Research On The Understanding Level Of Function Monotonicity Of The High School Students

Function is one of the most important contents of high school mathematics curriculum, the function is the first nature of the number of functions, but also a core concept throughout the function system. Expansion and extension of the monotonicity of the function is the function concept, or continued research refers to the function number, on the number of function and trigonometric function monotonous content based, should be, study and solve various problems in learning the specific functions and have a wide application. However, the monotonicity of the function has the complexity and abstractness, is a difficult point in the high school mathematics teaching, high school students to master the monotonicity of the function is difficult, here by the solo classification and assessment learning theory,starting from the definition of monotonicity of the function and application of monotone function district and the monotonicity of the function of the three level, the survey of high school students understanding level of function monotonicity. First tested by the questionnaire of students of monotone function understanding level of overall distribution, followed by that of students in understanding the monotonicity of the function of the main errors, and finally put forward to improve high school students of monotonic function of comprehension teaching strategies.Through the research,the understanding level of the function monotonicity of the senior high school students is as follows:1. High school students in the level of understanding of " monotone function definition " dimension is generally, most of the students can repeat function monotonicity definition but it can’t grasp the essence of the monotonicity of the function, be defined accurately described, and the rigorous evidence monotonicity of the function. In this dimension, high school students only achieved a single level of structure and multi structure, and the level of association structure and further level of abstraction should be further improved.2. Most senior high school students are in a single level of structure and multiple structure in the dimension of "seeking function monotone interval". Only a few high school students have reached the level of related structure. Students only remember the monotone interval of several commonly used methods and application conditions, do not trace, is merely formal to memorize and apply the formula and properties, the monotonicity of the function for understanding the nature of the is far not enough understanding. In this dimension, most students are in a single level of structure and multi structure, only a very small part of the students to achieve the level of the related structure.3. Effective data in "application of the function monotonicity" dimension shows that the students have a certain improvement in the understanding of the function and the application. Many students can make use of the monotonicity of the function to solve some simple application problems, some of the students to the monotonic function and derivative, parity and basic elementary function of the nature of the contents of the connection, to solve the slightly more complicated problems. In this dimension, the proportion of students with a single structure is significantly reduced,and the proportion of the students in the related structure level has increased.Girls atall levels of monotone functions on the understanding of the overall level of understanding is slightly higher than boys, but the gap between the two.4. Boys and girls in the level of understanding of the function of the monotonous and did not show a significant difference, the difference in the data are within ten percentage points. The level of understanding of the function of the science class is obviously higher than that of the liberal arts class, and the liberal arts students have a greater understanding barriers of the learning and mastery of the function monotonicity.The main factors that affect the function monotonicity of senior high school students are as follows:1. The abstractness of mathematics affect the understanding the monotonicity of the function of high school students.2. The old knowledge is not firmly grasp affect the understanding about related knowledge of monotonic function.3.The lack of mathematical intuition affect the understanding the monotonicity of the function of high school students.Based on the research of the understanding level and the main factors of the function of the senior high school students, the paper puts forward some suggestions on the teaching of the function of the present stage.