國中數學中 國中數學中全等三角形證明題教材編撰之研究

A Study of the Material Design for Teaching Congruent Triangles Proof Questions in Junior High School

李正斐(Jene-Fei Lee)

指導教授 ： 王牧民

中原大學/理學院/應用數學研究所/碩士(2017年)

https://doi.org/10.6840/cycu201700159

摘要

本研究目的是為了提升目前國中生數學中全等三角形證明題證題的能力，以及研究者的在全等三角形證明題教材的在職進修。故以國中數學領域課綱範圍為基礎，編寫國中數學中三角形的全等證明題教材，期能讓教師能藉由本教材提升數學教學的水準，並讓學生能體會到數學問題的本質，並提升敏銳的洞察力、邏輯思考推理、強化獨立研究思考的習慣，達到探索解題的層次。
架構完整的數學知識能幫助學生連結、聯想解題模式。透過本研究的結論，提出以下幾點建議供教師在教導學生學習幾何問題時參考：
培養學生解讀題目能力，並澄清迷思概念。
1. 「設計有系統的教材進行類比遷移」、「局部推理與模仿」等教學策略能有效的協助學生解決學習困難。
2. 觀察圖形變換，實證所學之幾何概念。
3. 充實教材內容，加廣教材深度。

關鍵字

全等三角形

並列摘要

The objective of this study is to improve the ability of proof at Congruent Triangles. The study developed teaching materials of Congruent Triangles for students based on the Mathematics Curriculum Guide in Taiwan. This material may help teachers improve the quality of their mathematical education, and it may also assist students to learn the base of Math problems. Moreover, this paper could provide the students more diverse methods to solve math problems, and could cultivate these students' sensitive observation, logical reasoning and independent thinking. This study wants to increase the students' interests in learning, and to strengthen their knowledge.
Based on those conclusions stated above, has raised the following recommendations as the reference for educational administrative authorities: .
1) It is important to teachers to have professional competence about image thinking, problem-solving diversity and implementation.
2) Observed the graph transformation to verify the geometric conceptions.
3) There is a need of enriching the teaching materials and increasing the remaining Congruent Triangles of geometry textbooks.

並列關鍵字

Congruent Triangles

參考文獻

中文部分

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2. 張家麟 黃毅英 林智中(2009)。學校幾何課程的重整-為何教和如何教演繹幾何? 數學傳播 34卷3期, pp. 13-33

3. 梁子傑(2005)。幾何原本導讀。台北市：九章。

4. 藍紀正、朱恩寬 譯(2002)。台北市：九章。