Learning The Basics Of Algebra For Middle-school Students: Difficulties And Possible Solutions

Algebra plays an important part of compulsory education in mathematics curricula, but during my career of a mathematics teacher, I observed that the comprehension of school algebra is a difficult task for the majority. In their exercises you will notice some representative mistakes, and most of them are incapable of problem solving. How to help our majorities? First, we must select an point of view which is appropriate, so that we can make an exquisite research on the content of school algebra and the course of algebra cognitive. Then we can found solutions.I summarized the literatures about algebra teaching and learning and chosen these production as the basal theory:(1)The framework for thinking about understanding (by James Hiebert.);(2)The theory that a mathematical concept has procedural-structural property (by J.Sfard.) and APOS theory about teaching mathematical concept;(3)The standpoint that teaching of algebra is teaching of algebra language. The 93 students in Grade 7 from two classes taught by my self were observed, I designed four experiment for them so that I could know how the teaching in classroom influence their algebra cognitive and the forming of their algebra idea. Based on these conclusion, some advises were given.When students learn algebra, they have these difficulties:(1)The understanding of letters and the concept of variable.(2)The sense to the constructional character of the algebraic expressions.(3)Understanding and using algebra language;(4)Abstracting the quantities and their relation, setting up model of equation and function. These difficulties are caused by the follow reason:(1)The cognitive level of the majorities are not enough to understanding the abstract of algebra;(2)There were overmuch procedural calculate in elementary school;(3)education about algebra had not been regarded as important things.The result of the experiments told us the follow things:(1)If we introduced letters to the students earlier, their cognitive about letters will improve;(2)When a matter is expressed by many manners by the students, the construction of this content will beneficial from it;(3)The equal sign has dual character, we must teaching it technically.(4)Training for cognitive of the structure of an algebra expression is helpful to students who have good school mark, but is not obviously effective to those who have not good school mark.Advises:(1)Attach importance to the concept of variable, teach it along with the learning of letters;(2) Teaching concept with dual character by the under the direction of APOS theory;(3)Attach importance to the teaching of algebra language;(4)Train the sense of the relation of quantities:equality and different;(5)Train the cognitive of the constructed character of algebra expression.