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新编全日制十年制《中学数学教学大纲》指出:“……对于容易产生混淆的概念,要引导学生用对比方法认识它们的区别和联系。……”这个意见提得十分中肯! 我在数学课中,也常常采用对比式进行教学,不仅讲授新概念时用得上,就是研究算理算法、分析论证、总结复习等,也都十分有效。粗略归纳起来,觉得至少有以下七个方面,可资对比。一、语言对比如所周知,讲述数学概念,必须要求高度精确的语言,亦即要用最简洁的话语,不漏、不重地说出概念的全部数学内容。我认为,这种语言,应该包含两个方面,这就是日常语言与数学语言,而尤其要重视数学语言。我在教学中,便常常将日常语言与数学语言并用,采取对比法,把概念的内容翻译为数学式子交给学生。
The new full-time 10-year “Middle School Mathematics Syllabus” pointed out: “... For the easily confusing concept, we must guide students to use a comparative method to understand their differences and connections....” This opinion is very pertinent! In mathematics class, it is also often used in comparative teaching, not only when teaching new concepts, but also in studying arithmetic algorithms, analysis and argumentation, reviewing and reviewing, etc., which are also very effective. Roughly summed up, I feel that there are at least the following seven aspects that can be compared. First, language pairs, for example, are well-known. When it comes to mathematical concepts, they must require highly precise language. That is, they must use the most concise discourse to express the entire mathematics of the concept without leakage or emphasis. I think that this language should include two aspects. This is the daily language and mathematics language, and especially the emphasis on mathematical language. In my teaching, I often use everyday language and mathematics together and adopt a comparative method to translate the content of the concept into a mathematical formula for students.