虛擬計算機的開發與教學研究—以探索數字樣式一般化為例

Abstract

本研究主要是使用Flash開發一台可以提供國中數學教師教學使用及幫助學生進行尋找數字樣式一般式探索活動的虛擬計算機，並將此套虛擬計算機實際運用於國中生數學教學以了解本虛擬計算機使用於教學的可行性，最後探討數字樣式一般化教學實施後對學生學習數字樣式一般化的影響。 本研究採不等組前後測準實驗研究設計，以台北市一所國中的兩個班級59位學生為研究樣本，隨機選取一班為實驗組，另一班為控制組，實驗組的學生接受虛擬計算機融入數學教學，控制組的學生接受對等的傳統教室教學，並以研究者自行設計之數字樣式探索測驗及課程意見表為資料收集的主要工具。實驗研究主要發現如下： 一、使用虛擬計算機輔助教學與傳統教學實施能夠達到相同的效果。 二、使用虛擬計算機輔助教學能增加學生學習的延宕效果。 三、使用虛擬計算機輔助教學能提升學生的數學學習態度，帶給學生持續的新奇感，營造輕鬆的學習氣氛，增強學生解題的自信心，並促使學生願意主動學習。 四、使用虛擬計算機輔助教學能夠幫助學生澄清錯誤觀念，釐清正負數的概念，填補學生過去學習上的間隙（gap），且能有效輔助學生探索等比數列數字樣式的一般式。 最後根據研究結果與發現，提出若干建議以做為教師教學改進與未來研究之參考。

The study investigates the effects and the feasibility of utilizing a virtual calculator in real mathematical classroom at a junior high school in Taiwan. The virtual calculator was developed by Flash. It is hoped that it can offer mathematical teachers a new kind of supplementary material to help students to explore number patterns and the concept of generalization. The study applied the nonequivalent–groups pretest–posttest quasi–experimental design. The samples are from two classes (59 students) in the 7th grader of a junior high school in Taipei. The researcher randomly selected one class as the experiment group and the other one as the control group. Students in the experiment group were taught with the use of the virtual calculator. Students in the control group were taught without using the virtual calculator. Major results of this study are as following: 1. The learning effect in the experiment group was the same as in the control group. 2. There was a carry-over effect in the experimental group. 3. The students in the experiment group have more positive attitudes toward mathematical learning than those in the control group. It was observed that classroom atmosphere was more harmonious in the experimental group. Moreover, using the virtual calculator in class sustained students’ curiosity, motivated students’ learning interest, promoted students’ active learning, and reinforced students’ confidence. 4. Using the virtual calculator in class can help the students to clarify the concepts of positive and negative numbers and to bridge the gap of weakness in the past. Moreover, students’ performance was better in finding the generalization form of a ratio sequence. Based on results of this research, suggestions for teaching and future study were provided.