Teaching Design Based On The Students’ Barriers In Understanding Derivative

As a high school elective course,calculus has become the curriculum in many countries. China’s "general high school mathematics curriculum standard(Experiment)"(hereinafter referred to as the "standard") emphasizes that calculus teaching should focus on the essence of derivative conception and pay attention to cultivating students’ ability of application and thinking; pay attention to the permeate the cultural value of mathematic thinking method education. In this paper,combined with the new curriculum standard, I made a questionnaire based on his situation of present derivative teaching and learning. According to the survey results and from the point of view of the problems of students, I design the test paper and investigate deeply from the interview. Getting the support of scientific theories by literature survey method, I determined the research subjects of this paper, mainly including:1. explore the causes of students’ barriers in understanding derivative.2. theoretical and practical study on the transformation of students’ barriers in understanding derivative. 3. study of case design and activities design based on the transformation of the students’ barriers in understanding derivative. Questionnaire on students mainly includes six aspects:(1) the habit and experience of individual learning in derivative(2) individual understanding in learning derivative in the area of knowledge and skills.(3) the personal achievement in the process and method of learning derivative.(4) the individual understand in learning derivative in the area of emotion, attitude and values.(5) the individual requirements to the derivative teaching(6) personal understanding of the mathematical culture of derivative. Test questionnaire includes the following four aspects:(1) the basic test for the concept of derivative.(2) test adapted from college entrance examination for derivative‘s application in function.(3) test from text for examples of optimizing problems inlife.(4)developing test for the thinking method of derivative. In this paper, the main conclusions of the study are two aspects, on the one hand, according to analysis, I find the factors of barriers in understanding derivatives, the factors include the feature of math subject, the abstraction of derivatives,the understanding level of senior students the rationality of teaching design and evaluation model. On the other hand is the strategy study on the derivative understanding including analysis of teaching material in the middle school, the derivative concept and symbol, the application of derivative, the moral education in the content of derivative, and the development of research activities.The study of this paper can provide some reference and experiences for the derivative learning in senior school and help the students overcome the barrier in understanding the derivative. Through the research activities, improve the students’ operational ability and ability of solving the problem and conclude some effective teaching strategies. The main creation includes four aspects: 1. the questionnaire isn’t the simple piling up, it’s designed in six aspects according to the students’ practical problems and the requirements of curriculum standard. 2. the design of test paper has great reference value. From the time, we can see the test paper is designed totally after the careful analysis of investigation, so it has strong reliability. The analysis of test papers is from the aspects of students’ no answer, part of answer, error answers, deeply understand the specific situation of the student answer and no answer, provide real materials for deep research on the students comprehension obstacles;the source of test paper is diversified, the question type includes the basic questions, the adapted questions from college entrance examination, the questions from textbook and the developing questions, this provides a good platform for the diversification of student evaluation. 3. the study emphasizes the importance of the development of research activities and provides a good case guidance for the model of research activities and diversity of evaluation. 4.this paper does a complete consolidation in the data for the test of derivative in the college entrance examination, makes a deep analysis for the test content, and puts forward a good teaching suggestion.