波利亚(George Polya，1887-1985) 以研究数学方法论闻名。他的数学方法论以发展解题技巧为核心。在他看来，所谓数学能力就是解决问题的才智。因此，其工作通常被归入数学教育而非数学哲学。同时，波利亚也是上世纪经典分析的名家，其工作领域还包括概率、数论和几何等。

波利亚在Mathematical Discovery (John Wiley & Sons, 1965)中提出“教师十诫” (Vol. 2, p.116)

Ten Commandments for Teachers

1. Be interested in your subject(对你的课程感兴趣).

2. Know your subject(理解你的课程).

3. Know about the ways of learning: The best way to learn anything is to discover it by yourself(理解学习的方式：学任何东西的最佳方式是自己去发现).

4. Try to read the faces of your students, try to see their expectations and difficulties, put yourself in their place(设法读学生的脸，明白他们的期待和困难，设身处地).

5. Give them not only information, but “know-how”, attitudes of mind, and the habit of methodicat work(不仅给他们信息，而且给“技能”、心态和有条不紊的工作习惯).

6. Let them learn guessing(让他们学会猜测).

7. Let them learn proving(让他们学会证明).

8. Look out for such features of the problem at hand as may be useful in solving the problems to come－try to disclose the general pattern that lies behind the present concrete situation(注意手头问题的某些特征，这些特征有助于解决今后的问题，设法发现在现在具体情境背后的一般模式).

9. Do not give away your whole secret at once－let the students guess before you tell it－let them find out by themselves as much as is feasible(不要马上给出你的整个秘密，让学生在你告诉他们之前猜测出来，让他们尽可能地自己发现).

10. Suggest it, do not force it down their throats(建议，而不是强迫性地灌输).

虽然波利亚是数学教师，但“十诫”体现了启发式、发现式教学的普通原则。对力学课教学也有借鉴作用。特别是尽量用推导的方式，避免用证明的方式。前者结论未知，后者结论已知。例如，Lagrange方程，明确最初的出发点是D'Alembert原理，最终的目标是建立广义力与动能(用广义坐标和广义速度表达)之间的关系。然后就可以尝试推导。需要时再导两个Lagrange经典关系。当然，动能运算形式不唯一，还有Nielsen方程。