鸡兔同笼问题“假设法”的由来

Origin of “Hypothesis Method” for Chicken and Rabbit in the Same Cage

“鸡兔同笼”问题最早可追溯至古代经典《孙子算经》,其独特的数学魅力使得许多小学算术应用题都可以转化为此类问题,而其经典的解法——“假设法”更是被广泛应用。然而,在当前的教学设计中,我们常常直接告诉学生使用“假设法”来解答这类问题,却忽视了对其背后的逻辑和原理的深入探讨。这种做法显然与“数学需要理解”的核心学习观念背道而驰。因此,本文旨在通过揭示“直观画图”和“直接算式”中所隐含的“假设法”思想,进一步明确和深化对“假设法”的理解和应用,从而为解决“鸡兔同笼”问题提供更为全面和深入的视角。

The problem of “chicken and rabbit in the same cage” can be traced back to ancient classical Sun Tzu’s Arithmetic Classics. Its unique mathematical charm makes many primary school arithmetic application problems can be transformed into such problems, and its classical solution “hypothesis method” is widely used. However, in the current instructional design, we often tell students to use “hypothesis” to solve such problems directly, but neglect the in-depth discussion of the logic and principle behind it. This practice obviously runs counter to the core learning concept of “mathematics needs to be understood.” Therefore, this paper aims to further clarify and deepen the understanding and application of “hypothesis method” by revealing the idea of “hypothesis method” implied in “visual drawing” and “direct formula,” so as to provide a more comprehensive and in-depth perspective for solving the problem of “chicken and rabbit in the same cage.”