中文摘要：

自然演绎的本质在于证明中可以随时引入假设。在总结出各个自然演绎系统的几个区别性特征之后,本文提供了一个自然演绎的教学案例,案例通过采取一个有更多“有假设推演规则”的自然演绎系统,并用证明序列的左侧序号来编撰和追踪证明者的证明思路和证明策略,从而更有利于学生熟悉和掌握各种逻辑证明方法和证明策略,有助于激发学生自主思考,提高学生逻辑思维能力和元定理的证明能力。

英文摘要：

The essence of natural deduction lies proofs. After summarizing some distinguishing features in that any assumptions can be introduced during our of different Natural Deduction Systems, this paper provides a teaching case on natural deduction, in which there are more deductive rules with assumptions. Further- more, by making use of the serial numbers of proof sequences, this paper encodes and keeps track of their thinking and strategies of the demonstrators. This paper argues that the said approach, which is more advanta- geous for the students to grasp the logical methods and proof strategies, is helpful to stimulate their independent thinking and develop their own proofs, and consequently to improve their logical thinking ability and abili- ties on proving metatheorems.