摘要
对大学新生开展关于极限的无穷观、极限印象和极限概念三方面的调查发现,大多数学生对无限的理解是潜无限的,他们对极限的认识强烈依赖渐近线印象,往往会被表面非本质的特征所迷惑,无法正确认识极限过程与结果之间的辩证关系.这既是极限发展的历史缩影,也是学生认知方面的局限所在.因此,必须从培养正确的无限观及构建标准印象入手,改进教学.同时,以历史为指导,让学生经历"胚胎式"发展过程,促进学生对极限的全面理解.
Survey on freshmen＇s infinite view of limit, limit impression and the concept of limit found that many students understand infinite as potential infinite; they strongly rely on asymptote when understanding the concept of limit, and they are usually puzzled by external facture so they can＇t understand the dialectical relation of potential infinite process and actual result. This is not only the epitome of the limit development, but also affects the students＇ cognitive limitations. Therefore, we must improve teaching methods to begin to cultivate students＇ correct infinite view and constructing standard limit impression. At the same time, with history as a guide, promote a developing process like the growth of embryo in students to help them understand limit comprehensively.
出处
《昆明学院学报》
2011年第6期12-16,共5页
Journal of Kunming University
关键词
极限
无限观
极限印象
潜无限
实无限
标准极限印象
非标准极限印象
limit
infinite view
limit impression
potential infinite
real infinite
standard limit impression
non-standard limit impression
