A Survey And Research On Seniors' Understanding Of Function

The concept of function is a very important concept in Maths as well as a hard nut in mathematics teaching in high school.The paper is an investigation of the seniors' understanding of the function concept,from the definition,representative method and application of a function.Aiming at a better understanding of the seniors' perception of the essential features of a function,The paper is expected to solve some confusions of function and search for the cause of them.Some conclusions after the survey and analysis:(1) Seniors' recognition of function concept develops in a curvilinear rising way. Senior 2 is the lowest point and senior 3 is obviously higher than senior 1 and senior 2.The perceptions of function between senior 3 and senior 1 as well as the senior 3 and senior 2 are quite ifferent.However, the perceptions between senior 1 and senior 2 are not so apparent.(2) There is no obvious distinctions between boy students and girl students on the understanding of functional concept, only with an exception for senior 3.(3) Function is understood differently.Some students identify a function according to the definition,but for more students they do so according to the images for the concept of function.(4) Seniors understand and master different representative methods of a function unbalancedly.They do best in analytic method, better in graph method,but worst in table method and they can't shift freely among the different representative method of a function. Seniors show obvious difference in understanding the analytic method and table method as well as understanding the graph method and table method,however,the difference between analytic method and graph method is not so obvious.(5) Seniors have difficulty in associating real problems in life with functional model in Maths,so they can't solve the problems properly with the aid of function.(6) Seniors tend to ignore the essential features of a function.Finally,some solutions are offered:(1) Teaching should be designed with the APOS theory.(2) Learn function with the aid of history of it.(3) Strengthen the use of table representation of a function.(4) Get to know the essencial features of a function.(5) Solve real problems with function models.