Journal of Basic Education


2007.第16卷第1期(Vol. 16 No. 1).pp. 81–96


How to Teach Heron’s Formula? An HPM Episode

洪萬生、蘇俊鴻(Wann-Sheng HORNG & Jim-Hong SU)


本文第二作者蘇俊鴻利用二至三節課的時間,為兩班高一學生(每班30人)提供「海龍公式」的三種證明:(1) 利用餘弦定律的現代教科書證明,(2) 清初數學家梅文鼎的證明,(3) 海龍自己的證明。並在課後請學生填寫回饋單,兩班共回收50份。本文將根據此教學插曲,說明HPM 介入的教學活動可能之影響。我們發現在HPM的引導下,無論教師或是學生才有可能從教材單元的知識內容中獲得某種程度的解放,得以可能「鬆綁」或「顛覆」教材中較「制式的」(conventional)面向,此次海龍公式HPM教學插曲正是一個例證。



The second author here, Mr. Su, used two to three class hours to introduce three proofs of Heron's Formula to two classes of tenth graders (30 students in each class): (1) the proof in modern textbooks using the law of cosine, (2) the proof by early Qing Dynasty mathematician Mei Wending, (3) the proof by Heron himself. He then asked his students to complete a feedback questionnaire, and a total of 50 questionnaires were returned. Based on this teaching episode, this article explains the possible influences of teaching activities integrated with HPM. We found that under the guidance of HPM, it is possible for the teacher or the students to have a certain level of "liberation" in the knowledge content of the textbook, to "untie" or "overthrow" the more "conventional" aspects of the textbook. This teaching episode of Heron's Formula illustrates that.