A Study on Teaching Material about a Lever Crank Mechanism in Junior High School Mathematics

現行の中学校学習指導要領では，数学科に課題学習が位置付けられている。課題学習では，各領域の内容を総合したり日常の事象や他教科等での学習に関連付けたりするなどして見いだした課題を解決する学習の実施が求められている。このような学習の題材として「機構」に着目した。機構とは機械の動きを作る仕組みのことである。本稿では機構の一種である「てこクランク機構」の動きを考察した中学校数学の授業実践の事例について報告する。In task-oriented learning in junior high school mathematics, mathematical problems relating to everyday phenomena and other subjects are required. In this study, a lesson about a lever crank mechanism was developed and analyzed. The analysis results suggest that the lesson using this mechanism was effective in achieving task-oriented learning in junior high school mathematics

Study of teacher off-the-job-training at an attached junior high school: the development of mathematics teachers

広島県内の中学校数学教師の実践力向上を目指し，授業を中心に据えた現職教員研修システムの構築を目的として，広島県中学校数学教育実践研修会を開催している。今年度は，６月と12月に実施した実践研修会に向け， チーム会を６回実施した。本研究では， 中学校数学教師が実践力を向上させていく場面を特定するために，実践研修会やチーム会のエピソード分析を行った。その結果，「珍しい公開授業は参会者に刺激を与えられること」，「公開授業で参会者は授業者の“術”も見ていること」，「良い教材について議論する協議会は有益であること」の３点を明らかにすることができた。このような若手教員の実践力向上を目指した研修会はあまり行われておらず，貴重である。今後は，さらに効果的な研修システムを創造し，実現することにより本会の内容を充実させ， 広島県の学校教育に還元していきたい。The focus of this study was on the development of mathematics teachers via teacher off-the-job-training at an attached junior high school. In this paper, we analyzed the comments of mathematics teachers participating in teacher off-the-job-training．The followings outcomes were identified: a) Demonstration classes were conducted in a unique way, where participants observed two classes in which the the same unit was taught but in different ways. This was beneficial to participants. b) Participants in the demonstration class were able to carefully observe the behavior of the instructor. c) This method enabled participants to fully discuss the strengths of the teaching materials

Improving Mathematics Lesson and Evaluation through Setting Inquiry Problem-Solving Activities

The purpose of this research is to make a theoretical framework for improving mathematics lesson and evaluation through setting inquiry problem-solving activities effectively in junior high and senior high mathematics lessons. To achieve this, we first carried out a questionnaire survey to capture how students perceive learning mathematics and, based on the results, made a framework incorporated these activities for lesson design and evaluation of student’s learning. Then, sample lesson conducted in a junior and senior high school based on the framework was analyzed to investigate its effectiveness and get some practical suggestions

A Study on Effective Support of Pre-Service Teachers in Practice Teaching : Focused on Students’ Mathematical Activity in Mathematics Lesson

本研究は，教育実習生の現状を調査し分析することを通して，教育実習における効果的な指導のための知見を得ることを目的としている。教育実習生に対して数学的活動の認識に関するアンケート調査を行い，提出された学習指導案とともに分析することによって，教育実習生が授業を構成する際の困難性について，特に数学的活動の位置付けに焦点を当てて考察を行った。数学学習における数学的活動の意義や現代の社会において求められる教員養成の役割に照らしてみるとき，教育実習においては次のような指導が効果的であることが示唆された。 　①授業の中で位置づけることが可能な数学的活動のタイプを特定させること 　②数学的活動との関わりで学習者の反応を捉えさせること 　③授業の中の情報共有の場面に意味を持たせること 　④教育実習生同士での議論を活性化させることThis study aims to provide suggestions about effective support in practice teaching by analyzing a survey of pre-service teachers. We discussed their difficulties in planning a mathematics lesson from the perspective of the construction of mathematical activities. We surveyed their conception of mathematical activities and analyzed their lesson plans. The results imply effective support is required in practice teaching as below: 1) Specifying possible mathematical activities in mathematics lessons 2) Understanding students’ reactions by referring them to mathematical activities 3) Making some situations of information-sharing meaningful in mathematics lessons 4) Activating the arguments among pre-service teacher

A Study on Effective Support of Pre-service Teachers in Practice Teaching(2): Through the Analysis of Small-group Learning in Pre-service Teachers’ Mathematics Lessons

本研究の目的は，教育実習生の認識に関する調査や実践される授業の分析を通して，効果的な実習指導に向けた示唆を得ることである。アンケートによる調査や学習指導案の分析によって，教育実習生が授業の中に小集団学習を取り入れる際の困難性が示された。また，小集団学習に関する利点やそれを実施する際の留意点に関して，教育実習生が多くの視点を持ち合わせている一方で，高等学校における小集団学習を取り入れた授業の経験が少ないことも明らかとなった。これらのことから，実習指導においては次のような点に重点を置いた支援が重要であると考えられる； 1) 小集団学習を位置づける目的を明確にし，個人の思考の場面も適切に確保すること 2) 小集団学習での目標を生徒に明確に示すこと 3) 小集団学習と個人あるいはクラス全体での学習との関連性を把握すること 4) 小集団学習と学習評価との関わりに注意を払うことThis study aims to highlight the implications of effective support in practice teaching by analyzing a survey administered to pre-service teachers. Through the analysis of teaching plans and questionnaire surveys, we identify the difficulties that occur when trainee teachers set up small-group learning in their lessons. From the questionnaires, we found that trainee teachers have many opinions about the advantages or disadvantages of such lessons, although they had little experience of small-group learning from their time at high school. The results of the analysis suggest that the following points are important when we instruct trainee teachers: 1) Clarify both the purpose of small-group learning and how to conduct individual learning; 2) Show students the aim of small-group learning; 3) Ensure trainee teachers review small-group learning for relating it to whole or individual learning; and 4) Ensure trainee teachers pay attention to the relationship between small-group learning and learning evaluations

Improving Mathematics Lesson and Evaluation through Setting Inquiry Problem-Solving Activities

The purpose of this research is to make a theoretical framework for improving mathematics lesson and evaluation through setting inquiry problem-solving activities effectively in junior high and senior high mathematics lessons. To achieve this, we first carried out a questionnaire survey to capture how students perceive learning mathematics and, based on the results, made a framework incorporated these activities for lesson design and evaluation of student’s learning. Then, sample lesson conducted in a junior and senior high school based on the framework was analyzed to investigate its effectiveness and get some practical suggestions

Invariant Differential Operators on the Schrödinger Model for the Minimal Representation of the Conformal Group

We consider the Schrödinger model of the minimal representation for the conformal group O(2n, 2)(n > 1) which was constructed by Kobayashi-Ørsted [Adv. Math. 2003], and enriched by a series of papers by Kobayashi-Mano [Memoirs of AMS 2011, etc]. We get the joint spectra of the differential operators on the model for generators of the center of the Lie algebra of U(k) × U(n-k) × U(1) for k = 1, ..., n-1. Further, we obtain the generators of the algebra consisting of all invariant differential operators for two compact subgroups I1 × SO(2n-1) × SO(2) and SO(2n) × SO(2) of O(2n, 2)