomiya (1787–1856, economic reformer and thinker). Tameyuki Amano (1861–1938, economist at Waseda University) introduced the teachings of Ninomiya into his Discourse on Thrift and Savings (1901) and his edited textbook New Commercial Reader (1911, 1913). In contrast, Tanaka regarded Ninomiya as a philosopher and authored A New Study of Sontoku Ninomiya (1912) by bringing focus into pragmatist, utilitarian, and individualist arguments in Ninomiya’s writings. Tanaka carefully examined Ninomiya’s concept of “chūyō (golden mean, constant mean),” which could serve as the criterion when a spectator questioned if something contributed to the happiness of a person or mankind in the world. Later Tanaka came to realize that Ninomiya’s concept of “suijō (concession)” should have something to do with Adam Smith’s concept of “parsimony.”

It is noteworthy that Dewey visited Japan in March and April 1919 and his lectures given at the University of Tokyo became the book Reconstruction in Philosophy in 1920. It is also important to remember that Dewey accepted the warm invitation sent by Hu Shih (1891–1962), his former student at Columbia University and a philosopher at Peking University, to visit China and then he spent more than two years on giving lecturers at Peking, etc.

With reference of Tanaka’s pragmatism, Dewey’s 1920 book, and Amano’s economics, this paper relates Adam Smith’s Theory of Moral Sentiments (1759) and The Wealth of Nations (1776) with the use of the idea of “contributing to the happiness of mankind.” It also argues that Western economic thought has developed from some part of Western philosophy and that Western philosophy and economic thought have deeply connected with Christianity.

　　In order to realize the lessons where students think autonomously and developmentally, the teacher’s consciousness about how to grasp the problem solving and thinking that the students do will influence.  With reference to Ernest’s（2015）  Fallibilism and Absolutism, we developed a questionnaire on teaching students to think autonomously and developmentally, and from the case studies of two teachers, we caught the trend of “classroom practice emphasizes teachers’ planned developmental guidance and short-term academic improvement, fixing instruction and support to control learners’ thinking and attitudes”.

　　These findings are findings within the scope of case studies, and are not findings that sufficiently demonstrate versatility.  In this study, we conducted a questionnaire survey on lessons where students think autonomously and developmentally for elementary, middle school and high school teachers nationwide.  The purpose of this paper is to analyze Akita prefecture data and obtain suggestions for guidance.

　　As a result of analyzing the data of 124 elementary school teachers, 71 middle school teachers, and 35 high school mathematics teachers in Akita prefecture, the following 2 points were clarified.

　　1. As  for teachers’ consciousness, there is a tendency for Awareness of Developmental Mathematics to be seen when the lesson is planned, while to increase absolutely Awareness of Mastery Mathematics  when the lesson is practiced.

　　2. In  the composition of each factor, “G.  Numerical values, conditions, content, and sequence of problems” was not included, indicating that teachers have an absolute, fixed view of mathematics and its teaching  as the subject of instruction, which may be considered a manifestation of their Awareness of Mastery Mathematics.

　　In the future, following the Akita prefecture data, we will proceed with the analysis of national wide data and clarify the trends of students and university faculty members.  In addition, we will proceed with the analysis of whether there is a difference depending on the number of years of teaching profession, or whether there is a relationship with the good results of the national academic ability / learning situation survey.  Furthermore, we will consider the training method using this survey.