美国早期教科书中的无理数概念

Concept of Irrational Numbers in Early Western Textbooks

1820—1969年出版的100种美国中学和大学代数教科书先后给出了8种不同的无理数的定义,20世纪20年代开始,才出现用＂无限不循环小数＂定义无理数.早期教科书中无理数概念的演变为今天的教科书编写和无理数概念教学,提供借鉴.教科书编写应体现无理数定义的多样化,并体现无理数是不能用整数和分数表示的数.可借鉴无理数定义的发展历史,运用重构历史的方式设计无理数概念教学,促进学生对无理数以及实数体系的整体理解和掌握.

During the period 1820-- 1969, one hundred algebra textbooks in America＇s middle schools and colleges had given eight definitions of irrational numbers. The definition that irrational numbers were infinite non-repeating decimals began at 1920s. The previous evolution of the concept of irrational numbers provided reference for the present textbook compiling and teaching. The newly-compiled textbook should reflect the diversity of definitions of irrational numbers and reveal that irrational numbers couldn＇t be expressed by integers and fractions. Furthermore, drawing on the development of irrational number, we could reconstruct the history in class to design the concept teaching of irrational numbers to promote students＇ overall understanding and grasping of irrational numbers as well as the real numbers.