德國無論是基於改革教育傳統，或因應少子化而有混齡編班的建置，其推 行時程都較台灣更久，在實施混齡教學上的經驗也更為豐富。本研究以德國一 份詳細的一、二年級混齡數學教材為範例，分析其內容與教學／學習設計。 此份教材除了著重學生數學相關的內容與過程素養（能力）之培養外，在 內容上具有五項特色，包括：1. 學習目標明確；2. 主題跨域結合；3. 教材結構 安排有序；4. 學習活動取材生活經驗且難度漸升；5. 教學策略從具體到抽象並 納入學生興趣與經驗。至於教學／學習設計之特色則在於：1. 教學階段的同與 異之調和；2. 工作階段的開放任務之設計。

Germany has a long history of implementing mixed-age classrooms, shaped by both educational reform traditions and demographic changes, compared with Taiwan. This study analyzes a mathematics curriculum designed for first and second graders in German mixed-age classes, focusing on content and instructional design. The curriculum emphasizes development of students’ mathematical knowledge and process skills and has five key features: (1) clearly defined learning objectives; (2) integration of cross-curricular themes; (3) well-organized materials; (4) gradual progression in difficulty, with the use of real-life experiences to enhance learning; and (5) instructional strategies that transition from the concrete to abstract, informed by the students’ interests and experiences. In terms of instructional design, the curriculum balances similarities and differences during teaching phases and incorporates openended tasks during working stages.

混齡教學、德國教育、數學教材

German education, mathematics teaching materials, mixed-age teaching