Research On The Evaluation Of Exponential Function Understanding

Conceptual understanding is an important foothold in mathematical learning.Students' 1 ack of understanding of concepts will hinder short-term mathematical learning and long-term mathematical application.Knowing how students understand conceptual understanding is a n important direction in current conceptual understanding research.The understanding of th e concept of exponential function is the important content of mathematics teaching in many c ountries.Based on the existing evaluation model of conceptual understanding,this paper proposes a new evaluation model with perception,representation,connection,and application as the f irst-level dimension,and then establishes the corresponding second-level dimension based o n the concept of exponential function.The main questions of the research are:1.What is the s tate of students' understanding of the concept of exponential function?2.Based on the stude nts 'understanding of the exponential function and mathematics learning situation,what is th e cause of the students' understanding state?what teaching suggestions can be made?3.Ca n students' math scores be used to measure their ability to understand exponential function c oncepts?During the research process,the first-year students were tested and analyzed about the c oncept of the exponential function concept and mathematics learning,and then integrated the students' final math scores in 2019,and obtained the following conclusions:(1)Students' ability to understand the concept of exponential function shows differences in class and gender.Students in class A and class C have a high scoring rate,while students i n class B have a low scoring rate.Examples dimensions and symbols indicate dimensions sc ore rate is high.Concept link scoring rate is the lowest.The gender difference between the c oncept connection dimension and concept application dimension in class A is the largest.(2)It is difficult to accurately discuss the situation when the base is less than 0 in the int erpretation dimension.The examples given by students have obvious limitations.The langu age of the presentation dimension is not accurate enough.The image indicates that the error rate is higher than that of the symbol.The conceptual connection dimension shows that the c onnection ability with the exponential and exponential power operation and the application o f the exponential function concept is low.The concept application dimension shows that stu dents' ability to solve the problem by incorporating the exponential function into a good kno wledge structure needs to be strengthened.(3)Students understand the concept of exponential function and state influencing factor s.Firstly,students do not have a thorough understanding of the concept of exponential functi on,do not have enough knowledge reserve before learning and do not apply new knowledge to solve problems after learning.Secondly,from the perspective of students' learning situatio n,it is mainly related to learning time,learning habits and students' non-intelligence factors.(4)To a certain extent,student performance can measure the level of the student's expo nential function to understand the score rate.But grades and students' ability to understand t he concept of exponential functions cannot be strictly equated.(5)There is a large gender difference between students' scores and the understanding of exponential function concepts,and there is almost no consistency.Finally,based on these conclusions,some teaching inspirations are put forward as below:(1)The teaching of the exponential function should first ensure that students have an accurate understanding of the knowledge of the previous section of the exponential function before starting;The explanation of exponential function base number and independ ent variable should be comprehensive and accurate;Examples of the introduction of the expo nential function should be extensive;When applying the exponential function to solve proble ms in life,attention should be paid to timely checking for defects,and building up a good kn owledge structure.(2)To understand the students' understanding of the concept of the expon ential function,scores is not the only criterion,specific and in-depth analysis should be done.