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題名 | 函數圖形與函數性質的認知發展層次=The Cognitive Development of the Graphic and Analytic Representations of the Function Concept |
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作者 | 蘇金石; Su, Jin-shieh; |
期刊 | 華岡理科學報 |
出版日期 | 19960500 |
卷期 | 13 1996.05[民85.05] |
頁次 | 頁143-168 |
分類號 | 521.163 |
語文 | chi |
關鍵詞 | 函數圖形; 函數性質; 認知發展; |
中文摘要 | 心理學家長期以來研究賽類受到視覺刺激的產生推理的原動力之關係有著極濃厚的興趣,而圖形也常常被利用為教授數學概念和啟發數學思考的工具。很多數學教育研究專家一致認為能夠把數學問題轉變為圖形的表徵,再透過瞭解及分析該圖形表徵的特性,而且能利用這些特性來幫助目題的解決是一種很基本及必需的數學能力。他們同時強調,學生能夠把數學問題轉變為圖形的表徵並不表示他們已瞭解及能分析出該圖形表徵的特性。 在大一微積分課程中,函數的概念貫串備個課程。而函數的部分性質皆可透過函數圖形的呈現來幫助學生們增加了解。事實上,若學生能夠了解函數的圖形意義與函數性質之間的相互關係,則學生便能從函數的方程式來分析及了解函數圖形的性質,以及從函數的圖形來分析及了解函數本身的性質。若學生不能透過視覺表徵來學習微積分概念,則微積分對他們來說只是一大堆繁瑣的符號演算,和複雜而無意義的「菜單」而已。因此,在大一微積分課程中,我們認為我們討論甘何畫出函數圖形最重要的目的應強調讓學生從描繪函數圖形的過程中,了解函數的圖形意義與函數性質之間的相互關係。所以,本研究的研究目的是希望透過適當的問卷設計,以期深卷了解並分析學生學習此概念時的認知發展層次,作為對教學上建議之用,並對我們提出的問題,透過嚴謹的研究方法來尋求答案。 |
英文摘要 | The function concept is, no doubt, one of the most important in all mathematics and one of which students seldom develop a satisfactory understanding. It is widespread one of which students seldom develop a satisfactory understanding. It is widespread agreement that the concept of function is very complex. It has a number of concepts associated with it, such as domain, range, continuity, limit and so forth. It also has different representations, such as algebraic, graphic and analytic representation. In fact, most of the concepts can be easily transited through the graphic representation of a function. Moreover, reading and interpreting graphs, and sketching graphs of functions are the most fundamental abilities that should be developed in learning the function concept. Many researchers emphasized that, although students can sketch the graph of a function, it does not mean that they can read and interpret the graph in order to have the analytic information of the function. It is our hope that our students can establish appropriate links between the graphic and analytic representations of function concepts. Therefore, the purpose of the study is to collect information about the nature of the students understanding of these two representations and attempt to describe the cognitive development which students may have. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。