A Study Of Students' Understanding Of The Fractional Meaning

The fraction is the key point as well as significant difficulty during the primary school.At the same time,fraction is the basis of ratio,percentage and specific value.Up to now,researches on the fraction are mainly the analysis of the concept of fraction and the analysis of the fractional applied problem.Those are discussing the teaching of fraction from the perspective of test-taking.Mathematical education is not only to teach students to memorize formulas and the problem solving methods,but also to teach students how to think logically.Mathematical education should make students to experience the pleasure of thinking training.That pupils know the fraction does not necessarily mean they can understand the concept of the fraction.Meanwhile,that pupils can correctly calculate fractional computations does not necessarily mean they can understand the meaning of fractional computation."How do pupils understand the meaning of fractions?" and "what level do students understand the meaning of fractions?" are the concerned topics of our study.In this paper,questionnaire is used to investigate students' understanding of the following meanings about fraction:(1)the meaning of fractional concept;(2)significance of the basic property of fractions;(3)the meaning of fractional operation.Among them,the meaning of fractional computation is divided into three levels.The first level.one can understanding essence of fractional operations.The second level is to general models of fractional operations.The last level is explaining algorithm.The questionnaire is designed based on the above three dimensions,which includes 9 topics.In order to study how students understand the fractional meaning,questionnaires were issued to the fifth and sixth graders of a primary school in Wuhan as well as three classes for grade 7 of a junior high school in Wuhan.A total of 350 questionnaires were issued and 324 questionnaires were recovered,among which 314 are valid questionnaires.The results of the collected data show that the students' understanding of the three dimensions of the fraction is different from that of grade and age,and there is no difference in the understanding level between male and female students.We can see that students' understanding of the meaning of fraction is constantly developing.It also shows that all investigated students grasp the basic concept of fraction and fractional operations as well as basic property of fractions well.However,their explanation for reasons why it can do so were not good enough.It reflected the characteristics of students of China.In China,pupils' basic memorization and calculation ability are outstanding,but their lack of ability to analyze the problems form of grim...