We make little or no provision for students to play an active and generative role in learning mathematics and we teach mathematics as if we expect that students will never have occasion to invent new mathematics.

• 对学生，我们很少甚至没有提供机会，让他们在数学学习过程中发挥积极性和创造性，我们讲授数学，仿佛期望着学生不会有机会创造数学的新领域。