1.关于破代数体系建立新体系的問題 现行中学数学教材,把算术、代数、几何、三角分科設立,造成內容孤立割裂,繁琐重复,因此应該打破这个体系,但破了以后是否可以建立一个以函数为中心的体系呢?北师大的九年一貫制方案中从六年級起就学习初等函数,把方程作为函数的零点来处理,这样虽然解决了过去中学代数中支离破碎的現象,但是,这样的体系是否可行呢?我們认为新的体系必須符合认識发展的过程,黑山小学教学改革成功的經驗告訴我們,抓住知識的规律是主要的,但是,先掌握哪些知識后掌握哪些知識成为能否多快好省的关鍵,先要儿童掌握函数概念,再去掌握一次函数,掌握了一次函数后再去掌握一次方程組,这样的处理是不太合适的。我们认为,根据实践論的精神,人們的认識是先看到事物的片面,看到事物之间的外部联系,然后才能从感性认識提 1. The problem of creating a new system for breaking algebraic systems The current middle school mathematics textbooks set up arithmetic, algebra, geometry, and trigonometry to isolate the contents and cumbersomely repeat them. Therefore, this system should be broken, but whether or not a system can be established after it is broken A function-centric system? In the nine-year program of Beijing Normal University, the elementary functions were studied from the sixth grade onwards, and the equations were treated as the zero point of the function. Although this solved the fragmentation phenomenon of middle school algebras in the past, however, Is this system feasible? We think that the new system must be in line with the process of cognitive development. The successful experience of primary school teaching reform in Montenegro tells us that the law of grasping knowledge is the main one, but what knowledge is acquired after mastering it first? The key to being able to save more quickly is to have children master the concept of functions, then master the functions once, master the functions once, and then master the equations once again. Such treatment is not appropriate. We believe that according to the spirit of practice, people’s understanding is that they first see the one-sidedness of things and see the external links between things, and then they can