先般の「お茶の間宇宙教室の提唱」、「街角宇宙教室の提唱」、「街角星空教室の提唱」に続き、「街外れ星座教室の提唱」を報告する。近頃、星を見なくなった。何故だろうか。多忙なのだろうか。星が見えないのだ。郊外や海外や高山で星を見て感動した投書など見ると今の都会では如何に星が見えないかがよく解かる。では、相模原市ではどうなのだろうか。アンケート調査を実施した。視界の広がる相模川の堤防、農道、街灯を避ける高い塔などでささやかな星ウォッチングが行なわれていた。夏の日のタ刻、南の空にさそり座の雄姿を眺めた時の感動は終生忘れられない。今でも心が安らぐ。精神的な豊かさを得るには星座観測が一番だが星空学習は危機的状況にある。大気汚染とネオン光害で都会の低い空には星が無い。夜は誘惑が多く事故や事件で危険が一杯だ。先人は百年計画で明治神宮の森を作り上げ世界に先駆けて京都議定書を作成した。遠い将来を見据えて緑化と省エネに励みつつ田園で星々を学習することを提案する。

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This research aims at clarifying the transitional process from elementary mathematics to secondary one, especially arithmetic to algebra, and from the viewpoint of Early Algebra, we focus on algebraic reasoning at elementary grades. However, it does not yet become clear enough. The purposes of this paper, therefore, are to clarify algebraic reasoning through the semiotic analysis of classes of the multiplication and division with fractions, obtain the implications to promote algebraic reasoning, and obtain the implications for the classes. The results are followings. (1) Algebraic reasoning was identified by the semiotic analysis of the classes from the viewpoint of generalization and justification. The characteristic of the reasoning depends on deductive reasoning grounded on a property of numbers and operations or a pictorial expression. (2) From the viewpoint of justification, we regard deduction using a model and a specific case as deductive reasoning, in the case of deduction using a model, it is important that the model is made a tool, in the case of deduction using a specific case, it is important to examine whether become the generic example or the representative special case, and to draw various deductive explanations. (3) About the implications for the classes, at the time of classes of the multiplication at the second grade and the unifying partitive division with quotative division at the third grade, it is important to make students understand that the relation of multiplication to division is reverse operations from concrete operations. At the time of classes of the division with fractions, it is natural to understand the method of calculation from a property of operations.

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