初三学生关于无理数的信念的调查研究

Investigation of Junior Students’ Beliefs about Irrational Numbers

从不可公度的存在性、学习无理数的必要性、无理数作为数的确定性以及无理数的不可循环性4个方面调查了初三学生关于无理数的信念．结果显示：学生对不可公度性的信念表现出与历史上数学家极大的相似性；40％多的学生缺乏对无理数学习的必要性的认识；大多数学生承认无理数是数，但近60％学生对无理数的无限不循环性缺乏坚定的信念．因此，教师在教学过程中，应注重知识发生的过程；应注重知识的来龙去脉；应注重学生对概念的理解．

This paper presents a study of grade 9 students＇ beliefs about irrational numbers, where four aspects are considered： the existence of incommensurability, the necessity of learning irrational numbers, the certainty of irrational numbers as actual numbers and infinite non-repetition of irrational numbers. It appears that students show great parallelism of beliefs about incommensurability compared with mathematicians in history. More than forty percent of students are devoid of knowing about why they must learn irrational numbers. Most students recognize that irrational numbers are actual numbers, but nearly sixty percent of students lack strong beliefs about infinite non-repetition of irrational numbers. Therefore in the process of teaching teachers should focus on the process of knowledge generation; should focus on the ins and outs of knowledge; should focus on students＇ understanding of the concept.