A Survey Of Seventh-grade Students' Ability To Generalize In Algebra

Junior high school mathematics has officially opened the door of algebra.Different from primary school,the object of operation in the field of algebra is no longer just specific numbers,but more complex algebraic formulas composed of letters,symbols and numbers.Unlike primary school,which only calculates the required results accurately through appropriate calculation,there is an idea in the field of algebra that can not be ignored: algebra is generalization.The purpose of introducing letters into mathematical language is to make a better generalization.It helps people to make abbreviations of complex language and summarize the implicit quantitative relationship to form a concise and comprehensive general expression.If the seventh grade mathematics teacher's goal in teaching is to simply use letters to replace a number,then students will not buckle the first button of algebraic thinking.Therefore,in order to explore the development status of seventh grade students' algebraic generalization ability,the author takes "letters express quantitative relationship" as an example to explore the following three problems1.What is the level of algebra generalization of the seventh grade students about the ability to express quantitative relations with letters?2.Is there a certain correlation between different algebraic generalization ability levels?3.Can we provide relevant teaching suggestions for front-line teaching?The sample of this study is 77 seventh grade students from a junior high school in Minhang District of Shanghai,who come from two different classes.The results of the two classes are obviously different,so it can reflect the generalization ability of the seventh grade students at different levels by using letters to express the quantitative relationship.The research results are as follows1.Through literature research,the author divides the algebraic generalization ability into three levels: Level 1-arithmetic generalization level,level 2-incomplete generalization level,level 3-complete overview level.2.Taking the level of algebraic generalization ability as the main line,through the test paper survey and interview,the author analyzes the students at each level from two aspects: the types of students' generalization and the strategies of generalization.The results show that only 6.5% of the students are at Level 1-arithmetic generalization level,45.5% are at level 2-incomplete generalization level,and 48.0% are at level 3-complete generalization level.3.Data analysis shows that there is a significant correlation between the types and Strategies of algebraic generalization ability and students' generalization level.To sum up,the seventh grade students have obvious differences in the ability of algebra generalization,and the front-line teachers can guide the students to take different and appropriate strategies to achieve algebra generalization according to the students' level.