臺灣博碩士論文加值系統

本論文旨在強調應用數學教具輔助數學教學之重要性；同時提出兩個數學教具之創新應用，包括：「幾何九九乘法表」與「魔力吸管變變變，立體平面超連結」。本研究提出「幾何九九乘法表」之製作過程與教學功能，以供數學教師於課堂中使用。「幾何九九乘法表」不僅能將抽象的數學概念具體化，更能激勵學童具體的數學思維。本論文藉由「幾何九九乘法表」，除了呈現代數與幾何之關聯性更說明代數與立方體的關係。
除此之外，一般的觀念總認為數學教具之取得需要大筆經費挹注，為了打破此一迷思，本研究所提「魔力吸管變變變，立體平面超連結」係採用日常生活中隨處可得的吸管與迴紋針，設計一個低成本且具備多功能的數學教具，幫助學童明瞭數學觀念以及數學觀念的連結性，尤其是提升學童們三維立體與二維平面互相轉換的空間幾何能力。本研究極力推廣經濟實惠的「魔力吸管變變變，立體平面超連結」，希望能幫助教師們廣為應用於數學教學中。
透過學童們親手做教具的方式，自然輕鬆地玩數學，更是培養學童專注力與提升學習興趣的最佳利器。學童們數學能力之培育並非一蹴可幾，著實需要數學老師費盡心力教導之，若能善用教具教學，不但能提升學習興趣，對於數學能力之培養，更能達事半功倍之成效。

The purpose of this paper is to stress the importance of the applications of the mathematics manipulatives to mathematics teaching. As the main innovation, we show “the geometric 99 multiplication table” and “the magic straw hyperlink between solid and plane”. First, we offer the operation of the geometric 99 multiplication table to mathematics teachers. The geometric 99 multiplication table can not only embody the conceptual abstractions but also promote the students’ concrete mathematics thinking. In addition, by utilizing the geometric 99 multiplication table, we can not only show the relationship between algebra with geometry but also indicate the linkage between algebra and cube.
While the general concept indicates that the mathematics manipulatives are expensive, the cheap mathematics manipulatives named the magic straw hyperlink between solid and plane can be offered by utilizing the cheap straw. The magic straw can help the students to learn not only the mathematics concepts but also the linkage between solid and plane.
In sum, learning by doing is a good mathematics teaching. The applications of the mathematics manipulatives cannot only increase the students’ learning interest but also upgrade the students’ mathematics ability.

第壹章 緒論 1
第一節 研究動機 1
第二節 研究目的與待答問題 3
第三節 名詞釋義 4

第貳章 文獻探討 5
第一節 表徵之相關理論 5
第二節 實體教具之相關理論 13

第參章 研究方法 19
第一節 研究方法 19
第二節 研究流程 19
第三節 研究工具 21

第肆章 分析與討論 23
第一節 古氏數棒 23
第二節 幾何九九乘法表 33
第三節 立方體立體與平面相關教具 41
第四節 魔力吸管變變變，平面立體超連結 49

第伍章 結論與建議 55
第一節 結論 55
第二節 建議 57

參考文獻 59

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