Investigation of Junior Students’ Beliefs about Irrational Numbers

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.