Research On Junior Middle School Students' Understanding Of Real Numbers

There are three important expansion in the development of numberal system in the history.The study of real numbers is a critical period in junior high school,which lays the foundation of follow-up study.In this paper,it uses questionnaires and interviews to study the understanding of junior high school students.And it explores the causes of barriers,try to provide sugguestions for teachers in effective teaching and for students to study well.Get the following conclusions:(1)In the concept of real numbers, Juniors'understanding are mostly affected by the relocation of rational .Nearly 20% students have different understanding of the essence between rational number and irrational number.(2) In the classification of real numbers, Juniors on the negative and real numbers are more well-defined classification of the irrational number and integer relatively fuzzy classification.(3) In the denotation of real numbers, Juniors will realize that the real axis with a number of one-to-one relationship between points and can express in a few axes,Nearly 70% students can't idertify the basic of symbolic language and its object.(4) In operation real numbers, Juniors are used to using calculators to deal with the root of the irrational numbers. There are some problems in operation real numbers,such as the order of the main computing,the unknown of the nature,the error-prone when in parentheses,the non-standardized in the product about numbers and radical expressin.(5) In the characteristic of real numbers,most Juniors have a high awareness on four computing rational,while they have low awareness on irrational numbers.(6) In the application of real numbers,most Juniors can abstract the mathematical problems from the practical problems and select the correct strategies.But their operation ability still need to be improved.The main obstacles in understanding real numbers of Juniors:(1)The abstraction of the real numbers'concept.(2)The way of thinking in math and the psychologic impact in study.(3)The convergence. of Elementary and Middle school.(4)The usage of the current teaching materials.(5)Some unreasonable exercise .According to these,comes to the recommendations:Adjust the teaching sessions in teaching real numbers,grasp the teaching standards of the curriculum accurately,pay more attention to the process of math knowledge and guide actively and thansfer effectively.