The Study On The Application Of Symbolic-graphic Combination In Elementary Number And Algebra

Combining numerals and shapes,the study probes into mathematical problems,analyzes mathematical information,clarifies quantitative relations,and finally solves mathematical problems with the help of the respective attributes of "numerals" and "shapes" and the mutual interpretation and conversion between numerals and shapes.The idea of combining numbers and shapes is closely related to and mutually supported by "numbers and algebra".Especially in the primary school number and algebra learning,with the support of combination of numbers and shapes,to give aid to students in building learning scaffolds,developing models,making abstract and generalized mathematics become image and simplified,students are easy to comprehend mathematics.Secondly,in the teaching of mathematics and algebra,it takes numbers and shapes as the key points and auxiliary shapes as tools to promote the understanding of logarithms;Or with the auxiliary number as the key point,continue to explore in depth in the comprehensive understanding of form;Focusing on the mutual interpretation of numbers and shapes to achieve mathematical understanding.Based on this,this study focuses on the primary school mathematics "number and algebra" this module,around the combination of number and shape of the application of research.Logarithmic form combining ideas in the application of number and algebra teaching of primary school were analyzed,and the targeted application strategy is put forward.The research mainly includes the following aspects:The first is to explore the basic theory of number-shape combination in elementary school mathematics and algebra teaching.Firstly,this study focuses on two forms of application of the combination of numbers and shapes in mathematics and algebra teaching in primary schools: to help numbers with shapes and to solve shapes with numbers.In other words,by virtue of the intuitionism and image of "shapes",the difficult mathematical laws,properties and quantitative relations are transformed to achieve the understanding of logarithm.Or use concise mathematical language,quantitative relations to describe the nature of the graph,grasp the inherent laws of the graph.Finally,based on the idea of combining numbers with shape and the cognition of numbers and algebra,the basic principles related to the application of the idea of combining numbers and shapes in the teaching of numbers and algebra in primary schools are puts forward.The second is to investigate the application of the number-shape combination in mathematics and algebra in primary schools.Some methods,such as investigation and case analysis,are applied for the purpose of the study.Through the analysis of teachers' questionnaires,interviews,combined with teachers' classroom records and teaching cases,this study is focused on the application of number-shape combination in mathematics and algebra in primary schools.It is found that the problems existing in the application of the idea of combining numbers and shapes in mathematics and algebra teaching in primary schools mainly focus on the following aspects: the concept and connotation of the mathematics combining thought of teachers need to be further clarified;the requirement of teachers' logarithmic combination thought in curriculum standard and teaching material is not clear;the combination of numbers and shapes is not effective in the application of numbers and algebra.The reasons for the above problems are as follows: teachers lack of theoretical learning and training related to logarithmic combination thought;teachers lack the reconstruction of logarithm and algebra content;teachers are short of effective teaching methods and strategies combining numbers and shapes.Secondly,this study analyzes the cases of the combination of numeral and figure in elementary school mathematics and algebra teaching,in order to understand the application of the combination of numeral and figure.Thirdly,through the analysis of the problems and causes of the application of the combination of numbers and shapes in the teaching of "numbers and algebra",this study comes up with the strategies of the application of the combination of numbers and shapes in the teaching of numbers and algebra.The strategy mainly revolves around the following aspects: to improve teachers' understanding and application level of number-shape combination thought;to reconstruct the teaching content around the combination of numbers and shapes;to realize the reconstruction of teaching objectives according to learning and teaching;support the creation of a teaching environment for teachers and students to communicate more;optimize teaching method and means by combining numeral and form with thought method.Finally,combining the theory of combination of numeral and shape and the cognition of the content of numeral and algebra,the application of combination of numeral and shape in the teaching of numeral and algebra in primary schools is expounded from three aspects: concept teaching,calculation teaching and problem solving teaching.To some extent,this study hopes to provide some guidance for the application of the combination of numbers and shapes in mathematics and algebra teaching.