The Study On The Meaning Construction Of Primary School’s Number And Algebra Teaching

Our traditional mathematics education teaching view was deeply influenced by behaviorism, so mathematics education focused on skilled algorithm. There is a large number of boring and formal exercises in mathematics textbooks, which are out of life and difficult for students to understand. With the new curriculum reform carried out, meaning construction teaching based on the theory of constructivism has become the trend of reform and development. Meaning construction teaching directed toward understanding points to pay attention to the realistic background, help students to complete the meaning construction of knowledge with multiple representations and multiple strategies. The teaching focuses on the mathematical internal connection of concepts, reflects the situational mosaic embodied in the formation of knowledge, strengthens the expression of algorithm and mathematical thought and method.The study is choosing the “number and algebra” modular for carrier. In primary school, “number and algebra” module follows such main thread that the operation of number, the introduction of symbols, algebraic thought obtained and function thought early infiltrated. This module is so rich that reflect the development of students’ thinking leap, leaping from arithmetic thinking to algebraic thinking. Compared with traditional teaching materials, number and algebra module relatively add a lot of new knowledge and valuable mathematical thought, such as estimated calculation, the strengthening of algorithm, the cultivation of number sense, early infiltration of function thought. Therefore, the research of “number and algebra” content is a work of the significance and value.The author studies the meaning construction of number and algebra content from the teaching point of view. The research is divided into six parts:(1)I elaborate the background and significance of meaning construction teaching, and I give research route and methods also.(2)Through a lot of literature retrieval, I sort out the related literature of number and algebra and the related theories of meaning construction, involving the research of number concepts development, number sense, arithmetic algebra and function research. Meaning construction teaching is based on the theories of constructivism teaching view, the reality of mathematics education theory, Dubinsky’s APOS theory. In addition, this paper illustrates the connotation and research framework of meaning construction teaching.(3)Using research method of literature analysis, I sort out the contents of “number and algebra” according to PEP primary mathematics 12 volume textbooks. I elaborate the meaning construction methods of the core concepts from the two dimensions of arithmetic and algebra, including number concepts, operational concepts, express numbers with letters, equation concept.(4)I elaborate the meaning construction methods of number and algebra core ideas, including number sense, functional idea, model thought.(5)Using the method of case analysis, I preliminary induce the research mode of meaning construction combined with fraction concept and functional idea teaching cases,which makes the meaning construction theory easy to operate.(6)Through the experiment, I sum up the research conclusions and raise the innovation and deficiencies of the article.The conclusions of this study are:(1)Meaning construction teaching has gradually become the focus in the international mathematics education and the development trend. Primary school mathematics materials add many meaning understanding contents and teaching pays attention to the students’ mathematical learning process of meaning construction. Meaning construction has become an important theoretical achievement of mathematical education practice in primary school in China.(2)Meaning construction teaching obtains the affirmation and attention of teachers. Found in the classroom observation, meaning construction teaching design can achieve better teaching effect. For example, students’ enthusiasm is high, thinking is innovative, elastic knowledge is easy to migrate.(3)The article follows such two main threads that the core concept and the important thought to study on the number and algebra meaning construction mode. I give meaning construction cases of concept in arithmetic and algebraic dimensions. Around number sense, function, model thought, the article discusses the methods of ideas meaning construction. It greatly expands the mathematical curriculum resources in primary school mathematics education and also provides a new way to teach number and algebra module.(4)In this paper, the case study method used in the meaning construction teaching can be used as an effective mode. Combined with fraction concept and functional idea teaching cases, I elaborate respectively meaning construction research mode of mathematical concepts and ideas. At last, I show two teaching designs of meaning construction in order to provide examples and patterns for readers to study meaning construction methods of concepts and ideas. Also it provides an effective method for peers of mathematics education to study teaching.The source of confusion is in the teaching practice and textbooks combing. Based on the analysis of literature and teaching theories, I define the connotation of meaning construction teaching, design the research framework of meaning construction teaching, and give meaning teaching method and case study according to thinking development sequence of number and algebra, and then apply in teaching practice.“Definition” and “design” may be a few of innovations belong to the author. I hope the research can enrich the theory of primary school mathematics teaching and has certain contribution to expand the mathematical curriculum resources.