數學素養導向的任務設計與教學實踐──以發展學童的數學論證為例

Task Design and Implementation for Mathematical Literacy: Developing Students’ Mathematical Argumentation

本文旨在提供國小階段十二年國教素養導向任務設計與教學實踐之範例，作為教科書編撰者落實到數學教材設計之參考，並協助教師瞭解課堂中數學素養培養的作法。本文首先探討素養內涵中數學論證的意義與重要性；其次，以數學論證為教學目標及以四年級「認識各種三角形及其性質」為教學脈絡，設計數學臆測任務，來詮釋從官方到書面課程的轉化；並以教師在課堂中的教學實踐說明從書面到實踐課程的轉化。本文提出數學臆測是培養素養內涵中數學論證的途徑之一。數學臆測能幫助學童建立較嚴謹的數學知識，能引出一叢相關的數學性質或概念，能培養學童提出證據以取信他人，以及能舉出反駁的例子或證據推翻他人的觀點之民主素養。本文於文末提供建議給教科書編撰參考。

This paper provides an exemplar for textbook writers and teachers to design tasks for mathematical literacy and implementing them into classrooms. Mathematical literacy is the kernel focus of the current innovations of 12-year compulsory education. This paper begins by briefly introducing the significance and the meaning of mathematical argumentation. Then, a task design for conjecturing integrated into mathematics content with recognizing various triangles and its properties as an example to illustrate the meaning of transforming intended curriculum into written curriculum. It is suggested that mathematical conjecturing is an approach to evoke mathematical argumentation as one aspect of mathematical literacy. Mathematical conjecturing is an approach for illustrating mathematics as a language and mathematics as scientific pattern. Mathematical conjecturing has a power of construing a series of connected mathematics properties or mathematics concepts as an approach to enhancing mathematical literacy. Moreover, mathematics as a language and mathematics as a pattern of science are achieved via conjecturing. Students convince others via warrants and reject the arguments of others using rebuttals or they support others’ arguments via warrants or backing. This paper concludes with remarks for mathematical textbooks for textbook editors and teachers.