摘要
除极限外，在《数学分析》中比极限更早的另一个重要而基本的概念是上确界（下确界）．这个概念和极限一样，是数学分析中的原始概念．原始概念的一个重要特征就是比较抽象，所以原始概念的教学是数学分析和高等数学教学的重点和难点．原始概念的5步教学法为：（1）以描述性定义为先导，引出数学语言的严格定义（是什么）；（2）与以往概念相联系，说明概念的来源（为什么）；（3）通过实例进一步解释概念，帮助学生理解概念的本质；（4）通过概念的运用，知道概念的用途；（5）与以后概念的相联系，拓展概念的深度和广度．
Excepting the limit concept, the another important and basic concept is the supremum （infimum） in the Mathematics Analysis and it existed earlier than limit concept. It is like the same of limit, they are the original concepts in the mathematics analysis. The one of important characters of original concept is very abstract. So the teaching of the original concept is the role point and difficult point in the teaching of mathematics analysis and advanced mathematics. This paper puts forward the five steps teaching method of the original concept basing up the teaching of supremum： I. Put the describing definition as the start, then give the strict definition of the mathematical language （What it is）; 2. Take the relation with the former concept, explain the origin of the concept （why it is）; 3. Give more explain of the concept through the real exarnple, to help the student understand the nature character of concept; 4. Know the application of the concept through the using of the concept; 5. Make relation with the later concept, to explore the range and the depth of the notion.
出处
《数学教育学报》
北大核心
2013年第4期94-96,共3页
Journal of Mathematics Education
基金
国家自然科学基金——自反算子代数与半积差(11171244)
关键词
上确界
原始概念
数学语言
supremum
original concept
mathematical language
