| Number sense is the students’general understanding of the numbers and the ability to use this understanding to make mathematics judgment and adopt effective strategies to deal with the problems concerning numbers and operations. It is one of the core concepts in the new mathematics curriculum standard has been emphasized, and one of the focus abilities concerned by the primary school "number and Algebra".This study according to the number sense" ability ", is divided into "understanding digital significance and relationship skills","comparative figures relative size of ability","to understand the operation of the digital sense and ability to influence","the development of various calculation methods and determine the answer reasonable ability","understanding and operation of multiple representations of ability" five components. The main purpose of this study is to learn about students’in the village’s number sense during the second period in the primary school, seeing whether it has meet the requirement proposed in the second period of mathematics curriculum standard’s. Analyze the students’wrong answers to the tests, and classify the errors and find out the reasons of the errors. This study methods is the literature research and investigation, and apply the adaptation of "students’ number sense test" as research tool, and take combination of the test volume and interviews in three rural primary schools(Longxi County Weiyang village school) in Gansu province, we tested256students of the second period and interviewed some students. To analyze the data, we use descriptive statistics and independent samples group T test and post hoc test (LSD). However, the difficulty of this study is how to prepare the number sense test. And then we come to the following conclusion:(1) Overall, the average test scores of student’s are relatively low, student’s ability of number sense is generally not high. Student’s ability of number sense is largely influenced by grades, meanwhile, student’s ability of number sense is increasing gradually to the grade, and there is a significant difference between the three grades.(2) Upon the five components of number sense. There is no significant difference between the fifth grade and the sixth grade in Their abilities to compare figures and to develop calculating tactics and judge the rationality of answers.The ability to understand the operation’influence on meanings of numbers and multiple representation of numbers and operation is not significant different between the fourth grade and the fifth grade. There are significant differences between the three grades in the other components, in addition to this; students perform better in the higher grade.(3)Among the components of number sense, all the students performed best in the ability to compare figures, followed by the ability to understand multiple representation、develop kinds of calculating tactics and judge rationality of answers understand the operation meaning and figure relationship.The ability to understand the operation’influence on the figure’s meaning is the worst.(4)There are three kinds of wrong answers among students:the traditional algorithm, the number sense deletion type and escape type. Students’number sense is deeply influenced by the traditional manual calculation, students who get the wrong answer seem unable to develop independent thinking and have their own thought. The number sense deletion type is the most important but serious one, if students do not abandon their wrong conception, the development of their number sense will be influenced, even their other mathematics ability. As for the escape kind, it was a small portion, but it is also one of the wrongs which is difficult to correct.Based on the above results, the author gives some suggestions for reference. Firstly, mathematics teachers in primary school should be clear about the importance of cultivating students’ number sense. Secondly, the teaching of "understanding the numbers" should pay attention to the significance of the number and the relationship between numbers; thirdly, pay attention to the operational meaning of numbers and teaching of algorithm; fourthly, strengthen the cultivation of students’awareness of estimation, focusing on the diversity of estimation strategy. Cultivation of number sense is a long-term process; it needs teachers’wonderful and targeted design in daily teaching, and then students’ ability of number sense would be improved.This study tries to have some innovation in the following two aspects:firstly is the balanced development of education reform, thus this study pay attention to the students in the western rural area; secondly is this study adopts empirical survey research methods, on the basis of quantitative analysis of students’ number sense errors were classified and discussed.There are some shortcomings because of the professional knowledge and research conditions and other factors, such as the sample is small and the data are really limited, and the test have not pay much attention to the students in different grades. Above all, the conclusion of this study need to be cautious in the extend... |
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