國中數學之三心幾何圖形的探討

The Study of Mathematics in the topic of Excenter, Incenter, and Barycenter of Geometry in Junior High School

鄧志浩(Chih-Hao Teng)

指導教授 ： 王牧民

中原大學/理學院/應用數學研究所/碩士(2013年)

https://doi.org/10.6840/cycu201300283

摘要

本研究目的在探討數學教學相關的理論，應用其原理，針對九年一貫課程中「幾何」主題中的「三角形的外心、內心、重心」單元進行教學設計，幫助國中學生三心幾何相關概念的學習，並探討幾何學習相關文獻，了解學生有哪些不容易掌握的概念，進而建構新的教材。

國中教材自從開放各家版本而不再統一編制之後，各種版本的教科書在坊間林立，令人目不暇給，讓學生、家長、甚至是老師們都手足無措，有鑑於此，本研究參考市面上數款的教材作分析、整合，將之整合成一個新的教材。

由皮亞傑提出的學習建構理論以來，教育學者認為一位學生的學習，是由最基本的觀念開始，由淺而深；所以編寫這份教材時，是以淺至深，循序漸進的方式讓學生對於三角形三心幾何的概念能夠有深入淺出的了解。

本文由收集文獻、分析各版本的教材，編輯成為新的教材，提供現場教師參考，依序分為四個章節：
一、緒論
二、文獻回顧
三、整合教材
四、反思與結論

各種教學模式或是版本都有其優劣，教師應該依照學生程度及學生的學習目標來做適性的選擇；進行幾何主題教學的時候，最重要的即是利用簡單的圖示開始，循序漸進地加以變化，並用更多元的方式作呈現，以至於達成學生最佳的學習效果。

關鍵字

國中 ； 幾何

並列摘要

This research focus on the discussing for theories about mathematic teaching, principles, and its application. Our teaching plan base on part of the Grade 1-9 Curriculum Guidelines, which in the topic of Geography, named ‘The excenter, incenter, and the barycenter of triangles ’. For helping high school students learning the geography of triangles, and reading the researches about geography-learning, then knowing which parts are the difficulties for students to learn, we can plan for a better contents

Since the high school teaching materials are so different from many publishers, many of editions and many of different versions there, so students and parents, even teacher are not knowing which one is better. In case of this, here decide to search all kinds of different teaching materials, and analyzing, conforming them into one brand new teaching material.

Base on the Constructivism Learning Theory from Piaget, Educators thought, a student must learning from the basic, and step by step upon; That makes us working on this teaching material with the same path, knowing about ‘The excenter, incenter, and the barycenter of triangles ’ in sequence.

This research from collecting studies, analyzing different teaching materials, and then conforming them into one brand new teaching material for current teachers. Here is four chapters ordering by below:

1. Introduction
2. Literatures and Review
3. Conformed teaching material
4. Reflection and Conclusion

Each teaching techniques have their pros and cons, teachers should choose the best by different students, by their different learning levels and different learning topics; As we teaching on topic of Geography, the most important thing is showing simple images and graphics, and approve them with forward process, with multi ways we can get the best effects from students.

並列關鍵字

Geometry ； Junior high school

參考文獻

張世忠(2009)。中小學數理教學理論與實務。台北市：五南

吳旭紳(2010)。問題導向之中學生數學教材教法研究。中原大學應用數學系研究所碩士論文

教育部(2009)。國民中小學九年一貫課程綱要-數學學習領域

黃政傑(2012)。中小學自編教材面面觀-政策與實務的對話。教科書研究，3卷1期，133-155

呂益昇(2006)。國三學生三角形外心與內心概念學習之困難因素及類比教學實驗的探討。國立台灣師範大學碩士論文。