臺灣、新加坡及巴西數學教科書中數學素養內涵之比較──以畢氏定理為例

Comparative Implications of Mathematical Literacy between Taiwanese, Singaporean, and Brazilian Textbooks: Using the Pythagorean Theorem as an Example

數學教育的目標在培養學生的數學素養，而教科書則是達成這個目標 的重要工具。本研究從PISA 的數學素養觀點分析臺灣、新加坡及巴西 數學教科書的內容，並以畢氏定理單元為例，分別從其內容結構、數 學識能及建模歷程三個維度進行分析，以提供教科書中數學素養內涵 的想法及架構。研究結果顯示臺灣和新加坡教科書之內容結構較為相 似，但數學識能的部分，卻只有「推理及論證」和「使用符號、運算 及正式語言」這兩個識能在三個版本的分布是沒有顯著差異的，而建 模歷程部分，在形成、應用、詮釋或評估三個歷程中，都各有一些面 向顯示三個國家的教科書有不盡相同的地方。上述結果顯示，雖然在 PISA 評量中臺灣與新加坡的學生表現接近，其教科書所展現的數學素 養內涵並不相似，但卻能提供編寫發展數學素養的教科書更多面向的 參考建議。

Developing students’ mathematical literacy is the primary goal of math education， and textbooks play a crucial role in this endeavor. In this study， we analyzed mathematics textbooks used in Taiwan， Singapore， and Brazil from the perspective of PISA mathematical literacy. Focusing on the Pythagorean theorem， we analyzed three dimensions (content structure， mathematical competencies， and modeling process) to provide a framework for elucidating the meaning and implications of mathematical literacy in textbooks. The results indicated that textbooks used in Singapore and Taiwan possessed a similar content structure， whereas only the “Using Symbols， Operations， and Formal Language” and “Reasoning and Argument” competencies were similar in all three textbooks. Some aspects of the modeling process， such as “Formulating，” “Employing，” and “Interpreting or Checking，” were presented differently in each textbook. In short， the meaning and implications of mathematical literacy presented in these textbooks differed， although students’ PISA performance was similar in Taiwan and Singapore. The results of this study may serve as a reference for developing mathematical literacy when writing textbooks.