Research On The Logarithm And Logarithmic Function Of Middle School Students Of Grade Ten

In this paper, the author takes a survey on mathematical belief of students of grade ten and its effect on the study of logarithm and logarithm Function by using questionnaires and interview. The big part of the research is the problems in logarithm and logarithmic function, the reason of the difficulty will be analysed from the students'mathematical perspective (including the view of mathematics, the talent in mathematics, the belief of mathematical learning and the belief of the mathematical nature), then three case studies will show how studens'mathematical belief affect their study. From the survey the author obtains the following results:1. Students'behavior in the view of mathematics, the talent in mathematics, the belief of mathematical learning and the belief of the mathematical nature are positive, but there are difference among them, the highest positive one is the view of mathematics, the last one is he belief of the mathematical nature;2. Students' only understand the number nature of the logarithm, most of them do not understand the computing process of the logarithm, due to the limitations of the comprehension, the notation of logarithm will be considered a factor so that it can be deleted;3. Compare to the logarithm, the student tend to the exponent;4. Students are aware of the domain of the logarithmic function should be greater than 0, but in the solution of inequalities and logarithmic equations that needed to consider the domain of the logarithmic function, students ignore this condition;5. The logarithmic function combined with other functions with the letter, the students'behavior in the range, monotonicity, and the image are relatively low scoring rate;6. From the perspective of mathematical beliefs of students, although their beliefs are positive, but due to the effect of the college entrance examination and the teacher, there limitations in the comprehension of the logarithm concept, due to the difficulty of the knowledge itself allows students to master their situation is not good;7. Through the analysis of three cases, we can see that:student whose belief is negative will have a huge negative impact on the learning of mathematics, they will produce a fear of mathematics, will have an escape behavior, while those who has positive belief, although the mathematics is difficult, but their interest in mathematics will help them face the difficult and not run away. Therefore, beliefs in mathematics affect their emotional experience of learning mathematics.Some suggestions are given at the end of this paper.