A Study on the Teaching of Parabolas in High School Mathematics

本研究は，高等学校の数学Ⅱにおける,放物線の定義と図形的な性質に関する学習指導の可能性を検討することを目的としている。そこで本稿では,数学Ⅱにおいて扱うことができる放物線に関するいくつかの問題について考察し,放物線の図形的な定義の理解に結びつけることのできる教材を利用した授業実践に関して報告する。授業においては，数学的活動を基盤とした展開の中にグループによる情報共有の場面を適切に位置づけ，協働的に課題を解決することによって，放物線の図形的な性質について理解を深めることができた。また，そこから派生する新たな問題に取り組むことによって，放物線に対する多様な見方を促すことができた。その一方で, 図形の性質を方程式を用いて探究する際の座標の設定など，いくつかの困難性も明らかとなった。This study aims to examine the possibility of the teaching definition and geometric property of the parabola in mathematics II. In this report, I recommend teaching materials for the parabola and describe the practice of mathematical lessons using such resources. I was able to further students’ understanding about the geometric property of the parabola via numerous mathematical activities. Furthermore, I promoted a variety of viewpoints regarding the parabola by working on a new problem derived from the solution to original problem. However, some difficulties were encountered, including the setting of coordinates when students searched the property of the figure using an equation

Teaching of Envelope in Junior High School Mathematics

学習指導要領の改訂にともない, 次期の教育課程では内容の整理・統合や精選の観点から, 科目の間や学年の間での内容の移行なども多くの箇所で見られるが, 特に注目すべき点は平面幾何の内容を, これまで中学校で扱っていたものも含めるかたちで, 多くの高校生が学習することになるという点である。そこで, 中学校から高等学校にかけての図形指導の体系を改めて整理する必要がある。高等学校での抽象化された内容を扱う前段階の中学校の図形領域での学習では, 生徒の具体的な活動にもとづいた思考を重視する必要がある。そこで本稿では, そのような意識のもとで中学校数学を見つめ直した中での, 1つの授業実践を報告する

Near-Optimal Control of Non-Linear Dynamic Plants with a Quadratic Performance Index

In this paper, a near-optimal control strategy is studied for high-order multi-variable non-linear dynamic plants under a quadratic performance index. The principal line of attack is to introduce the concept of instantaneous linearization and to apply the dynamic optimization technique originated by R. Bellman. The resulting configuration of the near-optimal control system presented here becomes a feedback one containing an on-line digital computer as a main control device. The general procedure proposed here is illustrated by the example of establishing the near-optimal control strategy for a dynamic plant with a non-linear characteristic. The control performance of the system is also discussed by comparing it with that of the system with the precisely optimal control strategy

A Study on Teaching Geometric Construction based on the Expectation of the Student Using a Computer

本稿では，作図に関する授業実践の分析を通して，高等学校数学の図形領域における学習指導の在り方について検討を行う。高等学校1年生の数学A（図形分野）の領域において，2本の線分の積が最小となる場合を考える作図の問題を扱い，コンピュータの利用による生徒の予想を足がかりとして展開する授業を実践した。この授業において，生徒は問題解決の過程を振り返ることによって証明の不備を補完し，条件を変えて課題をさらに発展させる活動を通して，図形に対する見方を深めることができたと考えられる。日々の授業を通して深い学びを実現するためには，問題解決の後に課題を主体的に発展させていくことが習慣化されるような，数学の学習に対する態度の変容を促すことが重要である。The purpose of this study is to examine the figure instruction of high school mathematics by analyzing the lesson with regard to geometric construction. I practiced a class based on expectation of the student using a computer, and the problem of drawing figures when the product of the length for two drawn lines was minimized was included by the class. The student supplements a defect of the proof by looking back on the process of the solution to the problem, and, through an activity to change the condition of the original problem and to develop the problem further, they were able to deepen the viewpoint for the figure. It is important that we promote transformation of the attitude of the student toward learning mathematics through developing the problem voluntarily

Distinct regulatory mechanism of yeast GPX2 encoding phospholipid hydroperoxide glutathione peroxidase by oxidative stress and a calcineurin/Crz1-mediated Ca2+ signaling pathway

AbstractThe GPX2 gene encodes a homologue of mammalian phospholipid hydroperoxide glutathione peroxidase in Saccharomyces cerevisiae. Previously, we have reported that the oxidative stress-induced expression of GPX2 is strictly regulated by Yap1 and Skn7 transcription factors. Here, we found that the expression of GPX2 is induced by CaCl2 in a calcineurin (CN)/Crz1-dependent manner, and the CN-dependent response element was specified in the GPX2 promoter. Neither Yap1 nor Skn7 was required for Ca2+-dependent induction of GPX2, therefore, distinct regulation for the oxidative stress response and Ca2+ signal response for GPX2 exists in yeast cells

Phenotyping of P105-Negative B Cell Subsets in Patients with Systemic Lupus Erythematosus

This study aimed to investigate phenotype of RP105(−) B cell subsets in patients with systemic lupus erythematosus (SLE). Flow cytometry was used for phenotyping RP105-negaive B cell subsets. Based on CD19, RP105, and CD138 expression, RP105(−) B cells consist of at least 5 subsets of late B cells, including CD19(+)RP105(int), CD19(+) RP105(−), CD19(low) RP105(−) CD138(−), CD19(low) RP105(−)CD138(int), and CD19(low) RP105(−) CD138(++) B cells. Especially, CD19(+)RP105(int) and CD19(low) RP105(−)CD138(int) B cells are significantly larger than other RP105(−) B cell subsets in SLE. By comparison of RP105(−) B cell subsets between patients with SLE and normal subjects, these subsets were detectable even in normal subjects, but the percentages of RP105(−) B cell subsets were significantly larger in SLE. The phenotypic analysis of RP105(−) B cell subsets suggests dysregulation of later B cell subsets in SLE and may provide new insights into understanding regulation of B cells in human SLE

Controlling Electronic States of Few-walled Carbon Nanotube Yarn via Joule-annealing and p-type Doping Towards Large Thermoelectric Power Factor

Flexible, light-weight and robust thermoelectric (TE) materials have attracted much attention to convert waste heat from low-grade heat sources, such as human body, to electricity. Carbon nanotube (CNT) yarn is one of the potential TE materials owing to its narrow band-gap energy, high charge carrier mobility, and excellent mechanical property, which is conducive for flexible and wearable devices. Herein, we propose a way to improve the power factor of CNT yarns fabricated from few-walled carbon nanotubes (FWCNTs) by two-step method; Joule-annealing in the vacuum followed by doping with p-type dopants, 2,3,5,6-tetrafluo-7,7,8,8-tetracyanoquinodimethane (F4TCNQ). Numerical calculations and experimental results explain that Joule-annealing and doping modulate the electronic states (Fermi energy level) of FWCNTs, resulting in extremely large thermoelectric power factor of 2250 mu Wm(-1) K-2 at a measurement temperature of 423K. Joule-annealing removes amorphous carbon on the surface of the CNT yarn, which facilitates doping in the subsequent step, and leads to higher Seebeck coefficient due to the transformation from (semi) metallic to semiconductor behavior. Doping also significantly increases the electrical conductivity due to the effective charge transfers between CNT yarn and F4TCNQ upon the removal of amorphous carbon after Joule-annealing