中等教育的一些重要的無理數教材研究

在筆者從事教職以來，發現學生從國小至國中第一個面對到的問題就是由有理數轉換到無理數的這個階段，總是容易有迷思，造成學習上的困擾，因此本論文主要是整理中等教育當中常見的無理數教材及相關的數學故事，先是從國中的根號開始，然後再加上圓周率π及數學常數e，這兩個數在高等數學中亦定義為超越數，希望能藉由這些教材及數學故事的整理，能讓引起學生的學習動機，進而讓教學成效更佳。

關鍵字

無理數；根號；圓周率；數學常數

並列摘要

Since the author started teaching, I found that the first problem students face from elementary school to junior high school is the transition from rational numbers to irrational numbers. It is always easy to be confused and causes learning difficulties. Therefore, the thesis mainly organizes the teaching materials about the irrational numbess and related math stories which are commanly seen in secondary education. Start with the root number, along with the pi and the mathematical constant e, which are also defined as transcendental numbers in advanced mathematics. I expect through the organization of these teaching matheriasl can teachers arouse students’motivation to learn, and help them teach more effectively.