An Investigation On Ninth-grade Students' Cognition Of The Quadratic Function

"Quadratic function"is an important component of the knowledge of functions and one of the key and difficult topics in junior high school mathematics teaching. It plays an important role in junior school mathematics textbooks. In order to investigate ninth-grade students'cognition of the quadratic function, in this paper, the following three areas are researched: (1)Ninth-grade students'cognition of the conception of quadratic function; (2)Ninth-grade students'cognition of the nature of quadratic function; (3)Ninth-grade students'application level for quadratic function. Through questionnaire survery and interview,we have the follow conclusions:(1)The levels of students'cognition on the concept of quadratic function are different, and the students'level of pre-structure,uni-structure,multi-structure and relation are 17.1%,40.2%,29.9% and 12.8% separately. Students'understandings present diversity, and the understanding on the point of view from"general expression","symmetry","correspondence","example"occupies 58%,21.6%,6.8%,5.1%. 8.5% of students do not form the image of the concept of quadratic function or form erroneous image of the concept of quadratic function.(2) Students of grade nine do better in identifying the size and direction of opening, learning simple natures of quadratic functions through the graph of a quadratic function than finding the axis of symmetry and coordinates of vertex of a quadratic function by applying the method of completing square.(3)Students of grade nine do better in applying"the analytic expression of a quadratic function","translation of a quadratic function"and the relationship between the graph of a quadratic function and the solution of corresponding quadratic equation than applying the most value and monotonicity of a quadratic function. In addition, students have difficulty in associating real problems in life with quadratic functional model in maths. Finally, some suggestions are offered: (1)Get to know the essencial features of a quadratic function; (2)Teaching should be designed with the APOS theory; (3)Solve real problems with quadratic function models.