Investigation And Analysis On The Development Of Primary School Students’ Sense Of Quantity

In the teaching practice,it is often seen that pupils are confused about progression rate and unit category of quantity when solving fractional word problems with implicant quantities.On the other hand,"sense of quantity" was proposed for the first time in the Compulsory Education Mathematics Curriculum Standards(2022)and is required as one of the core qualities.At the same time,based on the preliminary investigation,it is found that front-line teachers do not have a clear understanding of the concept of quantity and sense of quantity,and do not fully grasp the teaching practice of quantity.It can be seen that there are problems in teaching and learning about quantity,which restrict the effective cultivation of the sense of quantity of pupils.In order to solve the dilemma,this research establishes the research question: What is the specific and accurate connotation and extension of the concept of quantity? How to divide and construct the cognitive framework of sense of quantity? How to compile a measurement scale to investigate the development of pupils’ sense of quantity? How can we better develop pupils’ sense of quantity?Based on the above questions,this study mainly uses literature analysis,interview and test methods.Firstly,the connotation and extension of related concepts such as quantity and sense of quantity are clarified.Then,based on Piaget’s theory of stages of cognitive development,this paper constructs a cognitive analysis framework for the study of sense of quantity,and analyzes the survey questionnaires from three dimensions: total quantitative,specific quantitative and specific qualitative,and summarizes the development rules and existing problems of sense of quantity in primary school students.The rules of the development of pupils’ sense of quantity are as follows:(1)The development level of pupils’ sense of quantity is not high on the whole,but it increases with the increase of grade;(2)The development of primary school students’ sense of quantity has phased characteristics and can be divided into three stages,namely,the intuitive perception stage(which can be specifically divided into the primary perception stage and the advanced perception stage),the measurement and representation stage and the logical operation stage;(3)The fourth grade is a critical period for the development of primary school students’ sense of quantityThe research finds that there are some problems in the development of sense of quantity:(1)The development level of sense elements of quantity is weak and most students are still in the primary perception stage;(2)In the development of the representation elements of quantity,there is a problem that quantity cannot be represented from the overall perspective;(3)In the development of unit conversion elements of quantities,there exists the problem of unclear classification among units in the same quantity category;(4)The common problem in the development of quantitative comparison,quantitative inference and quantitative application elements is that the development level of quantitative meaning elements is low.Finally,based on the results of the survey and the problems existing in the teaching materials,this paper puts forward some suggestions for developing the sense of quantity of primary school students:(1)The content of the teaching materials should conform to the phased characteristics of the development of the sense of quantity of primary school students;(2)The cultivation of sense of quantity should pay attention to the basis of developing the meaning elements of sense of quantity and grasp the critical period of the development of sense of quantity,conform to the law of the development of sense of quantity,and pay attention to the penetration of sense of quantity in the learning of number and algebra content.