電腦數學實驗運用在高中數學統計單元教學之研究—以「大數法則」、「常態分佈」及「信賴區間」等單元為例

Abstract

本研究之主要目的，在比較採用「電腦實驗教學」方式與「傳統講述式教學」方式於高中數學科之「大數法則」、「常態分佈」及「信賴區間」等單元之學習成效、試題反應差異、學生的錯誤統計思維，並訪談學生接受電腦實驗教學後的態度及反應，希望藉此建立電腦實驗教學在高中數學科實施的適當方式，做為將來在高中推展電腦實驗教學之參考。 本研究之實驗設計採準實驗研究法，實驗樣本取自桃園縣某高中一年級兩班各47名學生，隨機分派一班學生為實驗組，另一班學生為控制組。實驗組學生採自由分組方式於電腦教室接受三個單元之電腦實驗教學，控制組同時接受相同三個單元之傳統講述式教學。 各項資料經統計處理獲得下列主要發現： 一、 學習成效：在「信賴區間」單元，實驗組學生在學習成就測驗後測及延後測的成績皆顯著地高於控制組的學生，可見在「信賴區間」單元實驗組的學習成效優於控制組。 二、 試題反應差異：實驗組與控制組的學生在學習成就測驗十九題題目中有二題的試題反應差異達顯著，此二題分別為投擲不同數量骰子所得點數和的機率問題，以及常態分佈中68-95-99.75法則的應用問題。 三、學生的錯誤統計思維有： 1、機率相等偏見。2、誤以為所有母體的性質都會呈現常態分佈。3、誤以為95%信心水準是母體中的比率。4、誤以為抽樣的品質會影響信心水準。5、誤以為母體愈大則抽樣必須愈大才能有相同大小的信賴區間。6、誤以為多做幾次抽樣調查就可提高準確率。 四、接受訪談學生中96%表示喜歡電腦實驗教學的上課方式而給予正面的回應。

The research used the nonequivalent-groups pretest-posttest quasi-experimental design to explore the performance differences between the computational experiments and the traditional teacher-centered approach in teaching high school statistics. The three leaning units used in this study were ’law of large numbers’, ‘normal distribution’ and ‘confidence interval’.

Participates were 94 students from two 10th-grade classes, each with 47 students, from a high school in Tao-yuan county of Taiwan. The researcher randomly selected one class as the experimental group, and the other one as the control group. Students in the experimental group are grouped according to their wills and received a computational experiments instruction in a computer laboratory. Students in the control group received the traditional teacher-centered instruction.

The major finding of this study are as following: 1. Learning effectiveness: Students in the experimental group performed better than those in the control group on the concept of ‘confidence interval’ in both the posttest and the retention test. 2. Students’ performance between the experimental group and control group were different in 2 of the 19 test questions. 3. The common fallacies found in students’ statistical thinking are: Students believe that (1) an experiment will result in the same result (the equiprobability bias). (2) all population distributions are normal. (3) 95% confidence level is a ratio of the population. (4) the quality and methods of sampling will affect the value of 95% confidence interval. (5) good samples have to represent a high percentage of the population. (6) the more random samples, regardless of how small they are, will result in a more similarity of the population.

Students in the experimental group generally hold a positive attitude toward this computational experiments approach. However, some learners also expressed their favor of a traditional approach. They worried about taking the entrance exam and considered the traditional approach would to be more effective and time-saving.