"The aim of this study was to develop an assessment method for non-cognitive skills specific to subject content and activities. To achieve this aim, the concept of non-cognitive skills was defined based on the five characteristic factors (BIG FIVE). Next, in order to develop an assessment method in line with the characteristics of the subject, we then focused on the non-cognitive skills specific to the content and activities of the subject and set up a theoretical framework by combining the three aspects of the Courses of Study goal "the ability towards learning and humanity" and the five characteristic factors of non-cognitive skills. A framework was set up.
Based on this framework, questionnaires for teachers' evaluation were developed in line with the scale development method, a social survey was conducted, and based on the analysis process, an optimal multiple regression model was determined and a method for multi-layering the evaluation judged by teachers in the survey was found."

The aim of this project is to study the characteristics and viability of the mathematics teaching based on the paradigm of questioning the world (called SRP) in Japanese secondary school. In SRP, students can use anything they need (such as internet and books) and study mathematics as necessary in order to construct an answer to a given question, like the researcher's inquiry process. Through four years of project period, we carried out several teaching experiments in various schooling levels, from elementary school to university, and in different formats (e.g., mono- or multi-discipline, long or short terms). The analyses of data allowed us to reveal the positive aspects as well as the challenges for implementing SRP in Japan. We could also disseminate our results through different international and national conferences and journals.

This study showed the following results; 1) the conception of non-cognitive skills special to contents/activities of a subject, 2) the methods for assessing non-cognitive skills raised by curriculum of explorative proving in school mathematics, 3) the universal design of specifying the teachers’ assessment methods. Concerning 2), we developed the models of teachers’ assessment on the contents in junior high school mathematics statistically. Concerning 3), we adopted the methods to develop the models of teachers’ assessment to UK teachers, and specified the problems to be solved accompanying with designing the method universal.

The purpose of this research as a whole is to build a theoretical framework for teaching of mathematical proof consistent in secondary education and develop a curriculum of this domain based on mathematical activities with using the framework. The main outcomes of this research are described in accordance with the following four working topics: ① analysing of earlier researches on mathematical proof;②clarifying the idea of teaching mathematical proof consistent in secondary education; ③ establishing a framework for networking mathematical activities within and between the domains for curriculum development; ④ developing some didactic situations based on mathematical activities.
In addition, an international seminar was held with foreign researchers, and some research results were published in a distinguished international journal in mathematics education.

In order to develop teaching methods based on the curriculum of explorative proving and verify their effect in lower secondary education, this study firstly defined the concept of teaching methods based on the curriculum of explorative proving as follows: the methods for realizing the shifts of learning levels in the frameworks for developing the curriculum of explorative proving. Next, according to each framework of four domains of lower secondary school mathematics (Algebra, Geometry, Function, Data Handling), domain-specific teaching methods were developed, and their effects and limitations were clarified.

UN set sustainable development goals (SDGs) as new issues. ASEAN Community has formulated the 7 priority areas for education and launched education reform for the first five years. The purpose of this research is to promote the development of teaching materials that will bring up children with future-building skills. A conflicting society can be overcame by using unknown variable, the future target of manipulation of potential relationships and plausible reasoning. Mathematical and statistical methods are essential for creating future scenarios. The research engaged teaching material development related to functional future prediction based on causality and future prediction based on probable reasoning, and lesson study with each country to develop the teaching material. On the APEC meetings, the research widely influenced the results to the world.

The aim of this research project is to advance understanding on the characteristics and the roles of two different settings for mathematics teachers professional development, the local or regional meetings for mathematics teachers on the one hand and the professional degree programme in the university on the other. The analyses of data collected in the two settings imply that teachers' collective work is not enough to develop theoretical knowledge on teaching and the resource provided to the teachers from outside plays a crucial role. Further, we specifies that it is the Japanese paradidactic infrastructure including lesson studies that allows different teacher learning.

This study firstly defined explorative explanations as activities produced by the interactions among generating propositions (planning/construction), generating explanations (planning/construction), examining/improving/advancing. Next, in all of four content areas of junior high school mathematics (“Number and Expression”, “Geometry”, “Function”, “Handling data”), four kinds of curriculum frameworks corresponding to these areas were developed with reference to the characteristics of explanation peculiar to each area. By applying these frameworks, tables connecting contents with activities along with National curriculum of Japan. Finally, the series of lessons based on the tables were planned and implemented, the feasibility of these curricula was confirmed, and research problems worthy to approach are identified.

In this research project aims at creating theoretical foundations of teaching mathematical proof and argumentation for the sake of curriculum development based on the mathematical activities throughout secondary schools. The research outcome is that we constructed a theoretical framework for curriculum development in the teaching mathematical proof by means of the idea of “local organization” introduced by Freudenthal and the idea of “mathematical theorem” proposed by Mariotti et al. In terms of this framework, we considered the mathematics curriculum and developed a teaching unit at the secondary school level. We also organized a thematic study group at the spring conference of Japan Society of Mathematical Education in June 2014, and made research presentations with regard to the objective of the curriculum development, a teaching unit as a model, mathematical activities through the unit, and curriculum assessment and literacy.

The purpose of this study is to develop multilingual (English / Chinese) systems available internationally for supporting the proof learning in order to improve the international learning situation of proof. To achieve this purpose, for the Japanese version of the already developed, with the addition of video content of manipulative demonstrations and the implementation of the functions to register the users, incorporating the content in Teacher's Guide book already. On the basis of these outcomes, referring to the curriculum and textbooks of Chinese and English-speaking countries, we have developed the Chinese version and English version of proof learning support system.

The aim of this study is to explore the ecology of proof in school mathematics of three different countries: France, US, and Japan. Through the analysis of mathematics textbooks and national curricula, I identified first several differences in the forms of proof and the functions of proof, and second different elements (conditions and constraints) that result in these natures of proof. In particular, I have shown that the "raisons d'etre" of proof, that is the reason why the proof is necessary in mathematics, are different in France and in Japan.

The study explores the nature of mathematical knowledge emerging during the activity in Japanese mathematics lesson. I show, as a result of the analysis of a concrete example, that the mathematical knowledge at stake in the lesson is formed as a result of the interaction with teacher's knowledge of different levels such as on the policy of institution, on the mathematical contents of textbook, on the method of interaction with students, etc. The result points out the necessity of understanding teacher's perception on the mathematical activity in order to better understand the state of knowledge during the activity. The study also identifies different states of knowledge taken into consideration in the descriptions of what is called "mathematical activity" in Japanese course of study and in previous research works in Japan.

Higher goal of this study is to develop the mathematics teaching materials which can be used in the world effectively. Specifically, the purpose is to arouse the desire to learn mathematics, to make use of the system of exhibition or educative system of the scientific museum as the institution to provide an opportunity to learn more deeply, to develop the mathematical exhibition and experiment materials for the scientific museums and to provide the concrete hands-on program of education on mathematical. With the cooperation of the National Museum of Nature and Science, Education Board of Ushiku city, Education Board of Tsukuba city, Kasukabe High School of Saitama Prefecture and Omiya High School of Saitama Prefecture, we did case development of the mathematical exhibition and experiment materials for the scientific museums for three years. The accumulated cases sorted by the field are as following six areas: (1) mathematical perspective, (2) mathematical transformations, (3) mathematical mechanism, (4) mathematical music scales, (5) mathematical measurement, (6) others. The developed products feature is to be able to learn various things not depending on the school year or the stage school. The report shows the case examples. The developed materials got a lot of attentions both domestic and international. Within Japan, it had attracted attention in the points of the connection and collaboration of elementary school and junior high school, the connection and collaboration of junior high school and high school, and the connection and collaboration of high school and university. Therefore we were requested of the publication of the case study book for the walk-in lesson. In the mathematical transformations, we developed the software and it can be viewed on the WEB. Outside of Japan, we realized the invited speaker at international conferences twice (South Korea, Hong Kong), and once the entire speech (Taiwan), a study presentation (Rome) and two courses abroad (Philippines, Honduras), Especially in the International Conference of the International Committee of Mathematics Education on the 100th anniversary, we watched the linage of the historical development of teaching materials in Europe. Also, we did the investigation about the way to present effectively. In the Philippines and Honduras the developed software will be used. By showing the product on the WEB, we realized the development of mathematical exhibition materials that are useful in the various situations as we expected. We are asked that they want to make use of the products in SHH and SPP. The exhibition in a museum is the future challenge, but the products have already been able to utilize in the educational field.

今年度は、本研究の初年度として、CAS等のグラフ描画ソフトを利用した認知的な働きのメカニズムを同定するための理論枠組みを整理し、理論分析を進めることを目的とした。本研究の理論枠組みとして、Brousseauによる教授学的状況理論とBalacheffによるコンセプションモデルを採用することにした。前者は認知的な活動が状況・場面によって特徴付けられるものと考え、後者は、教授学的状況理論に基づき、学習者の知識状態を学習の観点から記述するものである。これらの理論を用いて、まず関数グラフソフトGRAPESを利用した場合に、これまで日本で扱われてきた学習課題において学習者の認知的活動をいかに促すか分析した。状況を考慮した分析により、探究の授業が導入の部分においては、学習の焦点があいまいになってしまうことが示唆された。具体的には、教授学的契約の断絶が起きてしまう可能性がある。一方、授業の導入後に提起される課題においては、学習者が自らの問題として扱う可能性が示唆された。教授学的状況理論の言葉を用いれば、devolutionを起こしやすい。これらの分析結果を現在まとめている。また、これらの理論分析と同時にGRAPESを用いた予備実験を進めている。この他、「数学におけるテクノロジー国際会議(ATCM)」では、数学教育におけるテクノロジー利用に関し、日本の場合を共同で発表し、宮川健がGRAPESを担当した。

本研究の目的は、国際数学オリンピック(IMO)総合順位上位国と、我が国の秀でた生徒の教育方法を、出場者個別育成ストラテジの次元で比較調査することを通して数学における秀でた生徒を育てる教育のノウハウの相違を明らかにし、その結果から教育研究への範例、実践開発への教材を得て、国内、途上国における人材育成方略への提言をすることである。具体的には、1).入試選抜による特別学校を基盤とする中国の英才教育と、自主セミナーという機会均等・公正理念のもと、誰もが参加しえるブルガリア方式など、秀でた生徒を育てる教育に対する考え方の相違を明らかにする。2).本調査では、IMO出場者輩出校での教育方法・内容調査を行う。具体的にはカリキュラム(教科書、教材)、指導法、指導者、生徒、入学、進路、動機の項目毎に、英才教育のプロセスを質的に調査し、関連資料を収集する。3).収集資料を基に、カリキュラム・教材資料集を作成する。4).適宜、それぞれの立場でそれぞれの調査成果を報告するとともに、公開シンポジウムを平成18年度に行い、秀でた生徒をさらに鍛える数学教育の研究と実践の必要を広く喚起し、今後の展開を基礎付けることであった。本年度は、昨年度の訪問調査の成果を受けて、成果報告を中心に行った。まず、調査結果を、明治図書出版「教育科学数学教育誌」で連載するとともに、公開シンポジウムを実施した。公開シンポジウムには、78名が参加した。当初の目標どおり、各界の関係者に、公正な教育の動向を調査し、広めることができた。特に、ブルガリアの数学教育の価値が、比較相対として明確になった。

代数・幾何・微積分の発展的学習を促す「使える数学」の教材サイトとその指導事例開発を継続した。まず、1年目の成果8事例をUPした。展示室としては、江戸時代の数学、歴史原典にみる代数、楽しい探究の展示室が、数学のある風景などが増設された。続いて2年目に開発した「使える数学」コンテンツは、「球面三角法」と「古代中国の宇宙像」である。球面三角法は、15世紀に大航海時代、大海原で船が自分の位置を天体の運動と時から知ることを実現した、球面三角形の数理を扱うものである。「古代中国の宇宙像」は、当時の測量術(重差術)を前提に、今日的にみれば相似三角形と連立方程式で表しえる宇宙像を話題にするものである。使える数学は、従来「数学的モデリング」として、その過程に注目して話題にされてきた。それに対して本研究では、使える数学一つ一つを改めて発掘する方法論を採用した。その研究成果が認められ、引き続き海外での講演も行った。年度途中に、アクセス数の多さでバックアップサバーも含めて立て続けにハードディスクが壊れる事態に見舞われた。年度末、最終的にサバーの設置場所を移し、必要な相対パスに書き直し、再公開することになった。更新後の新成果公開サバーURLhttp://math-info.criced.tsukuba.ac.jp/Forall/http://math-info.criced.tsukuba.ac.jp/museum/