圖形類型、分布類型、用語方式與統計概念對中學生統計概念理解表現的影響

Graphical Types, Distribution Types, Oral Statements and Statistical Concepts for Statistical Concepts Performance of High School Students

吳捷蓮(Chieh-Lien WU)

指導教授 ： ARRAY(0xc692fbc)

中原大學/人文與教育學院/教育研究所/碩士(2009年)

https://doi.org/10.6840/CYCU.2009.00801

摘要

本研究的主要目的探討藉由圖型類型、分佈類型、用語方式及統計概念類型等因素對學生統計概念的理解表現的影響。研究者藉由二階段診斷統計概念的評量工具瞭解學生的統計概念理解表現。研究對象包含學過國三統計單元的國三學生及高中學生為研究對象，使用四因數混合設計變異數分析資料。
研究發現：(1)學生的平均數概念表現，會因圖形類型、分布類型及用語方式的不同而有所顯著差異。(2)學生的眾數概念表現，不會因圖形類型、分佈類型及用語方式的不同而有所顯著差異。(3)學生的中位數概念表現，會因圖形類型、分佈類型及用語方式的不同而有所顯著差異。
在平均數概念的表現中，圖形類型研究顯示學生熟悉長條圖形的樣本數的加總方式，但對於累積折線圖的以下累積次數的概念卻有迷思概念，這會影響計算平均數的結果。分布類型研究顯示學生使用以圖形視覺策略而造成平均數的錯誤，在左右偏態及常態分布類目中，學生以視覺策略可能會判斷正確，但在單雙峰類型、樣本數不同的題目中，學生若只以直覺判斷則會產生平均數概念的錯誤。在用語方式研究顯示學生透過統計用語的題目優於情境用語的題目。
在眾數概念的表現中，本研究發現學生對於「最多人的答對題數是多少？」，學生會以次數(人數)與答對題數混淆，而次數(人數)為回應，卻不是以答對題數回應，而產生錯誤的眾數概念。對於情境用語的問題，學生對於沒有具體的數據，而不以眾數概念來應用，以「不一定」來回答而產生錯誤。
在中位數概念的表現中，學生對於中位數概念只瞭解部分概念。學生會以中位數的個數的一半的位置數就當成是中位數，而忽略要以該位置的值才為中位數。還有學生會以圖形視覺方式找尋中位數的位置而產生錯誤。
綜合以上結果，據此結果提出建議，以供教學者及未來研究之參考。

關鍵字

分布類型 ； 圖形類型 ； 統計概念 ； 用語方式

並列摘要

The purpose of the study is to explore the effectiveness of performance of the students’statistical concepts by graphical types, distrubution types, oral statements and statistical concepts. Researcher found the performance of the students’statistical by two-tier assessment instrument. The samples were the grade 3 junior and grade 1 high school students who have learned statistical courses in junior high school. Mixed designed four-way ANOVA was used.
The major findings of this study are as follows: (1) Graphical types, distribution types, oral statements differ with the average concepts of students. (2) Graphical types, distribution types, oral statements don’t differ with the mode concepts of students. (3) Graphical types, distribution types, oral statements differ with the median concepts of students.
In the performance of students’average concepts, graphical types research indicted that student are familiar with the sum way in the chat line but mistook the below-accumulative frequency line chat. Distrubution types research indicted that student caused the mistakes in average concepts by using visual strategy. In the tests about skewness and normal distribution, students might answer correctly. However, in the tests about kurtosis, students have mistakes in the average concepts only by intuition. The oral statement indicted the tests about statistic are better than ones about situation.
In the performance of students’mode concepts, the finding of the study is students answered frequency instead of the numbers of right questions when they face “How many right questions do the most people get?” When they don’t specific data, they answer “I am not sure.”
In the performance of students’median concepts, students only understood the partial concepts. Students might think the half number as median and neglect the value of the ordinal number. Also, they mistook the location of the median by graphical visual way.
To sum up, the conclusion could be the indication for the teachers and feature research.

並列關鍵字

graphical types ； statistical concepts ； distribution types ； oral statements

參考文獻

林清山(1992)。心理與教育統計學。臺北：臺灣東華。

教育部(2003)。國民中小學九年一貫課程網要-數學領域。台北：教育部。

郭生玉(1985)。心理與教育測驗。臺北：東華書局。

Brown, Silver. (1989). Educational Progress, edited by Mary M. Lindquist, 28-34. Reston, Va.: National Council of Teachers of Mathematics, 1989.

Browne, Richard(2002). Statistics in the Revised National Curriculum for England. Teaching Statistics, 24, 1, p2-5.