國三學生對分佈特徵與分佈概念了解情形之研究

趙君培(Chun-Pei Chao)

指導教授 ： 譚克平

國立臺灣師範大學/理學院/科學教育研究所/碩士(2009年)

摘要

在資訊發達的現代社會，統計是必須具備的知能，分佈是統計中的重要概念，具分佈概念可掌握整體資料。本研究的目的為探討國三學生統計分佈特徵與分佈概念了解情形，並以此探討「九年一貫數學學習領域課程綱要」中統計分佈的編排。
本研究採調查研究法，研究對象為台北地區國三學生276名，以自編之經過效化的「統計分佈概念試題」為研究工具，得到下列發現：
1. 學生在「中心量數的概念」較「求取中心量數」表現差。
2. 學生在「變異量數的概念」較「求取變異量數」表現差。
3. 學生缺乏「形狀」概念。
4. 學生不擅描述資料分佈，多數學生僅使用一個分佈特徵描述一個資料分佈。
5. 若未給學生所有的資料點，多數學生無法畫出適當的統計圖形呈現分佈。
從本研究得知：在目前課程綱要下，國三學生較擅長計算量數，但分佈概念不足，探討「九年一貫課程綱要」後，提出兩點建議：
1. 課程內容宜加入統計分佈概念，包括分佈特徵。
2. 課程內容應重視分佈特徵的概念，尤其是「形狀」概念。

關鍵字

分佈 ； 九年一貫課程綱要 ； 統計

並列摘要

Modern society is abundant with quantitative information. To be an effective member of the society, every citizen should have basic statistics knowledge and skill. Distribution is a core concept in statistics, those who understand it well will know a lot about the data they have at hand. The main purpose of this study was to explore ninth graders’ understanding of the concept of distribution and its characteristics. Based on their performances, this study would then analyze and reflect on the arrangement of the content on distribution in the Guidelines of Mathematics Learning Area in Grade 1-9 Curriculum.

A self-designed questionnaire on the concept of distribution was validated on a group of 276 ninth graders’ in the Taipei Area. Further analysis revealed the following results:
1. Students’ performance in items related to the concept of central tendency was inferior to their ability in finding the central tendency indices.
2. Students’ performance in items related to the concept of variation was inferior to their ability in computing the variation indices.
3. Students were weak in their understanding of the shape of a distribution.
4. Students were not good at describing the distribution of a data set. Furthermore, most of them would only used one of the characteristics of a distribution to describe the distribution.
5. If students were not given all of the data values, most of them could not represent the distribution using appropriate statistical graphs.

As mentioned above, students were proficient in computing the indices of center and variation, but they were weak in their understanding of the concept in distribution. Based on these findings, this author analyzed and reflected on the arrangement of the content on distribution in the Grade 1-9 Curriculum and offered the following suggestions:
1. The content on the concept of distribution together with its characteristics should be increased and be more organized in the curriculum.
2. The various characteristics of a distribution should be emphasized in the curriculum, especially with respect to the shape of a distribution.

並列關鍵字

Distribution ； Grade 1-9 Curriculum ； Statistics

參考文獻

譚克平(2007)。國中教導盒狀圖的建議及介紹如何用EXCEL製作盒狀圖。科學教育月刊，305，20-34。

教育部(2003)。國民中小學九年一貫課程綱要數學領域。台北市：教育部。

Freund, J. E., & Williams, F. J. (1966). Dictionary/outline of Basic Statistics. New York: McGraw-Hill.

computer tools. Utrecht, the Netherlands: CD Beta Press.

Bakker, A., & Hoffmann, M. H. G. (2005). Diagrammatic reasoning as the basis for developing concepts: a semiotic analysis of students' learning about statistical distribution. Educational Studies in Mathematics, 60(3), 333-358.