Investigation Of The Logarithmic Function Understanding Level Of High School Students

This paper investigates the level of understanding logarithmic function of highschool students through questionnaire. On the theretical basis of SOLO,the writersolves several issues related to the model established by the logarithmic function fromthe perspectives of the monotonicity of the logarithmic function (comparisonbetween several logarithmic function and discussion on the monotonicity oflogarithmic function), its domain and the image relation between exponentialfunction and logarithmic function. The students’ understanding level of thelogarithmic function is analysed from the four aspects, studying the level ofunderstanding and the impact on the future of learning function.The research resultsare as follows:1.There is a big difference on the levels of students’ understanding of thelogarithmic function. They understand the logarithmic function domain and therelation between exponential function and logarithmic function best. Theunderstanding of the range base of logarithm function and the monotonicity takes thesecond place. They solve the problems of the model established by the logarithmicfunction with the highest enthusiasm, but it’s the most difficult.2.The students are better in the understanding of the comparison of thelogarithmic function’s images with a plurality of base, while accuracy is not high.Senior one students are not clear in the thinking of solving mathematical problems ofclassification.3.The majority of students require that the antilog of a logarithmic function begreater than zero in solving the domain of the logarithmic function, on which a smallpart of the students are not very clear.4. Students can transfer mathematical expressions and image in understandingthe relations of images between the logarithmic function and exponential functionwith a relatively high rate of accuracy. But in the same plane of rectangularcoordinates, there are still problems in judging the images of exponential function andlogarithmic function.5. It is an important part of curriculum standards for students to understand themodel established by the logarithmic function which is also the need to develop theability in new curriculum reform. While students see this question they will think the topic is too long, do not want to read, or hint that he will not solve it. They do notthink actively, causing that the problem of accuracy is not high. But in fact, accordingto the SOLO, the students’ understanding level of the model of logarithmic function isnot bad for the students who take the initiative to do the questionsFinally, according to the study the author puts forward some suggestions.