主体的に学ぶ力を育む算数・数学の授業の実現 : これからの時代に求められる資質・能力の育成を目指して<教育科学>

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The Study of Open-ended Approach in Mathematics Teaching Using Jigsaw Method : A Case Study of the Water Beaker Problem<教育科学>

The aim of study was to (1) create a lesson plan of an open-ended problem using jigsaw method (2) experiment the lesson plan in junior high school in Japan and (3) compare between expected and empirical result in class experiment. This study was conducted by reviewing the related literatures, creating the lesson plan and other instruments, experiment the lesson plan in junior high school in Japan and summarizing the result of teaching. The process of Mathematics teaching using the open-ended problem is the method that allows students to encounter Mathematics problems having the openness in processes, answers and developing of problem. The students will find the solution by using Mathematics knowledge based on their prior knowledge and their abilities. The jigsaw activity provides students learn to collaborate with others and improves their communication skills in order to explain the findings to others. The lesson plan about the water-beaker problem tilted with one fixed edge, was created along with jigsaw method which are as follows:(1) Expert activity was divided into 3 steps: 1.1) Brainstorming: Students are divided into groups to brainstorm what they want to examine the beaker from only one view (Front/Top/Side-view), 1.2) Sharing: Students regroup to share viewpoints of brainstorming group in own view, 1.3) Experiment: Students regroup to examine viewpoints by experiment in own view, (2) Jigsaw activity: Students regroup to group of all views (Front, Top, Side-view) to explain all findings. The lesson plan was tried out with students in 2nd year junior high school class of Saitama prefecture junior high school for 2 periods by Japanese teacher and the researcher. The results of experiment showed that students perceived the volume of water is constant and discovered a variation of water height which is the height of water at the tilted side increases but the opposite side decreases. Those are important foundation conditions to generate other amounts. Most students collected data in experiment by measuring so the teachers should encourage students draw a model of tilted beaker to help seeing the perspective in order to compute other amounts. It should be noted that the students were 2nd year junior high student and still have not study about irrational number such as square root of 2, Pythagorean theory. Therefore they could not find some exactly detail. On the other hand, they could find many changes about ratio, directly and inverse proportional which they have already studied. It means they could integrate their mathematical knowledge. Furthermore, most of them could not explain ideas clearly and accurately so the teacher should emphasize students to add more detail of change clearly. From this study, it shows that students’ thinking ability is satisfactory in flexibility but unsatisfactory in fluency and originality. They should be offered the improvement because these skills are important and beneficial effect on their lives. Teacher should pay attention to make familiar relationship with the students at the beginning and must be able to communicate with students naturally and explain simply in order that the learning process could be done smoothly and successfully. Communication skill is a very indispensable and important skill that teacher have to improve. About learning activities, the more openness of question teacher asked may be the greater of the challenge and interesting of question. Moreover, if teacher provided students make a condition of question by themselves, students will be engaged to the problem gradually and can understand the problem more deeply.textapplication/pdfdepartmental bulletin pape

算数・数学教育におけるメタ評価に関する研究

４ 若手研究及び基礎研究textapplication/pdfresearch repor

数学の学習評価をとらえ直す : 教育評価の重層性・双方向性に着目して<教育科学>

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数学的な見方・考え方の育成に関する一考察 : 中学校数学科における多様な考えとその扱いに焦点を当てて

本稿の目的は、中学校数学科における「数学的な見方・考え方」の育成について検討を行うことである。まず、国立教育政策研究所(2016) や「数学的な考え方」に関する先行研究のレビューをすることで、「統合的発展的な考察を通した創造的な学習活動」の重要性を指摘し、このような学習活動の前提として「多様な考え」や「練り上げ」に着目した。そして、教材の具体例として「中学2 年：文字式の利用」を示した。加えて、数学的な見方・考え方を育成するにあたって、教師の役割が重要であるということを指摘した。textapplication/pdfdepartmental bulletin pape

数学教師の力量形成に関する研究動向 : 状況論的側面に着目して<教育科学>

On mathematics education research in Japan, although research on “students” and “teaching materials (mathematical contents)” has been actively conducted, only a small number on “teachers” have been done. However, mathematics teacher education research should be regarded more as it is important for teachers to teach well. In this paper, we reviewed the positioning and problems of research on mathematics teacher education and how mathematics teachers’ ability is attained. We focused on themes such as a situated approach raised by Kaiser et al. (2017), “noticing” (Sherin et al., 2011) and teacher’s perception, interpretation and decision making (Blömeke et al., 2015). Then, we examined how a teacher’s knowledge (e.g., Pedagogical Content Knowledge by Shulman (1986, 1987) and Mathematical Knowledge for Teaching by Ball et al. (2008)) and views on mathematics (see, e.g., Dossey, 1992) is intrinsically linked to their mathematics teaching competence. Furthermore, we outlined the purpose and goal of mathematics education, and examined these previous studies. Finally, we concluded that “ability for mathematics teachers to teach well” was directly linked to teaching being a method “to enrich their knowledge and views on mathematics and to properly grasp the immutability and fashion of mathematics education”. Also, Ball (2011, p.xxi) put forward “Noticing is not purely neutral attention, but culturally shaped perception”. Because a situated approach depends on the culture of a country, we pointed out the necessity of considering the cultural aspects for mathematics teachers’ pre-service and in-service teacher training.textapplication/pdfdepartmental bulletin pape

昭和40年代の埼玉県における算数・数学科教員コミュニティの形成 : 長期研修教員制度と研究協議会用テキスト編纂を中心として<教育科学>

This paper is about the formation process of Mathematics Teachers’ Community in Saitama, when they had new mathematics movement in 1970’s. Because of so called “Sputnik crisis” in 1957, the modernization of mathematics education became one of the important issues in Japanese society. New mathematics concepts, such as set theory, function, probability, and so on, were strongly focused on by mathematics teachers. However, since such concepts were new to most of the teachers, Prefectural Board of Education had had hard time to train them to be familiar with such new mathematics topics. One of the strategies they used was “On the Job Training” for school teachers. Some capable math teachers were selected to have one-year sabbatical leave for university, and they have become regional leaders for teacher training or seminar. The major method they used was “Lesson Study”, and many teachers even tried to teach in other schools from where they were working. One of the best ways to do was having lessons on Saturday. Schools had regular classes in the morning, and additional lessons for Lesson Study were scheduled in the afternoon. Lesson Study had become widely implemented in all of schools in Saitama, and teachers’ community for Lesson Study implementation had been formed. In order to make Lesson Study in proper, they also tried to make teachers’ manuals about new math contents. Some capable teachers, who were selected for one year sabbatical leave and had training at university, tried to edit teachers’ manuals to show how to teach new mathematics concepts. Such manuals have been published every year for both elementary and lower secondary teachers. Teachers’ manuals have played important role to make school teachers to be familiar with new mathematics topics, and make them able to teach in proper. Mathematics teachers’ community played as not only editors of teachers’ manuals but also instructors at Lesson Study. They even had recruited capable younger teachers to be editorial members for teachers’ manuals, as well as to be recommended as future regional leader for having one year sabbatical leave and had training at university.textapplication/pdfdepartmental bulletin pape

『学習のふり返り』による「学習活動と評価の一体化」に関する研究

KAKEN: 17500593本研究では、算数・数学教育における「評価」を捉え直すための枠組みについて検討した上で、学習評価についての新たな視点について考察を進めた。日本語の「評価」に対応する2つの英語「Assessment」と「Evaluation」のもつ意味の違いに注目し、それらの概念の特質・特徴についてそれぞれ検討した後、Assessment的な評価の必要性、有用性に言及した。そして、両方の評価を併せ持つ事例として、アメリカにおけるレポート形式の評価の事例を健闘した。またAssessmentにおける自己評価の記述に関して、その「評価」としての側面と「学習活動」としての側面に注目した。 一方、先行研究の成果としての「メタ評価」を概観した後、学習評価そのものについての「目標論」「内容論」「方法論」「評価論」について検討を行った。「何のために評価するのか」、「何を評価するのか」、「誰が、いつ、どのように評価するのか」、「どのように評価がなされたのか」についてそれぞれ検討を行い、それらが教育評価を行う際の指標であると同時に、評価についての評価(メタ評価)を行う際の規準としても機能することを明らかにした。 更に、学習のふり返りと学習のまとめが相互構成的に構築されていく点に言及した上で、「学習活動と評価の一体化」という概念を提起した。更に、メタ的に再評価された評価(=学習活動)が学習者に客観的に捉えられた学習の成果である点を踏まえ、本当の意味での学習の成果とは、『知識・技能を獲得した自分(たち)を認識していること』であるとの新たな捉え方を提案した。二宮裕之(2005)「数学学習におけるノート記述とメタ認知一記号論的連鎖とメタ表記の観点からの考察-」『全国数学教育学会誌数学教育学研究』第11巻　pp.67-75　　　 二宮裕之(2005)「学習のふり返りとまとめに関する一考察一評価に対する「メタ評価」並びに「学習活動と評価の一体化」の視点から-」全国数学教育学会第22回研究発表会　 二宮裕之(2005)「学習のふり返りと学習のまとめ一学習者の立場からの「学習活動と評価の一体化」『新しい算数研究』2005年7月号,東洋館出版社,PP.36-38　　　問い合わせ中のため削除 Ninomiya(2005) "Note-Taking and Metacognition in Learning Mathematics: An Analysis in Terms of Semiotic Chaining and Meta-Representation'l', The Third East Asia Regional Conference on Mathematics Education,　Topic Study Group 6: Assessment　 二宮裕之(2005)「算数・数学学習の評価に関する新たな視点」『日本数学教育学会誌』第87巻第8号,pp.13-20　　　 二宮裕之(2005)「レポート形式による評価の可能性について-アメリカの事例から-」日本教科教育学会第31回全国大会　　 二宮裕之(2005)「算数・数学教育における「メタ評価」に関する基礎的考察」『日本数学教育学会第38回数学教育論文発表会論文集』pp.19-24　　　 二宮裕之(2006)「数学的記述表現活動とメタ認知・メタ評価」『日本科学教育学会科教研報』Not.21　No.1,pp.7-12　　　公開不可のため削除 二宮裕之(2006)「算数・数学学習における評価とその成果に関する一考察-レポート形式の　評価の事例を手がかりに-」『日本数学教育学会誌』第88巻第10号,pp.12-21　　 二宮裕之(2006)「算数・数学教育における「メタ評価」に関する研究(I)一評価についての評価論-」『日本数学教育学会第39回数学教育論文発表会論文集』pp.84-89　　　 二宮裕之(2007)「評価研究の新たな展望-評価についての評価(メタ評価)試案-」『日本科学教育学会誌科学教育研究』vol.31No.I,pp.58-59　　　 二宮裕之(2007)「数学教育におけるメタ評価に関する研究-メタ評価に関わる理論的検討-」全国数学教育学会第25回研究発表会　　学会問い合わせ中 Ninomiya(2007) "How do Japanese Teachers Evaluate Their Students in Their Lessons? " I, Isoda, Stephens et.al.(Ed.), Japanese lesson Study in Mathematics, World Scientific Publishing Co. Pte. Ltd., pp.68-71　　　 メタ評価を生かした算数指導の実際(明治図書『楽しい算数の授業』　平成18年4月-平成19年3月号　連載　　公開不可のため削除textapplication/pdfresearch repor

ライブコマースにおける時間制約下の衝動購買に関する研究 : クチコミと消費者知識による効果の検討

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数学教育におけるアクティブ・ラーニング : 数学教育の不易を踏まえて<教育科学>

In order to meet alternative skills and capabilities for new-coming society, whose keywords are computerization/informatization and internationalization, “Active Learning” is recently focused on strongly in Japanese education in general. We need to pay attention to have proper discussion for new technology era, but also we should pay more attention to our tremendous results and outcomes through what we have done in our history of Japanese mathematics education. Many teachers have been done marvelous mathematics classes, in which there are a lot of immutable and important factors. In this paper, proper and desirable mathematics education in near future is discussed by the keyword of “Active Learning”, with our LEGACY in Japanese mathematics education. First of all, general view for new era, such as “The Third Wave” by A. Toffler, is examined. Several documents, which are discussed from such point of view, from Japanese Ministry of Education are also examined, and “Process Skills”, which is one of the Key concepts, is discussed. Considering such new trends, however, traditional Japanese “Problem Solving type lesson” is also examined as immutable factor in Japanese mathematics education. Finally, implications are pointed out from our daily practices.textapplication/pdfdepartmental bulletin pape