A Study on “REIZUKURI” in Mathematics Learning:A Potential Variety of Integration in REIZUKURI Strategy

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  • 数学学習における「例づくり」に関する研究―例づくりの統合化可能な多様性―
  • スウガク ガクシュウ ニ オケル 「 レイズクリ 」 ニ カンスル ケンキュウ : レイズクリ ノ トウゴウカ カノウ ナ タヨウセイ

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<p>　　 The aim of this paper is to suggest a new aspect in REIZUKURI strategy.  The strategy with “Make up an example of” tasks induces students to do mathematics.  Their examples are about mathematical concepts and principles.  A teacher asks multiple examples to them repeating the term of “Another?”.  In this paper, observing examples and processes to make up an example, it is suggested that the strategy has a potential variety of integration.  There are three types of integration of a high order, intensive integration and extensive integration (Katagiri, 2004).  Each type can be assumed at the task of “Make up an example of two real numbers whose sum and product are equal”.  Processes to make up an example are adopted a conjecture with trial and error, equations, the quadratic formula, a fractional function, and so on.  If these form a group, it conforms to integration of a high order.  The relationship between simultaneous equations in two unknowns and a quadratic equation conforms to intensive integration in particular.  As year follows year, examples of two real numbers whose sum and product change from whole numbers to fractional numbers and irrational numbers.  Therefore, it conforms to extensive integration.  In addition, it is expected to facilitate the connection about contents of learning among schools.</p>

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