The estimating capacity is a vital component of the mathematical cognition,and it provides the foundation for the growth of advanced mathematical capacity.It is generally accepted that the mathematical estimation mainly consists of the following three parts:quantitative estimation,computational estimation and measurement estimation.The estimation has the extremely important status in our living and industry conditions,that is the faster.and more effective method to solve problems without accurate calculation.It also has been pointed in Mathematics Curriculum Standards on Compulsory Education that mathematical estimation is a significant method to cultivate the number sense among the students which helps students to understand the relationship between number and quantity in the real life.It is necessary to cultivate students' estimating capacity as considering the different circumstances.Other countries and regions also clearly establish the requirement of mathematical estimation in their mathematics curriculum.By designing the questionnaires for the second stage students' mathematical estimation,the students in grade 4,grade 5 and grade 6 from three primary schools in Nanjing,Changzhou and Suzhou have been included for the survey,according to that,the mathematical estimating capacity for the second stage students in different genders and ages has been analyzed.The relationship between mathematical estimating capacity and quantitative estimation,computational estimation and measurement estimation has been explored.Apart from that,the usage and understanding of second stage students,estimation strategies are also taken into statistics.Based on the research,the following points were summarized:1.The second stage students are short of the mathematical estimation,and among the three capabilities,the performance is becoming worse from quantitative estimation,computational estimation to measurement estimation.2.There is a positive correlation between the mathematical estimation of the second stage students and their quantitative estimation,computational estimation and measurement estimation,and there is also obvious relation between these three kinds of estimating capacity.The equation of linear regression for mathematical estimating capacity is represented as:Mathematical Estimation=Quantitative Estimation ×0.377+ComputationalEstimation ×0.452+Measurement Estimation ×0.507.3.There is a obvious relationship between the second stage students'estimation capability and their age(grade).The mathematical estimation of the second stage students increases as their getting older,however,it does not have too much differences between different genders.4.The selection of the estimation strategies will affect the result of mathematical estimation,to compare with that using no strategies and guess the results directly,choosing the appropriate strategy helps to decrease the estimation time and improve the accuracy.5.The understanding of the second stage students' estimation is not comprehensive,they believe that the estimation was based on direct guessing the results and neglect the the use of strategic techniques in the mental consideration process.6.The second stage student have already got some simple estimation methods but they have not yet formed the systematic problem solving strategy;they cannot yet use the estimation strategy to solve problems flexibly,however they tend to use well-known methods to repeatedly calculate or even get unreasonable estimation results.According to the above conclusions,two suggestions are raised to deal with the teaching of estimating in primary school:firstly,it is necessary to strengthen the cultivation of primary school students' estimation capability,teachers could focus on three aspects:emphasing the estimation education of primary school,intergrating the content of the textbooks and cultivating the awareness of students' estimation.Secondly,the guidance of pupils' estimation strategies should be strengthened,teachers should try their best to dig up the teaching materials,refining estimation methods,diligent in developing texts,guiding estimation techniques,skillfully designing problems and using estimation strategies. |