The Teaching-case Study Of Quadratic Equation With One Unknown Number In Junior Mathematics

The Equation in real life is not only an important method in establishing model, is also a very important part of mathematics curriculum. And the quadratic equation with one unknown number as an important part of the equation, is the focus of the students’learning and teachers’teaching. The changes of the quadratic equation with one unknown number in the "Compulsory Education in Mathematics Curriculum Standards (2011edition)"(hereinafter referred to as the" New Curriculum Standard "), become the focal point in the study of mathematics teachers today.This paper is based on the comparative study between the "Full-time Compulsory Education in Mathematics Curriculum Standards (experimental manuscript)"(hereinafter referred to as the "Experimental Manuscript") and the "New Curriculum Standard ".Firstly,the paper has expounded the value of the quadratic equation with one unknown number. The quadratic equation with one unknown number is not only the extend of the equation of a degree and the number of square root, is also the base of the Quadratic Function, the One-variable Quadratic Inequality and the Conic. At the same time, the quadratic equation with one unknown number is an important approach to solving practical problems. Then, this paper analyzes the changes of the quadratic equation with one unknown number in the contents and concepts of the "New Curriculum Standard". Firstly, in contents, the "New Curriculum Standard" increases "Being able to use the discriminant of quadratic equation with one unknown number root to discriminate if there is a real root and if two real roots is equal" and "understanding the relationship of the quadratic equation with one unknown number root and the coefficient ", and makes the latter as the elective content; Secondly, the "New Curriculum Standard" changes the " being able to use the factorization method, formula method, method of completing the square to solve simple digital number of quadratic equation with one unknown number " in the "Experimental Manuscript", to " can use the factorization method, formula method, method of completing the square to solve simple digital number of quadratic equation with one unknown number "; Thirdly, the "New Curriculum Standard" puts forward the concept of "Everybody can get good mathematics education". Finally, it proclaims the inspirations from these changes in classroom teaching. The author makes the teaching design for the content of " the relationship of the quadratic equation with one unknown number root and the coefficient", and implements teaching in class (3), grade nine, and latter, analyses the teaching process with the class teachers from four dimensions of the students’learning, the teachers’teaching, the nature of the subject, and the classroom culture. Then makes the secondary changes of teaching design, implements in the class (1), ninth grade, summarizes suggestions after a in-depth interviews with the teachers and students. In addition, from four dimensions, this paper also analyses and discuss two other teachers’teaching case about "quadratic equation with one unknown number solution----method of completing the square " and "quadratic equation with one unknown number solution----formula method", and put forward teaching suggestions.This paper, based on the comparison of the "Experimental Manuscript" and the "New Curriculum Standard" and the analysis of the case, firstly, clarifies that it is possible to proceed teaching the cross-multiply method,according to the student’s ability, so that should not be deleted. Then, puts forward teaching suggestions about the teaching of quadratic equation with one unknown number, they are:(1)Optimizing the cognitive structure;(2)Attaching great importance to the relationship between the "word language" and the "symbol language";(3)Emphasizing the relationship of the "equation" and the "quadratic equation with one unknown number";(4)Theory with practice;(5)Highlighting the focal point;(6)Step by step;(7)Being good at design;(8)Teach according to the student’s ability;(9)Paying attention to the exploration. At last, the paper illustrates the problems should be paid attention to in teaching, such as to have rigorous language, avoid ignoring individual, pay attention to the cultivation of the ability, realize the main body, appropriate incentives and pay attention to the reflection.