Algebraic Reasoning And Teaching Research In Elementary School Mathematics Curriculum

Algebraic reasoning is an important part of mathematical reasoning,which embodies the mining of quantitative relations,which helps students to change program thinking and provide qualitative richness for their mathematics learning.This study focuses on the infiltration of algebra reasoning in primary school arithmetic teaching.On the one hand,it is difficult for primary school students to learn algebra knowledge after entering junior high school.The number facts in primary school arithmetic teaching are the important foundation of the relationship structure.Algebra reasoning teaching can help them to closely grasp the connection between seemingly trivial arithmetic operations.On the other hand,through combing the related research of "algebraic reasoning",it is found that the domestic research still focuses on the development of algebraic reasoning ability in middle school,and mainly on the practical research of front-line teachers,focusing on the research of students’ algebraic reasoning problems and general teaching strategies,lacking the support of normative theoretical research and empirical research.Therefore,this study grasps two clues that affect the teaching quality of algebraic reasoning,one is the knowledge logic in the course,the other is the cognition of students and teachers on algebraic reasoning,which is used as the analysis element to carry out the research of algebraic reasoning.First of all,combining the research results of algebraic reasoning at home and abroad,focusing on the three parts of algebraic content,it is realized that algebraic reasoning can be divided into three reasoning methods: analytical reasoning,creative reasoning and practical reasoning,aiming at finding the conclusion that highlighting the unique equivalence relationship and change relationship of algebra from mathematical or practical problem situations.Among them,pure algebra knowledge learning and problem-solving learning have different algebra reasoning processes.Based on the analysis of algebra reasoning process,this study combined with solo classification theory to carry out a preliminary division of the development level of algebra reasoning ability of primary school students.Secondly,taking the curriculum standard and the elementary school mathematics textbook of Jiangsu Education Edition as the text analysis object,we can understand the basic requirements,optional contents and methods of the practical training of students’ algebra reasoning ability in primary school mathematics,and grasp the distribution,reasoning methods and reasoning development level of the early algebra content as a whole.After analysis,both the curriculum standard and the teaching materials embody the stages and levels,but the core idea of focusing on the content of algebraic reasoning remains to be sorted out by the teachers.Then,this study selects students from three different levels of schools and 33 primary schoolmathematics teachers as the research objects,and uses questionnaire tools to understand students’ thinking performance of algebraic reasoning and teachers’ understanding of algebraic reasoning and its teaching.The development level of primary school students’ algebraic reasoning ability is mainly based on on the multi-structural level and the transition level from multi-point to relational structure.The factors that affect their smooth development of algebraic reasoning include the lack of implementation norms of algebraic reasoning,and the strangeness of relevant abstract algebraic concepts.In contrast,teachers have better ability of algebraic reasoning,but the core idea of algebraic reasoning needs to be mastered,and the teaching understanding lacks certain process.Finally,this study believes that in the teaching of mathematical algebra reasoning in primary schools,teachers should grasp the differences and connections between arithmetic and algebra,and guide the implementation of teaching from the basic,procedural and structural aspects.The analysis of teaching materials and learning situation can help to explore learning theories and design teaching activities.The details are as follows: in general arithmetic,students’ experience of digital model should be broadened,written records should be linked,thinking process should be displayed,equivalence relationship should be focused,natural transition should be realized,exploration process should be enriched,and symbolic consciousness should be created;in functional thinking,counting activities should be accumulated,general expression should be promoted,quantitative relationship problems should be fully utilized,and change ideas should be permeated;in modeling language,dilution should be made Form,pay attention to the essence,stimulate students’ problem consciousness,change the problem form and promote knowledge construction.