九年一貫數學教科書之順序性、繼續性及銜接性分析：以統計與機率主題為例

Abstract

臺灣九二課綱將數學學習領域分為五大主題，過去研究多針對數與量、幾何等主題進行分析，較少涵蓋統計與機率的內容，且國中小數學課程內容的銜接性一直是課程發展的重要議題。因此，本研究目的為透過分析架構評估不同版本教科書，在統計與機率主題內容的順序性、繼續性及銜接性。 根據文獻本研究將課程銜接性定義為：教科書需依課程綱要完整呈現分年細目建議次序的學習內容，並符合相同概念再次出現的原則。本研究採內容分析法，對象為教育部審核通過的數學教科書，依市佔率挑選出三個版本（南一、翰林與康軒）。分析架構是以九年一貫課程的數學學習領域之課程綱要和分年細目為基礎，研究過程中藉由專家效度、同意值、追溯檢核等策略以驗證本研究信實度。 研究結果顯示，在順序性效標方面，三版本於一、四、五及六年級的概念呈現上，表現情形相同，年級內的概念存有順序性的關係，例如統計圖概念的安排順序依次為長條圖、複雜長條圖、折線圖及圓形圖。在繼續性效標方面，三版本教科書其各個概念重複出現時，概念深度、文字陳述難度會隨年級增高，且呈現的圖示數量會依年級遞減。概念內容重複次數最多為表格概念，出現次數較少的為有關製圖型的概念內容。在銜接性效標方面，三版本在年級內並無重複出現有關直接或交叉對應表格以及製成統計圖的概念內容，此外，各版本皆透過統計圖表的呈現用以輔助說明題意，省略冗長的文字描述，並連結其他有關統計與機率的概念內容。整體而言，教科書在順序性及繼續性的表現上，與銜接性的表現沒有直接的相關。 本研究結果希冀可做為教科書編排及教師教學之參考，以期進行有關統計與機率的教學活動時，能完整呈現該主題概念的意涵。

In 2003, five themes were identified in the curriculum guidelines of Grade 1-9 Mathematics. Among them, the theme of statistics and probability were relatively unstudied in mathematical education research. Additionally, the articulation of the grade 1-9 mathematics curriculum has always been an important issue in curriculum development. For the reason, the purpose of this study was to examine the sequence, continuity, and articulation of the contents of three mathematics textbooks in the theme of statistics and probability. Based on the literature, the curriculum articulation is defined as the way in which the contents of textbooks are organized with regard to the sequence and continuity suggested by curriculum guidelines and competence indicators. This study employed methods of content analysis and the subjects of this study were Han-Lin, Kang-Xuan, and Nan-Yi mathematical textbooks which were chosen in the condition of being examined by Ministry of Education and the market share. The analysis scheme was developed based on Competence Indicators by Grade in the Mathematics Learning Area. In the processes of analysis, some strategies such as triangulation and audit trails were adopted to ensure the trustworthiness of this study. The analysis showed that the three textbooks presented appropriate sequences of concepts in the first, fourth and fifth grades. A sequence was also found within a grade; for instance, the concept of statistics graphs would start from bar graphs, complex bar graphs, and then broken-line graphs and circle graphs were introduced. In terms of continuity, when the same concept was repeated in the textbooks of different grades, the difficulty of concepts would increase by grade, and the number of the pictures would decrease by grade. The concepts of data tables were repeated often, while the graphs constructed concepts were seldom repeated. The three textbooks did not show curriculum articulation in the concepts of one or two dimension tables and constructing graphs. In addition, rather than using verbal descriptions, the three textbooks included statistical graphs and tables to explain the meanings of mathematical problems and to connect the other concepts about statistics and probability. In summary, the analysis suggested that the sequence and continuity had no direct relation with articulation in the mathematical textbooks.