Research On Quadratic Function Learning In Rural Junior Middle School

The quadratic function is one of the important contents in the mathematics course of middle school.It is not only the basis of learning unary quadratic inequality and conic curve in high school,but also provides an important mathematical model for solving practical problems.In the teaching practice,we feel that there are still problems in the teaching of quadratic function in the middle schools in Yu county.Therefore,based on the teaching objective requirements of secondary school quadratic function proposed in the compulsory education mathematics course standard(2011 edition),this paper conducts tests,questionnaire surveys and interviews on the status of secondary school quadratic function study for students in grade 9 in Yu county around the following points:Accurately to understand the concept of quadratic function,ways to understand the concept of quadratic function,to master transformation methods of between analytic expressions of quadratic function,and to determine analytic expressions of quadratic function from coordinates of several points,correctly to draw image of quadratic function and point out the vertex coordinates,symmetry axis and opening direction,to understand properties of quadratic function with aid of the image and to solve practical problems by quadratic function knowledge.On the basis of tests,questionnaires and interviews,the author obtains the relevant first-hand information and makes in-depth analysis and draws the following conclusions:(1)The students' problems in learning quadratic function are as follows:They do not understand the concept of quadratic function properly;They have difficulties in finding the analytic formula of quadratic function;They lack the idea of combination of numbers and figures and they lack flexibility of the application of function images and properties;the ability of function modeling is insufficient,and the ability of solving practical problems of quadratic functions is insufficient.(2)The reasons come from two aspects.First,the students' attitude is not correct subjectively and their confidence is not enough.The learning methods are relatively single,too dependent on formulas and memorizing by rote.They are not fond of drawing and summarizing in their study habits and lack of preview and review.They are too passive and confined to the classroom in their ability development.When they encounter difficult problems,they wait passively or choose to give up.Second,for teachers:explaining the concept of quadratic function ignores students' acceptance ability;failing to understand students' mastery of the analytical solution of quadratic function in detail;the drawing of function images is not standardized enough,and wrong demonstration affects students'analysis of quadratic function properties;there are fewer practical problems with life-related function,ignoring the summary and reflection of the reasons for students' mistakes.(3)The teaching countermeasures are put forward:Teachers can explain the concept of quadratic function with examples and consideration of students' basic knowledge to deepen students'understanding;Teachers can use the idea of classification to find the analytic formula of quadratic function,and teach students learning methods;Teachers can permeate the idea of combining numbers and figures and do analysis of function with modern technology and function image;Guiding students to model reasonably and improve the practical application ability of quadratic function.In addition,teachers are advised to set an example for students and actively reflect on teaching.Students should improve their interest in learning quadratic function and pay attention to forming good learning habits.(4)The teaching strategies are applied to teaching practice,and specific teaching design is given to improve the teaching effect of quadratic function.