Study On The Cognitive Construction Of Junior Middle School Students' Algebra Learning

The middle school students undergo the transformation from the arithmetic thought to the algebra thought,from the number symbol operation to the letter symbolic deduction operation,as soon as they begin the Algebra study.In this process the abstraction is gradually gained.The core of algebraic thinking is generalization;the essence is formal symbolic operation,or rule-based reasoning;the key is to find generalized relations,and symbolic of these relations.This is a challenge to the junior high school students who have just entered Algebra learning,and teachers need to use strategies to guide them effectively.First of all,through the collection of junior high school students' Algebra learning errors,it is found that students often have the following errors:(1)Algebraic procedural errors,(2)Algebraic operation errors,(3)Identification errors of the special forms of basic concepts and basic rules,(4)Formula Structural error.Second,Grade seven students were chosen as subjects because the first semester of Grade Seven was in the initial stage of Algebra learning.Students begin to learn the concepts and operations of "Algebraic expression","Integral expression" and "Fractional expression".Through the investigation of Grade seven students‘ cognition,the cognitive characteristics of Grade seven students with the above errors were found as follows:(1)The algebraic meaning of the symbol hasn't been established,mainly including the operational symbols(+?-? ? ?(?) ?a~n),the character symbol(+?-),the relationship symbol(equal sign,inequality sign),and the binding symbol(parenthesis).(2)Algebraic operation rules haven't been established,mainly including the rules of multiplication,the rules of positive and negative,the rules of chang the terms about without making equation or inequation untrue.(3)Algebraic constraint rules are not established,mainly including that Divisor can not be zero,Denominator can not be zero.(4)The structure of the formula is not established,mainly including the structural characteristics of the multiplication formulas.Thirdly,based on the characteristics that "Structure " is obtained after "Procedure " in the construction of mathematics knowledge,this paper studies students ' understanding of Algebraic procedure,and then studies students ' understanding of the structure of formulas.This study compares the content arrangement of "Algebraic expression","Solving linear equation in one variable","Inequation and its properties" in primary and middle school textbooks,and finds out the differences of the treatment of the same content in primary and secondary school textbooks,the difference of thinking requirements,and finds out the countermeasures of the primary and secondary school cohesion,and puts forward the teaching design about the initial lesson of these contents.Then this study reconstructs multiplication formula teaching design through the study of the multiplication formula in the middle school textbook arrangement,comparing different order teaching experiments on Square difference formula and Perfect square trinomial.Therefore,three major countermeasures are obtained:(1)Algebraic learning needs to establish algebraic procedural expression.(2)Equations and inequations learning need to establish algebraic transformation rules.(3)Multiplication formula learning needs to establish algebraic structural expression.Finally,according to the experimental conclusion,the paper puts forward three suggestions for teaching material arrangement in junior middle school,and obtains the instructional strategies to construct the cognitive structure of algebraic learning.(1)Constructing basic concepts of algebra by grasping key words and positive and negative examples.(2)Experiencing the process of "literal language" (?) "symbolic language" to establish the algebraic meaning of symbols.(3)Establishing the symmetry of equal sign and the direction of inequality sign by using of intuitive daily tools.(4)Improving the cognitive level of algebraic concepts by "Imitation-Variant-Expansion" layered advance.(5)Understanding the rules of solving the Equation and the Inequation through the concept formation process.(6)Establishing the cognitive structure network of knowledge by comparing the relation and the difference between the concepts.(7)Grasping the whole knowledge by classifying and brainstorming to understand algebraic constraint rules.(8)Experiencing the process of law discovery to understand the connotation of algebraic formula structure and to form an accurate deduction of algebra.