探討以概念改變策略促進代數符號理解對代數成就表現及學習興趣之影響－以一元一次方程式為例

Exploring how the algebraic symbol comprehension promoted by conceptual-change strategies affects middle school students’ performance and learning interest of algebra－An investigation of linear equation with one unknown.

顏德琮(TeTsung Yen)

指導教授 ： 邱美虹

國立臺灣師範大學/理學院/科學教育研究所/碩士(2001年)

摘要

從過去學者的研究發現（Küchemann,1981、郭汾派、林光賢與林福來,民78、袁媛, 民82）代數符號具有多種意義（特定數、一般數、變數等等），而學生對各種代數符號意義也有不同層次的理解，因此本研究主要目的是要探討學生對代數符號意義的理解與代數成就表現的關係。
本研究共有兩個部分：研究一從128位國三學生在代數成就評量試卷以及代數符號理解試卷中的表現探討理解代數符號意義與代數成就表現間的相關性。研究二調查197位（五個班級）未學過代數課程的國一學生對代數符號是否存在另有理解；再從這五個班級中挑出表現接近的兩個班級作為實驗組（40人）與對照組（36人），在實驗組學習一元一次方程式過程中加入五次運用概念改變策略並強調符號意義的班級活動，期望提升對代數符號的理解及學習的興趣，最後再比較與對照組間的差異。本研究另從實驗組挑出六位學生，藉晤談、觀察等資料收集方式瞭解其在學習、活動歷程中的概念發展。
從研究一的結果發現國三學生的代數成就表現與符號理解情形之間具有高度相關性。研究二的結果發現學習代數前有近六成的學生將符號視為代表特定（範圍）的數或對代數表示法是存在另有的理解，而某些另有理解方式對代數學習是會造成負面的影響；透過本研究的學習活動，實驗組學生對符號代表一般數及變數的理解明顯優於對照組，但在後測中的代數成就表現與對照組則無明顯差異，而是某幾種錯誤類型出現的比例較低以及對數學抱持較正面的學習態度；此外，由本研究亦可發現透過教師安排、引導下，學生是樂於有意義地使用代數符號及規則。

關鍵字

代數 ； 代數符號 ； 概念改變 ； 學習興趣 ； 一元一次方程式

並列摘要

Based on the research of Küchemann (1981), Kuo, Lin, & Lin (1989) and Yuan (1993), algebraic symbols can be regarded as different meanings (e.g. evaluated numbers, generalized numbers and variables), and comprehended in different ways. The purpose of this thesis is to explore the relationship between the students’ comprehension of algebraic symbols and the performance of it.
This study consists two parts. First, it began with 128 nine-grade students participating a test to build the correlation between the understanding of algebraic symbols and the performance in algebra. Second, 197 seven-grade students from five classes, who haven’t learned algebra formally, were the subjects. The exploration cares about how these subjects comprehend the formal algebraic symbols before learning. Among these five classes, two performed similarly were assigned as the experimental class and controlled class to join the advanced study. In the experimental class, the designed instruction of linear equation with one unknown, five external activities were designed to promote the understanding and conceptual change of algebraic symbols. Meanwhile six students from experimental class were selected to be interviewed and observed about their learning in and after each activity.
The result of this study reveals strong correlation between the comprehension of algebraic symbols and their performance of learning algebra. Sixty percent of subjects regard the formal algebraic symbols as fixed numbers or with different rules before learning. Some alternative conceptions become the obstacles in comprehending algebra. The experimental class performs better to take algebraic symbols as generalized numbers and variables. However, in the post-test, no significant difference was found between the students in the experimental class and those in the controlled one except some error types and attitude in learning. This study also reveals that students would be glad to learn and operate algebraic symbols meaningfully if teachers guide them appropriately.

並列關鍵字

algebra ； algebraic symbol ； conceptual change ； learning interesting ； linear equation with one unknown

參考文獻

邱美虹（民89）：概念改變研究的省思與啟示。科學教育學刊，8（1），1-34。

戴文賓、邱守榕（民88）：國一學生由算術領域轉入代數領域呈現的學習現象與特徵。科學教育，10，148-175。

張景媛（民83）：數學文字題錯誤概念分析及學生建構數學概念的研究。國立台灣師範大學教育心理與輔導系教育心理學報，27，175-200。

謝孟珊（民89）：以不同符號表徵未知數對國二學生解方程式表現之探討。國立台北師範學校數理教育研究所碩士論文。

林靜雯（民89）：由概念改變及心智模式初探多重類比對國小四年級學生電學概念學習之影響。國立台灣師範大學科學教育研究所碩士論文。