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数学是一门逻辑严谨性很强的学科,它的知识系统性强,前面的知识是后面知识的基础,后面的知识是前面知识的延伸与发展。《数学课程标准》把“能通过观察、实验、归纳、类比等获得数学猜想”作为推理能力的一种表现。类比是一种相似,它是从一种特殊到另一种特殊的推理,实现从具体到抽象,从旧知识到新知识,从已知领域到未知领域的迁移过程。这个过程要经历分析、类比、猜想、得出新结论,这就是创新的过程,数学知识的迁移过程。
Mathematics is a discipline with strong logical rigor. Its knowledge is systematic. The former knowledge is the basis of the latter knowledge. The latter knowledge is the extension and development of the previous knowledge. The Mathematical Curriculum Standard takes “the ability to obtain mathematical conjectures through observation, experimentation, induction, analogy,” as a manifestation of reasoning ability. Analogy is a kind of similar, it is from a special to another special reasoning, from concrete to abstract, from old knowledge to new knowledge, from known to unknown areas of the process of migration. This process has to go through the analysis, analogy, guess, come to new conclusions, this is the process of innovation, mathematical knowledge transfer process.