课前思考:认识负数,教材中虽然没有给正数、负数下定义,只是通过列举的方式让学生知道怎样的数是正数,怎样的数是负数。然而,对于负数,学生并不是一概不知。在许多学生的心中,对负数已经有初步的感觉。若阅读了德国数学家斯蒂菲尔的《整数算术》著作就会发现,构建负数的理性认识,困难之处不在于概念本身的高度抽象性,而在于人怎么跨越和扩展自己的已有认识。因为从现代数学数系扩展 Thinking before class: Understand negative numbers. Although there is no definition of positive numbers and negative numbers in the textbooks, students can only know what kind of numbers are positive and what is negative by enumeration. However, students are not always aware of negative numbers. In many students’ minds, there is already a preliminary feeling of negative numbers. If we read the book “Integer Arithmetic” by German mathematician Stiefel, we will find that the difficulty in constructing a rational understanding of negative numbers lies not in the high degree of abstractness of the concept itself, but in how people cross and extend their existing understanding . Because from the expansion of modern mathematics