数式的一致性和式的特殊性

The Consistency of “Number and Algebra” and the Particularity of Algebraic Expression

摘要: 数与代数是基础教育阶段的主要对象并具有丰富的内容，是数学学习和研究的基础。在新课标实施过程中，不少专家学者特别强调了数与式的整体性学习。在数与代数的学习中，在研究策略上关注数与式的一致性是重要的，但在具体学习过程中还要关注到代数式的独特性，只有理解代数式相对于数来说其特殊性所在，才能深刻理解从数到式的思维飞跃。把代数式理解为可以按照任意规定的法则处理任意的符号及其关系的一个符号的体系，这是在算术中从未考虑也难以实现的方法。

Abstract: Number and algebra is the main object of basic education stage and has rich content, is the foundation of mathematics learning and research. In the process of implementing the new curriculum standard, many experts and scholars have emphasized the integral learning of number and formula. In the study of number and algebra, it is important to pay attention to the consistency of number and formula in the research strategy, but it is also important to pay attention to the uniqueness of algebraic expression in the concrete learning process. Only by understanding the particularity of algebraic expression relative to number can we deeply understand the thinking leap from number to formula. To understand an algebraic expression as a system of symbols that can deal with arbitrary symbols and their relations according to arbitrary rules is a method that has never been considered in arithmetic and is difficult to realize.