The Investigation Of The Senior Students Of Function Concept To Understand

The concept of function which plays a really important role in the field of mathematicsis not only the core of modern mathematics but also the important content of high schoolmathematics teaching. Meanwhile it is a difficult learning point of students as well as focusof teaching in senior high schools. The accurate grasp and deep understanding of conceptfunction has a direct effect on mathematics learning results. Facing abstract concept, whatare the problems in learning and understanding? As instructors, how can we help studentslook for tools of understanding and realize the cognitive leap?This study selected217students as the research object, who are studying in grade oneof NO.2high school in Bijie City, Guizhou Province, to investigate their understanding ofthe concept of function. According to new mathematics curriculum standard requirementsof high schools, combined with the classification and evaluation of SOLO learning theoryand referring to the relevant scholars and senior high school mathematics teachers, theunderstanding of function can be divided into four levels--level0, level1, level2and level3. Among them, the3rd level is the most complicated, while2nd level is higher than the1stlevel. Thus level0is the easiest one. First,217students were questionnaire on thefollowing three aspects: the definition of the function (domain, range, and correspondingrelation), the expression and application of function. Then, select several representativestudents to interview and analyze statistically by the Excel based on the above materials.At last, the factors, which affect understanding of function of high school students,were analyzed according to understanding of the function concept, to explore teachingstrategies that can promote high school students’ understanding.From the study we can find that:1. Students in the especial key class can understand the concept of function quiet wellwhile key class is weaker than the former one. In the ordinary class, most of students can’tgrasp the conception. As for the domain of definition, range, the corresponding relation offunction and the expression, the situation is that there are more students in level2or level3than other levels in especial key class, most are in level2in the key class and most are in level1or level2in the ordinary class.2. Generally speaking, as to understanding of the concept of function in grade one inhigh school, there are3.69%students in level0,18.89%students in level1,35.94%students in level2and41.47%students in level3.3. Common problems of understanding of the concept in grade one are as follows.(1) Students do not understand the nature of concept thoroughly;(2)The definition of “corresponding to said” of function is obscure;(3)Students usually misunderstand three elements of function (domain, range, andcorresponding law);(4)Expression of function can’t be understood thoroughly.According to the common problems in the understanding of function, the reasons whystudents hardly understand were analyzed and finally put forward to some reformedmeasures to improve the function concept teaching, combined with the specificcircumstances of high school students.（1）Contact real life to help students understand the concept of function;（2）By “talking about Mathematics”, let students understand Mathematics deeply;（3）Help students understand the spiral type teaching method;（4）Design the changeable practice to promote understanding;（5）Use reflections on the application to improve cognitive comprehension;...