Research On Understanding Level Of Logarithmic Function And The Influencing Factors Of High School Students

In mathematics study, "understanding" is undoubtedly the most important one, it has become a central topic which the world’s mathematics education focused on after "problem solving".The logarithmic function as one of the six basic functions,has a significant contribution in science, computer and other fields.Based on "logarithmic function" as a breakthrough point, this paper explore the high school students "logarithmic function" the understanding level and its influencing factors. In the first this article introduced the selected topic background,research questions and research significance, by collating relevant "logarithmic function" and "understanding" of related literature and data, and then detailed combing the related articals of the SOLO evaluation system theory. We selected 261 High School Students from the Senior High School in Urumqi and Xinjiang Normal University Attached High School as our research object.Using self-made questionnaire, supplemented by ways such as classroom observation, interview after class to explore senior high school students "logarithmic function" level of understanding and the factors affecting their understanding. This article divided the "logarithmic function" into three big dimensions investigation:the definition of“Logarithmic Function”, the image of the “Logarithmic Function”, the property of the “Logarithmic Function”.There are four main conclusions drawn in this paper:First,the level of students understanding(1) from the overall,their understanding level is not high:their is a better grasp in the dimension of the definition of“Logarithmic Function”,but there are still some students stay in the Unistructural Level, students has a poor performance in the dimension of image of the“Logarithmic Function”,the number in the Unistructural Level is the majority,in the dimension of the property of the “Logarithmic Function”, students has a long way to go.(2)The Key Classes’ understanding level are significantly higher than regular classes in each dimension.(3)The students’ understanding level in grade 11 is significantly higher than the students in grade 10,while the students’ understanding level in grade 12 is significantly higher than the students in grade 11,though the students’ understanding level in grade 12 is higher than the grade 11,but did not reach significant level.(4) in each dimension, male students scored an average which is higher than girls, but the difference was only in the image of the “Logarithmic Function” and the dimension of range, there was no obvious difference between other dimensions.Second,the main problems in students’ understanding:(1)bad symbol sense;(2)bad computing power,there isn’t a knowledge network in their mind;(3)weak drawing knowledge;(4)confusing the domain and range.Third,the factors affecting the high school students’ “Logarithmic Function"understanding level :(1)objective aspect:the difficult content about the “logarithmic function”,the tedious operation of “logarithmic function”,too less class capacity;(2)subjective aspect:poor symbol sense,a less learning about the origin and the role of the “logarithmic function”,a weak understanding on the contact between the Exponential Function and the Logarithmic Function and so on.Fourth, the suggestions and enlightenments:(1)strengthen the teaching of symbols;(2)internalize the relevance knowledge;(3)using the multimedia teaching;(4)increase the teaching hours appropriately.