方程式定性分析在運動學的教學與研究

運動學是物理學的入門單元，其目的在於幫助學習者了解科學家如何以數學符號記錄、描述真實世界的現象。然而，許多學生在學習之後，面對如方程式(equation)、運動圖(motion diagram)、曲線圖(kinematic graph)等符號，卻無法直接在概念上轉化為具體的影像。本研究強調方程式之定性分析，協助學習者不經計算即可從方程式各係數或曲線的概念，讀出對應之運動。教學活動設計藉用電腦之運算特性，發展微型世界(microworld)，提供學生進行動態探索之學習環境；並配合活動引導，讓學習者嘗試分析、解釋、以及檢驗自己對運動方程式與曲線圖的概念。教學單元分為兩部分，第一部分利用電腦模擬，幫助學習者建立方程式、運動圖、曲線圖等符號系統與相對實體運動的關係；第二部分則是透過實體運動作為中介，幫助學習者對以上各符號系統，發展系統轉換之認知能力。本研究以大一物理系學生為對象，以ANOVA分析學習者的先備物理、數學能力，一般解題能力，以及教材使用方式等因素，對學習者符號轉換能力之影響，同時探討大一學生的認知及相關先備能力，能否發展出將抽象符號轉換為實體運動之能力。結果顯示學生僅需了解相關基本定義，透過分析推理之引導訓練，無論物理與數學之先備能力高低，大多數學生能將相關符號轉化為概念之推理。

關鍵字

方程式定性分析；曲線圖；電腦輔助教學；運動學；物理教育

並列摘要

The objective of learning kinematics is to help students understand how scientists describe the real world with mathematical symbols. However, after learning kinematics many students are still unable to convert the equations, kinematic graphs, and motion diagrams into real motion. This study focuses on students' cognitive ability of qualitative analysis with equations (QAE). QAE in kinematics emphasizes the conversion of equations and kinematic graphs into real motion without numerical calculation. The instructional design with computer microworld creates an exploring environment which allows students to analyze and explain various situations and evaluate their understanding of the kinematic symbols. The learning activities are composed of two parts. The first part helps students relate the various symbol systems to the real motion. The second part helps students develop the cognitive ability to convert conceptually among the various systems through the corresponding motions without calculation. The subjects are freshman physics majors. The effects of prior physics ability, prior mathematics ability, numerical problem solving ability, and instructional method on qualitative symbol converting ability are analyzed by ANOVA. The results show that most students are able to convert among various symbol systems with the understanding of basic definitions, regardless of their prior high school physics and mathematics abilities.

並列關鍵字

Computer Assisted Instruction ； Graph ； Kinematics ； Physics Education ； Qualitative Analysis on Equations

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