数学应用题的情境设置与问题提法——对高中新教材中一道应用问题的疑问与讨论

Contextual design and posing of the application problems in mathematis

在数学教学中,培养学生掌握其所学内容的适用条件的重要方法之一,就是让学生解应用题.但这需要对相关问题的准确描述.然而,现在有许多在设计上存在严重缺陷的应用题流行于中学课堂,致使学生在学习数学的过程中更加困惑.笔者将对高中数学新教材[1]中的一道应用题及其解答[2]提出质疑,并予以探讨和分析.指出该题中的条件设置中存在严重缺失,且所提问题也有逻辑错误,由此说明在应用题的编制过程中,其情景设置与设问之间的协调性是必须特别予以注意的重要环节.

In the mathematic instruction, solving application problems is one of the important methods for fostering the students＇ ability to grasp the conditions of a mathematic theory. But this needs accurate description for an appliction problem. Some application problems which are very popular in the middle school classes have defaults in design which puzzle students. This paper analyses an application problem appeared in the new textbook for senior middle schools, and points out that there are serious deficiencies and logic errors in contextual design ,and emphasizes that the consistency between contextual design and posing are very important.