本研究針對臺灣、日本與新加坡三國的中學數學教科書，分析幾何計算任務的認知複雜度，並比較各國教材在平行線截角性質與四邊形性質單元中的題目設計特徵。研究採用內容分析法，透過量化分析統計不同版本教材的解題複雜度與圖形複雜度，探討教材間的差異及其對教學的潛在影響。
研究結果顯示，新加坡的 GCN 任務的認知複雜度最高 (平均 11.87) ，其次為日本 (10.59) ，而臺灣最低 (9.64) 。日本教材在圖形複雜度上較高，但解題複雜度則相對穩定。新加坡教材在 G3 水準時大幅提升圖形與解題的挑戰性，而臺灣教材則在不同版本間展現不同的難度梯度。其中，臺灣 K 版與 N 版在例題與練習題的難度變化上存在顯著差異，K 版的習作難度跳躍較大，而 N 版則較為均衡。日本教材高度依賴習作來提升學生挑戰性，而新加坡教材則主要透過課本提供高強度練習。進一步分析解題複雜度與圖形複雜度的關係發現，當解題複雜度提高時，圖形複雜度通常較低，顯示教材可能透過調整圖形複雜度來控制學生的認知負擔，使其更能專注於數學推理與計算。
基於研究結果，本研究提出教學建議，鼓勵教師根據教材設計特點調整教學策略。在教學時，應適當地補充較高複雜度的例題給予學生足夠的學習機會，使其能夠順利地獨自處理較高複雜度的練習題。在不同難度的題目中，教師可適時引導、提供鷹架，讓學生發展多步驟解題策略以提升其數學推理與計算能力，或是圖形拆解策略使其能夠順利理解圖形複雜度較高的任務圖形。此外，教師可透過對比不同版本的教材，設計分層練習，確保學生能夠循序漸進地掌握數學知識。本研究亦建議未來可進一步探討不同教材對學生數學學習成果的影響，以提供更具體的數學教育改革建議。

關鍵字：幾何任務、GCN任務、認知複雜度、內容分析

This study focuses on middle school mathematics textbooks from Taiwan, Japan, and Singapore, analyzes the cognitive complexity of geometric calculation tasks, and compares the design characteristics of questions in the units of parallel line truncated properties and quadrilateral properties in each country's textbooks. The research uses content analysis method to quantitatively analyze the problem-solving complexity and graphic complexity of different versions of teaching materials to explore the differences between teaching materials and their potential impact on teaching.
The research results show that Singapore has the highest cognitive complexity of GCN tasks (average 11.87), followed by Japan (10.59), and Taiwan has the lowest (9.64). Japanese textbooks have higher graphics complexity, but the problem-solving complexity is relatively stable. Singaporean textbooks greatly increase the challenge of graphics and problem solving at the G3 level, while Taiwanese textbooks show different difficulty gradients between different versions. Among them, there is a significant difference in the difficulty of examples and exercises between Taiwan's K version and N version. The K version has a larger jump in difficulty of exercises, while the N version is more balanced. Japanese textbooks rely heavily on exercises to challenge students, while Singaporean textbooks mainly provide high-intensity exercises through textbooks. Further analysis of the relationship between problem-solving complexity and graph complexity revealed that when problem-solving complexity increases, graph complexity is usually lower, indicating that teaching materials may control students' cognitive load by adjusting graph complexity, allowing them to focus more on mathematical reasoning and calculations.
Based on the research results, this study puts forward teaching suggestions and encourages teachers to adjust teaching strategies according to the design characteristics of teaching materials. When teaching, examples of higher complexity should be appropriately supplemented to give students enough learning opportunities so that they can successfully handle higher complexity exercises on their own. For questions of different difficulty, teachers can provide timely guidance and scaffolding to allow students to develop multi-step problem-solving strategies to improve their mathematical reasoning and calculation abilities, or graphic disassembly strategies to enable students to successfully understand graphically complex task graphics. In addition, teachers can compare different versions of teaching materials and design layered exercises to ensure that students can master mathematical knowledge step by step. This study also suggests that the impact of different teaching materials on students' mathematics learning outcomes can be further explored in the future to provide more specific mathematics education reform suggestions.
Keywords: geometry task, GCN task, cognitive complexity, content analysis

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