小技巧與大智慧
解數學題時，時常會碰到各種刁鑽的做法，令人摸不著頭腦，令學習者望而生畏，對數學敬而遠之。
波利亞（Pólya）叫這些做「把戲」，但如果把戲可以重複使用，就變成了方法。
“An idea which can be used only once is a trick. If one can use it more than once it becomes a method.”
Pólya, G., & Szegö (1978). Problems and Theorems in Analysis I (trans. D. Aeppli), p.viii. Berlin: Springer-Verlag.
教數學，應避免介紹太多把戲，免嚇怕學生。相反地，能明白的，能重複運用的方法，令人增長智慧，也可帶來滿足感，多學無妨。
關鍵是：能點出把戲的一般性，教了無害；辦不到的，就只會令學生死記，打擊學習動機。
測考的意義
“The main purpose for a test is not to measure something, it is to teach something.”
George Pólya
Taylor, H., & Taylor, L. (1993). George Pólya: Master of discovery, p.109. Palo Alto, CA: Dale Seymour.
學習無捷徑
“All practical teachers know that education is a patient process of the mastery of details, minute by minute, hour by hour, day by day. There is no royal road to learning through an airy path of brilliant generalisations.”
Alfred North Whitehead
見 p.6 of
Whitehead, A. N. (1929/1967). The aims of education and other essays. New York: Free Press.
相傳 Euclid 也曾有類似說法：
“There is no royal road to geometry.”
見 p.25 of
Stillwell, J. (1989). Mathematics and its history. New York: Springer-Verlag.