Why the details matter: Learning from Japanese Kyouzai kenkyuu

Have you ever heard someone say, “It’s exactly the same question, just with different numbers”? Sometimes a teacher might say this about a practice test or a set of exercises in a textbook. The implication is that the details of the numbers make no substantive difference to the problem. In mathematics task design, careful thought is not always given to the particular numbers used in questions; in some circumstances, these might even be randomly computer-generated. However, in Japanese mathematics teaching, the numbers used in questions (and the details in general) are taken extremely seriously. In this article, we will explain why the details of tasks matter so much. We will show across four mathematics topics with different ages of students how the detailed choices of examples can be critical for students to learn what is intended

Analysis of the final comments provided by a knowledgeable other in lesson study

Lesson study has been implemented in schools around the world as a method of professional development for teachers. Lesson study consists of five steps, among which the “Research Lesson” and “Post-lesson Discussion” are central. During the Post-lesson Discussion, after the teacher has commented on the lesson, all of the observers discuss the lesson, and the “knowledgeable other” (koshi), a specially invited expert, provides final comments. The quality of these final comments is critical to the learning of the lesson-study participants, and, consequently, the koshi plays an extremely important role. However, few studies have examined the nature and structure of the final comments that koshis provide. This study analyzed the final comments made in three elementary-school research lessons in Japan by a highly distinguished university mathematics educator with considerable teaching experience and an outstanding reputation as a koshi. We found that his final comments clustered into seven categories, which we named: (1) considering the didactical value of mathematical content; (2) use of representations; (3) fostering positive attitudes to learning; (4) incorporating students’ ideas into whole-class discussions; (5) giving attention to what students write down; (6) giving attention to the content of the board-work; and (7) teacher growth through reflection. These categories provide insight into the nature of final comments that are regarded as being particularly useful and may form the basis for less-experienced koshis to structure their final comments in lesson study.</div

Intramolecular Hydrogen Atom Transfer Hydroarylation of Alkenes toward δ-Lactams Using Cobalt-Photoredox Dual Catalysis

Intramolecular hydroarylation of alkenes through hydrogen atom transfer (HAT) represents a robust method to prepare benzo-fused heterocycles. However, the reported methods have limitations in a variety of accessible cyclic scaffolds. Here we report a dual cobalt- and photoredox-catalyzed HAT hydroarylation of alkenes that is characterized by higher efficiency in the synthesis of a δ-lactam compared to established protocols. The proposed mechanism is supported by experiments and DFT calculations

Silane- and peroxide-free hydrogen atom transfer hydrogenation using ascorbic acid and cobalt-photoredox dual catalysis

Hydrogen atom transfer (HAT) hydrogenation has recently emerged as an indispensable method for the chemoselective reduction of unactivated alkenes. However, the hitherto reported systems basically require stoichiometric amounts of silanes and peroxides, which prevents wider applications, especially with respect to sustainability and safety concerns. Herein, we report a silane- and peroxide-free HAT hydrogenation using a combined cobalt/photoredox catalysis and ascorbic acid (vitamin C) as a sole stoichiometric reactant. A cobalt salophen complex is identified as the optimal cocatalyst for this environmentally benign HAT hydrogenation in aqueous media, which exhibits high functional-group tolerance. In addition to its applicability in the late-stage hydrogenation of amino-acid derivatives and drug molecules, this method offers unique advantage in direct transformation of unprotected sugar derivatives and allows the HAT hydrogenation of unprotected C-glycoside in higher yield compared to previously reported HAT hydrogenation protocols. The proposed mechanism is supported by experimental and theoretical studies

ニチジョウ バメン ニオケル カクリツ ノ イミ ニツイテノ セイト ノ ニンシキ ニ カンスル イチコウサツ

1. 研究の目的・方法/2. 調査の実施/2.1 対象と実施時期/2.2 調査方法/2.3 調査問題/2.4 調査の結果/3. 調査結果の分析/3.1 問題1(2)「サイコロの問題」/3.2 問題2「誕生日の問題」/3.3 問題3(1)「降水確率の問題」/3.4 問題4「3囚人問題」/4. まとめと今後の課