Study On Senior Grade One Students’ Difficulty In Understan Ding Functional Concepts And Relevant Countermeasures

Lots of scholars and experts at home and abroad have carried out researches on functional concepts and have made many great achievements. Since senior grade one students have just entered high school from middle school, their abstract thinking is still immature. Thus, they are relatively unfamiliar with the learning contents and methods of math in senior high school stage. As a difficult knowledge point of senior high school math, functional concepts are what they have to face at the very beginning. Therefore, the current situation about senior grade one students’ study of functional concepts is quite worrying and functional concepts are still greatly concerned by many people. First of all, the paper compiles a quiz about functional concepts as the questionnaire. The paper also conducts an interview among the teachers, aiming to investigate into the difficulties for senior grade one students to learn functions at the current stage and why they find it hard to learn functions through detailed data analysis. Besides, based on suggestions given by the teachers and document literature referred to, the paper comes up with some measures to improve senior grade one students’ learning and understanding of functional concepts.On the basis of the SOLO taxonomy theory, the paper studies senior grade one students’ comprehension level of functional concepts and deeply probes into commonly seen difficulties senior grade one students have in understanding functional concepts and relevant causes. The paper tests students’ comprehension level of functional concepts based on the three elements of function and function application, and function representation methods. Moreover, the paper interviews three teachers teaching senior grade one students in this school. Excel is utilized to analyze the data so as to find out senior grade one students’ difficulties in understanding functional concepts and relevant causes, and then come up with corresponding countermeasures. 210 students from three classes of senior grade one in No. 1 Senior High School in Caoxian County, Shandong Province are selected as the research objects.As indicated by the research:1. In general, the comprehension levels of functional concepts of senior grade one students in No. 1 Senior High School in Caoxian County, Shandong Province can be divided into the follows: about 3.67% senior grade one students’ comprehension level of functional concepts is at level 0; the comprehension level of functional concepts around 18.86% grade one students is at level 1; approximately 35.96% students’ comprehension level is at level 2; about 41.47% students’ comprehension level functional concepts is at level 3. As indicated by the results, nearly 58.53% senior grade one students’ comprehension level of functional concepts is below level 3, which is not that ideal as a whole.2. Most students in experimental classes can basically understand functional concepts and the majority of students are at level 2 and 3; students in key classes are slightly less competent and most of them are at level 2; however, most students in ordinary classes cannot master functional concepts and most of them are at level 1 and 2. As for the concrete mastery of functional concepts, senior grade one students can only solve some simple problems related to function definition such as domain of definition, range and corresponding relation. When it comes to complicated functions, they usually do not know how to solve them. They also lack a comprehensive mastery of the methods to express functions. As for the application of functions, they can understand the most part of a problem, but they just cannot list out the analytic expression.3. Main difficulties in understanding functional concepts:(1) Senior grade one students’ comprehension of the connotations of functions is still ambiguous(2) Senior grade one students do not understand correspondence quantities in functions(3) Senior grade one students cannot correctly understand the three elements of functional concepts(4) Senior grade one students lack a clear understanding of the conversion of analytical method, tabulation method and image method of functionsBy analyzing the data gained by the questionnaire survey among the students and the interview conducted among the teachers, the paper summarizes the difficulties for senior grade one students to learn functional concepts, analyzes and finds out the causes and puts forward some teaching suggestions:(1) Integrate the formation process of functional concepts into teaching design(2) Explain the variable statement of functions to students(3) Flexibly convert the function representation methods(4) Discover the existence of functions in real-life examples(5) Teachers should strengthen the abilities and apply multiple teaching methods...