Investigation On Eighth Grade Students’ Mastery Of Quadratic Equation With One Variable

Quadratic equation of one variable is an important content of junior middle school mathematics,and is generally considered to be one of the difficulties in solving equations in middle school.In this paper,the eighth grade students in a middle school in Shanghai were investigated on their mastery of quadratic equations with one variable,and the following three questions were studied:(1)How do grade 8 students understand the quadratic equation of one variable?(2)What strategies do grade 8 students use to solve problems related to quadratic equations with one variable?(3)What mistakes did grade 8 students make when solving problems related to quadratic equations of one variable?Through the test paper survey of 177 eighth-grade students from 5 classes in a middle school in Shanghai,and interviews with their 5 mathematics teachers,the following research results are obtained:(1)Students’ understanding of the quadratic equation of one variable is mainly presented through symbol language,text language and image language.In the survey results,47.13% of the students prefer symbolic language comprehension,50.18%prefer written language comprehension,and only 2.69% prefer image language comprehension.(2)The most common method used by students in solving quadratic equations of one variable is the formula method.In the 6 questions of the test paper,the students who use formula method,collocation method,factorization method and direct opening method to solve the equation account for 49%,18%,19% and 14% respectively.The proportion of students who used single,two,three and four methods to solve equations was 35%,23%,21% and 21% respectively.The most common steps for students to solve the word problems of quadratic equations with one variable are as follows: 1.Second,construct the quadratic equation of one variable;Third,solve the quadratic equation of one variable;Fourth,to judge the solution of the equation.Survey data showed that 69 percent of the student practices included only the first step,48 percent included only the first two steps,31 percent included only the first three steps,and 22 percent included all four steps.In addition,some students did not consider the characteristics of the questions themselves and adopted a single solution method for all the questions,such as formula method.This part of the students only understand the formula of the root of the quadratic equation without understanding the relation between the form of the equation and the solution method when solving the quadratic equation.(3)Students made 6 kinds of mistakes in the concept understanding of quadratic equation,5 kinds of mistakes in solving equation and 3 kinds of mistakes in the application of equation.The three kinds of errors with the highest frequency are:ignoring the value range of quadratic coefficient in the general formula of quadratic equation with one variable;Wrong use of formula;Error handling of perfect square equals negative value in collocation method.Finally,according to the research results of this paper,relevant teaching enlightenment is proposed,hoping to be helpful to teachers’ classroom optimization.Finally,hoping to be helpful to teachers’ classroom optimization.