The Investigation Of Senior One Students’’ Functional Misconceptions Based On The Two-tier Diagnostic Assessment

The famous German mathematician Klein (F·B:Klein,1849-1925) called function as the "soul" of mathematics and considered function as the"cornerstone" of middle school mathematics. China’s famous mathematicians and mathematics educators Chen Jiangong pointed out:the core of mathematics education is about developing the functional concept. The "new curriculum" emphasized that function concept appears and reappears throughout high school mathematics. So, function plays an important role in high school mathematics. However, students’inconsistent concepts appeared during the process of studying function concept, which was because of the complexity of the function, the abstraction of symbols and the restriction of student thinking development. We call the concepts as"misconceptions of function". Misconceptions of function have a great negative impact on students’learning functional concept. So teachers should know about students’misconceptions and transform the misconceptions through reasonable teaching strategy. For that reasons, this paper will serve "The research in Senior One students’misconceptions of function and the transformation of misconceptions" as a research subject. According to the research theme, the author has done some research on the following aspect:First, review domestic and overseas’research on the misconceptions of function and the checking tools through the literature materials’ collection. Determine the direction by combining with the current domestic research and illustrates three major basic theories of this paper:cognitive constructivism theory, cognitive development theory, APOS theory.Second, Based on the literature search, learn from the design flow of two-stage questionnaire proposed by Treagust and design the two-stage questionnaire of misconceptions of function, have enriched the questionnaire about functional misconceptions in mainland China,and check the questionnaire, finally complete the formal questionnaire through analyzing the reliability of Spss.Third, select 316 students of 5 classes for testing,who are all from the high school where the author worked. Then the answers to the questions are shown in the form of cross tabulation and bar graphs. the survey results show that students have the following several aspects of the misconceptions of function:(1) math equation with variables is function(2) if a volume changes with another quantity, then this is the relationship of function(3) each function can have the image, each image corresponds to the only function(4) the function value is variable with the change of independent variable(5) each function is derived, and the analytical formula is the only one(6) the image of function is continuous, discrete points can not be the image of function(7) the piecewise function is composed of several different functions(8) the function can’t be represented by a mappingAccording to the spss analysis on the questionnaire data, there was no significant difference between the scores of male and female students in the function concept of two-stage questionnaire,so the result did not reach (P> 0.05).It showed there is no gender difference in the understanding of the concept of function, and the male and female’s scores in the conceptual domain are generally low. The result proved that high school students misunderstand the concept of function seriously.Fourth, through the analysis on the questionnaire results, discusses the reasons why students have the misconception. There are five main reasons:one is the complex and abstract of the functional concept, and the second is the development of student thought, and the third is the convergence problem of junior and senior middle school, the forth is the students’will, the last one is teachers’problems.Fifth, according to the analysis on the causes of students’misconceptions, propose five teaching strategies of transforming students’misconceptions:one is the cognitive analysis strategy about the history of function, and the second is the strategy of concept map, and the third is the changed-type teaching strategy,and the forth is the advance organizer strategy, and the last one is the teaching strategies based on APOS.