Teaching Research On The Concepts Of Calculus In High School

As an important basis and starting point of modern math, calculus has been widely considered and used as a crucial research tool in many natural sciences, such as physics, astronomy, and economics. Since the abundant thinking patterns implied in calculus play a significant role in developing students’ thought abilities, it will be necessary to set up calculus courses in high schools, for one thing, to keep up with the scientific and technological developments, for another, to meet both the developmental and educational demands of high school math.This paper resorts to questionnaire, test and interview, aiming at leaning about high school students’ study situation of concepts of calculus. On this basis, the road of current math reform can be more practical and beneficial. This paper attempts to answer the following three research question.1. Can high school students learn concepts of calculus beyond limit concept?After consulting previous relevant studies, questionnaire surveying and interviewing, the writer concludes that it is very useful to analyses examples before teaching the concept of limits, because this way of teaching follows the laws of students’ cognitive and psychological developments, so it’s more impotent to learn the limit idea than the limit concept.2. How is high school students’ cognitive situation of concepts of calculus?With the method of testing subjects, this paper studies and analyses high school students’ cognitive situation of concepts of calculus from four perspective, rate of change, the meaning of derivatives, the meaning of definite integral and the application of calculus in mathematics and daily life. The later questionnaires surveys students’ attitudes and interests in calculus, and shows their cognitive situation of limits thinking and knowledge about history of calculus.3. What are the main cognitive difficulties of high school students in learning concepts of calculus and what are the reasons?The main cognitive difficulties of the concept of derivative of high school students have been found by anglicizing of test results. We also find out its causes by concepts of calculus characteristics, students’ cognitive development levels, and teaching methods of teachers.The last part of this paper gives some suggestions about class teaching of concepts of calculus and class designing. Firstly, concepts can be represented from different perspectives but the essence of concepts should be highlighted; Mathematical thinking had to be referred to; focus on practical applications of calculus; teaching can be combined with multimedia; the last but not least, students should be guided to learn the history of calculus and its cultural values.