Research On Learning Progressions Of Logarithmic Function For Senior High School Students

The construction of learning progressions pays attention to the internal structure of knowledge.It is not only an important tool for the study of students’ conceptual cognitive structure,but also an important trend of the current development of international education.Combining learning progressions with logarithmic function can more truly describe the thinking development process of students’ logarithmic function.Based on this,this study takes the students of three grades in senior high school as the research object,takes "logarithmic function" as the research theme,establishes the learning progressions level of logarithmic function of senior high school students,applies it to the evaluation of the concept learning of logarithmic function of senior high school students,describes their learning performance in detail,and gives corresponding teaching suggestions and academic evaluation suggestions.This paper adopts the methods of literature analysis,investigation and statistical analysis to solve the following three problems:(1)how to describe the advanced hypothetical learning of senior high school students when learning logarithmic function?(2)How to test and revise the advanced learning of logarithmic function hypothesis according to Rasch model?(3)What is the learning performance of senior high school students of different grades under the advanced learning of logarithmic function?In order to solve the above three problems,this study is divided into the following stages: first,sort out the relevant research on learning progressions theory and logarithmic function,and then establish the advanced framework of hypothetical learning of logarithmic function according to the existing literature,curriculum standards and teaching materials.Then there is the empirical research on the framework,that is,according to the framework,the teacher questionnaire and test questions are prepared,some students from a senior high school in Tianjin were selected for the pretest,the test results are analyzed based on Rasch model,and the test tool is modified for formal test.Finally,it is the research on the current situation of logarithmic function learning of senior high school students.A formal test is conducted on 260 students in three grades of a senior high school in Tianjin.According to the formal test results,the law of logarithmic function learning process of senior high school students is analyzed as a whole,and corresponding suggestions are given according to the analysis results.Through the analysis of data,this study draws the following conclusions:(1)The learning progressions of logarithmic function is divided into five levels.Level 1 is the initial perception of the concept and image of logarithmic function,and can judge whether the relationship between two variables is logarithmic function according to the relationship or image;Level 2 is an in-depth understanding of the concept of logarithmic function and image,and can find the definition domain of logarithmic function and the fixed point passed by the image;The relation between the size of logarithmic function and other functions can be compared;Level 4 is the solution of simple problems in logarithmic function,and can use the properties of logarithmic function to solve inequality problems;Level 5 is the flexible transformation of knowledge.Students have a complete concept of logarithmic function and can use mathematical ideas and methods to solve the comprehensive problem of logarithmic function.(2)The learning progressions level of logarithmic function of senior high school students is concentrated in level 4,that is,students can use the knowledge of logarithmic function to solve some simple problems.(3)There are significant differences in the advanced level of students in the three grades.Senior one is mainly concentrated in level4,senior two is mainly concentrated in Level 3 and level 4,and senior three is mainly concentrated in level 4 and level 5.The level of the three grades showed an upward trend,while the second year of senior high school was mainly limited by forgetting,so the overall level was low.(4)From the overall logarithmic function level,there is no significant difference in the average ability of male and female students,but from the proportion of men and women at all levels,the proportion of boys at a higher level is higher than girls,that is,boys perform better than girls in solving the comprehensive problems of logarithmic function.Finally,according to the specific performance of senior high school students in the process of logarithmic function advancement,the corresponding teaching suggestions and academic evaluation suggestions are given.In teaching,teachers should pay attention to the curriculum,adjust teaching methods,and pay attention to the application of ideological methods and knowledge.In the academic evaluation method,teachers should enrich the evaluation system and increase the setting of open questions,so as to understand the students’ thinking and mistakes,so as to make the teaching more targeted.