试拟中学数学第一章

为了使中学数学改革做到“少而精”和“深入浅出”,本文试拟了“第一章”前三节的一个提纲。该章标题为《量与数》,其中利用“量之比”定义实数并证明其算律。此章不但是代数而且是几何之基本。此外,也为极限及微积分做一良好准备。

A Proposal for Chapter One of Middle-School Mathematics

To reform middle-school mathematics achiv ing the requirements "fewer but better" and "deeper but easier", an outline of the first three sections of "Chapter One" is suggested in this note. This chapter will bear the title"Quantities and Numbers", in which real numbers will be defined as ratios of quantities and the laws of operations proved. It will form a basis of both algebra and geometry. Besides, it will be a good preparation for the limit concept and the calculus.