高中學生在程式設計情境對函數概念的反思

Abstract

摘 要 本研究旨在透過HTML、JavaScript程式設計活動，瞭解學生函數的概念心像、探討學生函數概念學習的困難與迷思概念。本研究採質性研究法，以新竹某高中一、二年級共13名學生為對象，實施實驗活動，由活動過程的觀察、紙本資料、訪談等資料內容進行深入之分析。 研究結果發現： (1) 函數為單一代數式所定義的迷思概念，影響學生分段定義函數的學習。 (2) 學生未充份瞭解數學符號的涵義，非但無法運用符號來進行思考，甚至造成學生利用代數式表達規律性的困難。 (3) 過度強調變量之間的關係，影響學生對於常數函數的學習。 (4) 定義域與對應域概念模糊，阻礙學生合成函數概念的發展。 關鍵字：程式設計、質性研究法、函數、概念心像、符號、迷思概念

Abstract The purpose of this study was to understand how senior high school students changed their concept image with HTML and JavaScript programming activities. In the mean time, we investigated their learning difficulties and isconceptions. The study was based on activity reports, pretests, posttests, interview details gathered from thirteen senior high school students. Upon analysis of those data, we found that： (1) Students have great difficulties in understanding the abstract meanings of mathematics notations and symbols. (2) Students could not use algebraic expressions to formulate patterns fluently. (3) The concept image that a function is to be defined by a single formula hindered students from understanding piece-wisely defined functions. (4) Missing the proper understanding of the domains and co-domains of functions led to the difficulties in developing the concept of compositions of functions.