素養導向之數學教材設計與發展 Design and Development of Mathematical Literacy-Oriented Subject Materials

為培養學生能適應快速變遷的社會及面對未來挑戰，教學設計必須考慮相關的知識、技能、思維、態度等學習要素。而數學常展現於日常的活動、科技的發展、社會及經濟現象的解讀等生活及各種研究中，因此，「數學素養」一詞成為國民基本教育課程中的重要理念。然而，許多文獻都在探討數學素養的意涵及其目標，卻很少說明培養數學素養的教材設計。本研究從彙整現有文獻中的數學素養意涵，從而提出「知」識、應「用」、「觀」點與「學」習是數學素養的構成要素，而教材設計可從現實問題轉譯為數學問題，利用數學結果詮譯情境意義的學習迴圈，並配合APOS 理論之起源分解說明數學知識的認知發展，發展以數學「知」識為核心，發展具內含及外顯特質的「用」、「觀」、「學」之素養導向教材。在此架構中，素養教材設計不限於同時包含迴圈中的所有元素，且知」、「用」、「觀」、「學」是教材設計之方法而非必須依循的發展順序，教材設計者應考量學習者的認知及數學概念的發展，設計配合知識的應用、對數學的觀感、終身學習的思維及技能為導向的數學教材。本研究提供設計實例以說明教材設計的可能方向，並由此提出未來相關研究建議。 To help students’ adapt in a rapidly changing society, subject materials should incorporate learning components that feature knowledge, skills, thinking, and attitudes. Mathematics is commonly used in daily life, and it is vital for technological development and explaining economic phenomena. The term “mathematical literacy” is regarded as the main idea behind compulsory education in Taiwan. However, studies have often explored the objectives and implications of the mathematics curriculum rather than the design of subject materials for mathematical literacy. In this paper, based on a review of the literature, we propose that knowledge, application, disposition, and learning are the four components of mathematical literacy. Mathematical literacy-oriented subject materials can be designed based on a learning loop, which first translates real-life problems into mathematical problems and then uses the mathematical results to explain the context. This learning loop framework illustrates cognitive development of knowledge based on the genetic decomposition of APOS theory. The framework can be used to develop literacy-oriented mathematical subject materials with knowledge at the center, incorporating application, disposition, and learning and possessing implicit and explicit features. When designing teaching materials, some components can be excluded. The components of knowledge, application, disposition, and learning serve as the approach to teaching design rather than the sequence of cognitive development. The designers of subject materials should consider the development of both learners’ cognition and understanding of mathematical concepts. Moreover, the skills of knowledge application, mathematical perspective, and lifelong learning should be included in subject materials. Herein, several examples of possible directions for the design of subject materials are proposed, alongside suggestions for further investigations.