| Function is a common thread for high school mathematics curriculum.Function monotonicity,which is the core concept of function system,is the most important basic property of function.Function monotonicity is complex and abstract,which is a difficult point in senior high school mathematics teaching.High school students have difficulty learning function monotonicity.Thus,the research on how students understand function monotonicity has been done to help teachers teach function and some targeted teaching suggestions are to be offered as follows.Based on SOLO classification evaluation of learning theory,the research involves tests on three dimensions design,which are the concept of function monotonicity,the judgement of function monotonicity plus the monotone interval monotonicity and the application of function monotonicity.The test questions were distributed to students from ten classes in Grade 2 and Grade 3 and the level of understanding of students was divided and the test data was statistically analyzed.In order to know about the factors that affect the understanding of "function monotonicity" especially the non-intelligence factors and find out the correlation between the understanding level and the non-intelligence factors part of the participating students from Grade 1 and Grade two are selected,who are surveyed by mathematics learning characteristics questionnaires.It is found that the students performed averagely in understanding the concept of function monotonicity.Most of them reached level U and M.In the dimension of monotonicity judgment and monotonicity interval,40%of students reached M level,and 11%reached R level.More than half of the students in the integrated application dimension reached the M level,and the comprehensive application dimension level of the function monotone understanding was the highest.In terms of the level of comprehension,the level of senior three students is higher than that of the senior two.In terms of sexes in comparison,boys are obviously far better than girls on P level,U level and M level and slightly better on R level.The survey statistics show that the correlation coefficient between the level of understanding and mathematics learning characteristics of non-intelligence is 0.24.Since the correlation coefficient is less than 0.3,a conclusion can be drawn that the level of understanding and mathematics learning non-intellectual characteristics has certain correlation,but the relationship is relatively weak,having no significant influence.Based on the results of the study,it is suggested that unit teaching design of function monotonicity should be involved in teaching practice while teaching function monotonicity.Unit teaching design should be made on the basis of the whole system of high school mathematics,clarifying the specific understanding of function monotonicity at different content for high school students.As for the teaching process of the contents related to the function monotonicity,mathematical thinking methods,such as classification,combined number form and equivalent transformation should be permeated to the teaching in order to deepen the students' understanding.The students' mathematics accomplishment should be cultivated through function monotonicity understanding of core concepts.Students are expected to perceive the significance of function monotonicity and find out the changes of function value by visual imagination.Students will be able to fulfill their understanding of function monotonicity once they understand the transformation of the constant to the variable by logical reasoning.In the abstract aspect of mathematics,the concept of monotonicity of functions is abstracted based on the intuition of the image,and the mathematical terms are used to represent it.In terms of computing power,it is very important to define the monotonicity of monotonicity and solving the monotonicity of functions with derivative.At the same time,the students should be preparation to improve their understanding of the problems and tests. |
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