• 作者： 顏放麟; 羅昭強
• 作者服務機構： 國立台灣師範大學數學糸; 中國文化犬學應用數學系
• 中文摘要： 函數的概念，在數學領域中佔有十分重要的地位。但學生在學習函數概念時，往往會感到困難。根據皮亞傑研究所得，孩童發展的函數基本概念乃是兩個變量的關係。一個變量的改變，會使另一變量跟隨某一比例而改變。因此，我們認為孩童最早發展的函數概念是線性函數。事實上，我國國中數學課程中，就包含有線性函數概念以及二次函數概念。若學生能了解此二函數概念，不僅對他目前的學業有所幫助，進一步來說，對他將來學習其他的數學概念也大為有益。 因此，本研究嘗試探討我國國中生在學習此二函數概念時的認知發展過程。本研究的樣本為120位國中學生，並根據他們回答問卷的情形，從中抽出30人作面談對象，從而對此二函數概念建立基因分解。
• 英文摘要： The function concept is, without doubt, one of the most fundamental in all mathematics andone of which students seldom develop a satisfactory understanding. In accordance with Piaget'sidea that the most elementary function concept developed in a child's mind can be consideredas a relation between the magnitude of two quantities, the variation in one bringing about thevariation in the other in the same proportion, it can be seen that the first emergence of functionconcept is linear. In fact, the concepts of linear function as well as quadratic function playan important role in Taiwan's junior high school mathematics curriculum. If students graspthese concepts, their future study of mathematics is eased. The primary goal of this research is to collect information about the cognitive developmentof the concept of functions for junior high school students in Taiwan. The study was an attemptto measure the extent to which the concept of a function had been mastered. Precisely, theaim of the research was to study the possibility of finding out both how the concepts of linearfunction and quadratic function were developed and how they were learned. With this in view,we particularly tried to work out the genetic decomposition of these concepts and provide anappropriate cognitive model of them.
• 中文關鍵字： linear function; quadratic function; genetic decomposition
• 英文關鍵字： --