國中資優數學中一元二次方程式教材編撰之研究

A Study of the Material Design for Teaching Quadratic Equation with One Variable to Mathematically Gifted Students in Junior High School

呂筱萍(Hsiao-Ping Lu)

指導教授 ： 王牧民

中原大學/理學院/應用數學研究所/碩士(2016年)

https://doi.org/10.6840/cycu201600177

摘要

本研究是為了解決國中數學資優生的特殊學習需求，以及研究者的在資優教材的在職進修。故以國中數學領域課綱範圍為基礎，編寫國中資優數學之一元二次方程式的教材，讓教師能藉由教材提升數學資優教學的水準，並讓數學資優生能體會到數學問題的本質，並提供給學生多樣化的解題方法，培養資優生敏銳的洞察力、優質的邏輯思考推理、強化獨立研究思考的習慣，提昇探索解題的層次，並加強補充腦中知識。研究結果如下：
一、 國中資優數學之一元二次方程式的教材，能提供學生不同的解題策略且在驗證答案的過程中，培養學生多元思考、獨立思考、創新發現的特質。
二、 研究者所編製的國中資優數學之一元二次方程式教材，最後研發出的解題技法，能符合研究目的。
三、 足夠的數學知識能幫助資優生連結、聯想解題模式。
四、 熟練的運算能力，也是協助資優生在複雜的運算中，找出清晰的計算脈絡，以達成解題的完整。

關鍵字

一元二次方程式 ； 數學資優生

並列摘要

The objective of this study is to provide a better solution for mathematically gifted middle school students' special need. This study also wants to contribute to the professional training in the gifted education. The study developed teaching materials of quadratic equation with one variable for gifted middle school students based on the Mathematics Curriculum Guide in Taiwan. This material may help teachers improve the quality of their mathematically gifted education, and it may also assist mathematically gifted students to learn the base of Math problems. Moreover, this paper could provide the gifted 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. Followings are the results of this study:
1. The teaching materials of quadratic equation with one variable can provide the students different strategies for solving Math questions. In the processing of seeking the answers of the questions, students can learn the abilities of multiple thinking, independent thinking, and creativity.
2. The teaching materials and the methods of solving the Math problems that this study developed fitted its own objective.
3. The study found that enough Mathematical knowledge can help the gifted students to connect different models and methods together to solve the math problems.
4. Experienced arithmetic capabilities can assist the gifted students to have clear train of thoughts in order to solve the math problems completely.

並列關鍵字

Quadratic equation ； Mathematics Gifted Students

參考文獻

33.吳武典 (2003)：台灣資優教育四十年 (一)：回首前塵。《資優教育季刊》126(3). 1-11.

18.劉貞宜(2000)。數學資優生的解題歷程分析。國立臺灣師範大學特殊教育研究所論文。

34.陳麗玉 (2006)：桃園縣國民中學英語資僅教育實施之研究。國立政治大學學校行政碩士在職專班論文，未出版，臺北。

39.孫瑜成. (2004). 國中資優學生人格特質, 壓力調適及其相關因素之研究 (未出版之碩士論文). 國立彰化師範大學, 彰化縣.

42.劉永政. (2015) 兩種不同表徵對於國二學生數學解題之探討─以「一元二次方程式」為例, 國立中山大學教育研究所碩士論文,高雄.