A Research On The Barriers For Senior High School Students To Understand Knowledge Of Derivative And Its Application Under The New Curriculum Reform

Calculus,which is called the milestone of the mathematic history,is another great creation with epoch-making significance after the Euclidean geometry in the history of mathematics.Derivation is one of the core concepts of calculus and it plays a very important role in people's lives and study.After the application of the New Curriculum Reform,there are some adjustments in the content of the derivative and its application in senior high school mathematic materials.It is emphasized that the teaching of derivative should focus on the essence of the concept and pay attention to cultivate students' ability of application as well as thinking logically.The mathematic thinking mode and relative mathematic culture should be combined with each other and be taught to students.It has been a consensus in the modern education that the teaching should serve for understanding.It is very important for the mathematic researchers to find out how to help students understand relative knowledge about derivative and make clear of the reasons for the difficulties in understanding.This paper aims to do research on the understanding barriers produced in the process of the learning of derivative and its application for students in senior high school and then find out the reasons for those understanding barriers through analyzing the experimental results and data.Finally,relative educational suggestions will be put forward with the purpose to provide certain reference as well as experience for the teaching of derivative in senior high school.This paper is a research which is carried out under the background of the New Curriculum Reform based on the constructivism theory through designing questionnaires and tests,and the research is about the understanding barriers existing in the process of the learning of the derivative and its application for students in senior high school.After analyzing the experimental results,the writer finds out the reasons for the understanding barriers can be list as following:(1)Students cannot make clear of the abstract concept and the geometric meaning of derivative.It is difficult for those students to understand the average change rate and the instantaneous rate of change,extreme value and the most value.And the students cannot master the meaning of those new mathematical symbols very well.(2)The basic knowledge foundation of those students is relative weak,and their comprehension and intuition are poor as well so it's hard for them accept new knowledge.(3)The studentsare lack of flexibility of thinking,their understanding of the geometric meaning of derivative is easily influenced by the mindset.And they are lack of the ability of mathematical modeling when they solve the real applicational problems of derivative.(4)The learning habits of the students are relative bad and they cannot hold on for a long time and they do not full of patience in solving comprehensive problems about derivative.(5)For those complicated derivative questions,the students are afraid of them to some extent so that some of them may be lack of confidence as well as interest.Based on the analysis of the understanding barriers that have been pointed out above,this paper aims to provide relative teaching proposals as following:(1)The abstract concepts should be made specific,and more and more examples should be proposed in order to give image support.(2)The teaching of basic knowledge should be put more attention to so that the calculation ability of mathematics can be improved.(3)Mathematic thinking need to be focused on to cultivate the thinking competence.(4)Teacher should change their teaching methods to help the students cultivate good learning habits.(5)Students are better to gain more positive emotional experience so that their learning motivation can be strengthened.