The Analysis And Teaching Practice Research On The Learning Status Of "logarithm And Logarithm Function" For High School Students

The logarithm and logarithm function is an important part of high school mathematics.The logarithm is from the United Kingdom.In the process of studying astronomy,mathematician Napier played an important role in history in order to simplify the calculations.Today,although logarithm operation has been replaced by an advanced computer,the logarithmic knowledge is already in the knowledge system of mathematics,it has become an important part of high school mathematics learning.However,because the logarithm form is more abstract,the logarithm sign is not easy to understand,and the logarithm operation is not as specific and intuitive as the previously learned operation.Logarithm function as one of the basic elementary functions,it has the characteristics of the abstraction and symbolicity of the function itself,combined with the logarithm of the correlation of the nature of the operation,resulting in students with its learning and mastering difficulties High school students,in particular,do not understand the basic concepts of logarithm and logarithmic function Accurate enough,not enough solid grasp of the relevant nature,resulting in the follow-up learning every logarithmic problems will appear fear emotion.This paper attempts to do some investigation and summary of the current status of the logarithm function learning of the first-year students,and hopes to make some positive improvements to the current hours and the current situation of logarithmic function teaching.This article is based on the general high school mathematics curriculum standard(experiment)" to analyze in detail the teaching content and teaching requirements of the "logarithm and logarithmic function",and use questionnaires to further understand the high number of students on the logarithmic time,The difference between the grip of the function and the "standard" requirement.The main questions in the survey include the following two major aspects: the image and nature of the logarithmic and logarithmic operations,logarithmic functions.The issuance of the question and answer is carried out in a layered manner and is divided into three levels of ABC,which is consistent with the hierarchical teaching of the author's school.Subsequently,several random interviews were conducted to understand and analyze the specific reasons for the differences.The author obtained the student's learning status from the above-mentioned weekly survey analysis.That is to say,different levels of students have similar passions in the study of logarithm and logarithmic functions,and they also have their own points of view.Common grounds are(1)lack of knowledge of background knowledge;insufficient understanding of the history of logarithm inventions,and the inability to recognize the value and significance of logarithms.(2)Absence of analogy and correct migration;(3)Lack of development and application of mathematical thinking methods;(4)Lack of ability to use mathematics to solve practical problems in the central government.Different points are specifically expressed in the following aspects: In the study of logarithms,the students in the C-th layer only saw the logarithm of the number,and most of the students did not see it as representing one side of the calculation process,thus understanding the logarithmic symbols.The limitations have led students to put logarithm "Log" is used as a factor to perform an approximate operation,and the overall knowledge and understanding of hours is not deep enough.The knowledge of simple knowledge can be applied.The concept of the student's understanding of diligence and related operational properties,but in the pair and index relational operations,biased sentences are thought in the form of exponentials,especially when they involve the problem of a time-series equation,which is often converted into an exponential form and then performed operations,while in the logarithmic function part,complex functions with parameters or complex forms are involved.To understand the difficulties,at the same time,from the simplistic to logarithmic domain definition problem,we can see that students all know that the logarithm of the true number should be greater than zero,but when solving logarithmic inequalities,solving logarithm equations,and the need to consider the value of real numbers,Students tend to ignore the condition that the true number is greater than “zero”,which leads to the error of the final result.The students at the a-level can grasp this basic knowledge and have basic mathematics ability in the process of solving problems,but the mathematical thinking method The ability to solve problems in mathematics needs to be improved.When the logarithmic function is compounded with other functions that contain letters,students have difficulty understanding the complex functions.In particular,the compound function contains.The number of passionate brothers,such as the monotonicity of "same-increasing differences",such as the complex function definition domain and value domain problems,etc.The author combines his own teaching practice,put forward more effective hours and logarithmic function teaching strategies,For reference,it mainly includes the following points:(1)Optimize the teaching process and continue to implement “layered teaching”.(2)Emphasis on the teaching of mathematical symbols and analyzes the essential meaning of the symbols.(3)Strengthen the background of knowledge generation to promote students' All-round development.(4)Cultivate students' confidence in mathematics learning and increase their ability to study mathematics.(5)The spiral of the main study has risen,gradually increasing the depth of understanding.