Research On The Development And Character In Number Sense Of The Pupils

"Number sense"has become a frontier subject for enquiry in psychology and mathematics education since Dantzig formally put forward the terminology, which has been studied several decades outside China. In 2001, China regulated for the first time that number sense should be the learning contents for day schools in the course of mathematics in"Criteria for Compulsory Education of Mathematics (in experiment)"."Number sense", the common phrase in the western mathematics education, entered the mathematics curriculum at the stage of compulsory education of China and has become a core concept. More and more educators in mathematics began to take notice of number sense and raised their points of views, suggestions and solutions to them in the perspectives of both theory and practice. However these studies did not conduct significant investigations of the situations of number sense in primary schools of China, which may provide the present situation of number sense of primary school pupils in China. A further systematic and deep-going investigation is required to provide the present situation of number sense of primary school pupils. Theoretically speaking, the enquiry into the connotation and essential elements of number sense needs furthering; practically speaking, a systematic project on the cultivation of number sense of primary school pupils has not formed, in particular, the problem of number sense of primary school pupils in the mathematics classroom has not aroused the sufficient attention of the practitioners.I have, in the current literature, found that the past development and the feature research on number sense of primary school pupils concentrated more from the psychological perspective, mostly focusing on it randomly and partially and lacking systematic and all-round study of the development law and the features of number sense of primary school pupils from the perspective of mathematics education, which then lacks the basis for the construction of the mathematics curriculum in primary schools. Therefore, my research makes an attempt to analyze the connotation and the essential elements of number sense of primary school pupils from the perspective of the curriculum, to observe the development law and the features of number sense of primary school pupils and divide the development stages and put forward valuable suggestions for the mathematics curriculum design and material development, and the cultivation of number sense.It is a tough job to define number sense, for different researchers have different understanding of the connotations of number sense. The author gives the definition that"number sense is the comprehending of the relation between numbers, and the ability to infer and solve problems in the use of the relationship of numbers and number models."The author divides the essential elements of number sense into six parts, namely, the meaning of number, the presentation of number, the relation of numbers; the calculation of numbers, the evaluation of numbers and the problem- solving of numbers.First of all, our country of this study was based on the current number of primary school math curriculum content and implementation of a sense of reality, near primary school teachers to conduct a survey and for in-depth interviews with some teachers, while elementary school math classroom into a sense of the content of a few in-depth understanding of the teaching situation , also on the version of Beijing Normal University and two sets of teaching materials related to the number of PEP sense to set up and presentation of the contents of a comparative study in order to thoroughly investigate a more comprehensive sense of the field of primary and secondary schools the number of the status of implementation of curriculum.and divides the development of number sense into three stages from the perspective of the mathematics curriculum: the stage of number awareness, the stage of number symbols, and the stage of models (problem-solving) in order to find out the development law and the features of number sense in the examinations of the primary school pupils.Then the author selected a sampling of about 700 pupils in Grades 2, 3, 4, 5, and 6 in four primary schools of different levels as subjects for research and conducted interviews of some pupils and teachers. From the results of the examinations and the statistical analysis the author arrived at the development law and the features of number sense of the primary school pupils and the stages of development of number sense of the primary school pupils. The major findings include:In the investigation of the development law and the features of number sense of the primary school pupils in the light of the grade, I found that there is a significant difference in the development levels between Grade 2 and Grades 3, 4 and 5 in terms of number sense of the pupils. There is no significant difference in the development levels among Grades 3, 4 and 5. There is a significant difference in the development levels between Grade 5 and Grade 6. Generally speaking, there is a gradual rise in the development levels of number sense as the pupils grow older.I have, from the score change in the examinations in terms of number sense of the pupils of different grades and the results of the significant tests between the grades, found that the number sense of primary school pupils develops as grade or age grows, which in general can be divided into three sets: Grade 2 as the first set; Grades 3, 4, and 5 as the second because their levels are similar and Grade 6 as the third. There is a significant difference among the three sets in terms of the significant score rates of the number sense elements of the primary school pupils. Therefore, in the process of the development of number sense of the primary school pupils, there can be three stages of development at which the three sets reside: the first stage belonging to Grade 2; the second stage Grades 3, 4 and 5; the third stage Grade 6.Based on the above studies, I suggest that in the design of the contents of number sense of mathematics curriculum at the primary schools the meaning of number, part of the presentation of numbers, the relation of numbers and the calculation of numbers be taught in Grades 1 and 2; the presentation of numbers, the relation of numbers, the calculation of numbers and part of the evaluation of numbers and the problem-solving of numbers be dealt with in Grades 3, 4 and 5; the evaluation of numbers, the problem-solving of numbers and other significant contents be coped with at Grade 6. And specific suggestions for the related contents of mathematics are also put forward.There is still room for further reflection and research on some issues in my research. At the same time the extension and expansion of my research are also very significant. It is hoped that the related research will become the basis and evidence for the construction of basic education of mathematics in primary schools.