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An Attempt at improving some verbal Expressions in Mathematics Education

提高数学教育中某些言语表达的尝试

基本信息

批准号：
01580284
负责人：
MORI Masao
金额：
$ 0.83万
依托单位：
CHUO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1989
资助国家：
日本
起止时间：
1989 至 1991
项目状态：
已结题

项目摘要

Recent experiments prepared by the author have shown that more than 90% of the subjects of the experiments think they themselves do not have satisfactory understanding about "the necessary condition and the sufficient condition" given in Japanese. These Materials are usually taught in the tenth grade in Japan. And most of our subjects are 1st and/or 2nd grade science course students of two private universities located in. The metropolitan area. Our experiments also revealed that more than 70% of the subjects bear a correct memory of the statement, however, more than 80% were not confident about the validity of their own memory. It means that they know no measure to check their memory.Most of teachers or authors of mathematical textbooks seem to be aware of this kind of students' perplexities caused by the description. Nevertheless, the present author thinks that a large part of their interest is to accustom students to the usage rather than to try to give alternative good expressions.He proposes a concrete procedure, namely to provide improved expressions, and intends to diminish this kind of students' hardship.He discusses the typical case where the following statements are valid:(1) q is a necessary condition for p.(2) p is a sufficient condition for q.and introduces as usual, subsets P and Q of some large set U, which are characterized by the conditions p and q, respectively, and are consequently supposed to satisfy the relation PCQ.Our experiments pointed out that students' central complaint about the Japanese counterpart of the sentences (1) and (2) is that it is hard for them to discern between the necessary condition and the sufficient condition even when they clearly understand the inclusion relation PCQ.Our proposed texts for the definition of these conditions have been tested to show that they help more than 40% of our subjects to grasp the meaning of the conditions and to distinguish them.

作者最近准备的实验表明，90%以上的实验对象认为他们自己对日语中给出的“必要条件和充分条件”没有令人满意的理解。这些材料通常在日本十年级教授。我们的大多数科目都是位于大都市区的两所私立大学的一年级和/或二年级科学课程的学生。我们的实验还显示，超过 70% 的受试者对这句话有正确的记忆，但超过 80% 的受试者对自己记忆的有效性没有信心。这意味着他们不知道如何检查他们的记忆。大多数教师或数学教科书的作者似乎都意识到这种描述所引起的学生的困惑。尽管如此，作者认为他们的兴趣很大一部分是为了让学生习惯用法，而不是试图给出替代的好的表达方式。他提出了一个具体的程序，即提供改进的表达方式，并打算减少学生的这种困难。他讨论了以下陈述有效的典型情况：（1）q是p的必要条件。（2）p是q的充分条件。并引入像往常一样，一些大集合U的子集P和Q，分别由条件p和q表征，因此应该满足关系PCQ。我们的实验指出，学生对句子（1）和（2）的日语对应部分的主要抱怨是，即使他们清楚地理解包含关系PCQ，他们也很难辨别必要条件和充分条件。我们提出的这些条件定义的文本是测试表明，它们帮助超过 40% 的受试者掌握条件的含义并区分它们。