國中階段符號感意涵與評量方式之探究

Abstract

數字是算術的重要元素，符號則是代數的重要元素。代數是國中數學課程與教學不可或缺的重要主題，然而從研究者教學經驗發現，相較於數字計算等一般化算術，國中學生較不容易掌握代數符號。九年一貫課程綱要在數與量主題中提及應培養學生的數感，且數感在國內外已累積相當多研究。那麼代數主題裡是否也應培養學生具備「某種感」呢? 答案是肯定的。Arcavi(1994)指出，符號感為代數教學的重要一環(Arcavi, 1994)。雖然符號感漸漸開始受到重視，但符號感的相關研究仍十分稀少，國內更是尚未出現符號感的相關研究。因此本研究主要目的為分析符號感意涵，整理與開發出符號感構成要素，進一步設計適合國中階段的符號感評量方式。 故本研究共有兩大部份：研究一透過文獻分析、小組討論、專家審查等內容流程，探索符號感意涵，進一步整理、開發符號感的可能構成要素。研究二則依據研究一所整理的符號感構成要素，設計適合國中階段的符號感試題，經過多次試寫、小範圍施測與訪談，最後請專家審查，逐步修正試題，最後於正式施測階段找117位學生進行測驗，分析學生的作答表現。 從研究一結果將符號感分為三大向度，每個向度下有數個子成分，共七個子成分。從研究二的結果發現開放式問答題型較適用於符號感測驗，且學生作答表現可對比出明顯具備符號感與欠缺符號感的情形。並由此作答表現進一步呼應研究一所整理之符號感構成要素。Number is the important element of arithmetic, while symbol is of algebra. Algebra is a major project in junior-high-school math curriculum and instruction. However, from my own teaching experience, I found that it is more difficult for thejunior high school students to master algebraic symbol than to master general arithmetic. Grade 1-9 Curriculum Guidelines tells that we should develop students’ number sense; also, there are a lot of studies concerning number sense whether foreign or native. Then, when it comes to algebra, should students be developed some sense? The answer is absolutely yes. Arcavi (1994) announced symbol sense is the principal key to algebraic instruction. Although we become to take focus on symbol sense, we still do much rare relative study, not to mention the internal study. Therefore, my major study propose is to analyze the meaning of symbol sense as well as sort and build the construction of symbol sense and moreover, to design a suitable symbol-sense assessment for junior high school students. There are two parts in my study. My first part is to inquiry the meaning of symbol sense by analyzing document, panel discussion, and experts’ investigation. My second part, depending on my first part, is to design a suitable symbol-sense assessment for junior high school students; through trying tests many times, testing within narrow range; and after experts’ investigation, I revised my tests step by step so that on the formal stage, I found 117 students to do my tests and analyzed their answering performance. From my first part, there are three major dimensions dividing symbol sense; each has several minor elements, and total seven minor elements. From my second part, I found that the open essay questions are proper to symbol-sense assessment, and they contrasted students who have symbol sense with those who do not. The students’

answering performance may also respond to the construction of symbol sense in my first part.