| 摘要: | 本研究採用內容分析法，探討德國「Lambacher Schweizer Mathematik」6至8年級數學教科書中函數單元之「教科書內容頁數」、「單元數」與「教學例題數」佔比、「教學例題之認知需求層次分析」、「函數單元教材編排順序之分析」，以及「其它單元與線型函數單元的連結分析」。研究範圍是從函數觀念的導入開始，一直到線型函數的正式教學，所以不含二次函數的正式教學單元。為了方便讀者觀察德國LS版教科書的特色，選擇臺灣H版教科書與德國LS版來做對照。
研究結果顯示：在「教科書內容頁數」中，德國LS版函數內容在8年級佔比18.3%，整體佔比為6.3%；在「單元數」中，德國LS版函數單元數佔比為21.7%；在「教學例題數」中，這三年的教科書內，共有56題函數單元的教學例，德國LS版從六、七年級開始出現函數概念例題，八年級正式進入函數單元；在「教學例題之認知需求層次分析」主題中，德國LS版以無連結之程序性計算為主，德國LS版較注重高認知需求層次發展；在「函數單元教材編排順序之分析」中，德國LS版函數教材隨著年級提升將基本架構加深加廣，重視螺旋式課程；在「其它單元與線型函數單元的連結分析」中，德國LS版函數單元的對外連結分布於五年級至八年級的單元中。
相對而言，臺灣H版教科書僅在八年級安排函數單元，頁數佔比較高，單元數佔比較低；認知需求層次以無連結之程序性計算為主，概念理解問題佔比較高；函數單元在八年級集中教學；函數單元的對外連結分布於七至八年級的單元中。
;This study employs content analysis to investigate the functions units in the "Lambacher Schweizer Mathematik" mathematics textbooks for grades 6 to 8 in Germany. The analysis focuses on the "proportion of textbook content pages," "proportion of the number of units," "proportion of the number of teaching examples," "cognitive demand levels of teaching examples," the "sequence of teaching materials in the functions unit," and the "connections between other units and the linear functions unit." The research scope starts from the introduction of function concepts up to the formal teaching of linear functions, excluding the formal teaching units of quadratic functions. To facilitate readers′ understanding of the characteristics of the German LS edition textbooks, a comparison is made with the Taiwan H edition textbooks.
The research results indicate that in terms of the "proportion of textbook content pages," the functions content in the German LS edition accounts for 18.3% in the 8th grade, with an overall proportion of 6.3%. In terms of the "proportion of the number of units," the functions units in the German LS edition account for 21.7%. Regarding the "proportion of the number of teaching examples," there are 56 teaching examples in the functions units over the three years. The German LS edition introduces function concept examples starting in grades 6 and 7, with the functions unit formally beginning in grade 8. In the "cognitive demand levels of teaching examples," the German LS edition predominantly features procedural calculations without connections, indicating a greater emphasis on developing higher cognitive demand levels. In the "sequence of teaching materials in the functions unit," the German LS edition deepens and broadens the basic structure of functions as the grade level increases, emphasizing a spiral curriculum. Regarding the "connections between other units and the linear functions unit," the functions units in the German LS edition are linked with units from grades 5 to 8.
In contrast, the Taiwan H edition textbooks only arrange functions units in the 8th grade, with a higher proportion of pages but a lower proportion of units. The cognitive demand levels primarily involve procedural calculations without connections, with a higher proportion of conceptual understanding questions. The functions units are concentrated in the 8th grade, and the connections between the functions units and other units are distributed across grades 7 and 8. |
