| Mathematical concepts are the starting point for mathematics learning and are the basis for students to learn mathematics in high school.The concept of function is one of the important mathematical concepts in junior and senior high schools,and is the core content of mathematics in middle school.At the junior high school stage,the textbook formally introduced the concept of functions,and regarded functions as an important part of numbers and algebra.After entering high school,functions have become the most difficult content in high school mathematics learning.They are the focus of the compilation and revision of new textbooks and the main line running through the high school mathematics curriculum.Research has found that middle school functions become one of the hardest concepts to teach and learn.The research on the understanding of the function concept of senior high one students has important practical value in mathematics education research.This research focuses on two issues: What are the typical errors in the understanding of the concept of function by senior high one students? And analyze the specific reasons from the perspective of the function itself,the characteristics of students' thinking,and the teaching strategies of teachers.This study mainly used the methods of testing,structured interview and literature method.487 senior high school students from provincial key middle schools were selected as subjects,and 6 students with typical wrong answers were selected for faceto-face interviews in the test results.Preliminary research has led to the following conclusions:1.The typical mistakes of senior high school students in understanding the concept of function are mainly concentrated in the following five aspects:(1)The typical errors about the concept of function itself,focusing on the view that "the function is a change relationship between variables".(2)The typical errors about the correspondence of functions,such as students thinking that "the correspondence of functions is the analytic formula of functions".(3)The typical errors made by students about function graphs are as follows: firstly,they think that all functions can draw function graphs;secondly,they think that function graphs are all continuous straight lines or curves;Identify function images in multiple images.(4)The typical errors about the relationship between functions and equations.For example,students often confuse functions and equations,thinking that x is an independent variable.For example,students confuse "graph of function" with "curve of equation".(5)The typical errors about the concept of the same function are mainly as follows: students only consider the domain of definition and ignore the corresponding relationship,or only consider the corresponding relationship and ignore the domain of definition.2.The main reasons for the typical errors in the understanding of function concepts by senior high one students:(1)The abstraction of high school function concepts and the diversity of representation forms(2)The negative transfer of junior high school function content(3)The teachers' own cognitive biases and lack of effective teaching strategies.Based on the above reasons,the author puts forward several suggestions:(1)Make a good connection between the content of functions in junior school and high school(2)Strengthen students' understanding of the essential characteristics of functions(3)Strengthen students' awareness of function representation and transformation(4)Strengthen the cultivation of students' logical thinking ability.The innovation of this research lies in: drawing on the effective function understanding framework,and designing three dimensions of function concept understanding on the basis of analyzing the essential properties of function concept,so as to analyze the typical students' understanding of function concept errors,correct students' misunderstanding of functions,improve classroom teaching strategies,and find some practical learning methods and teaching methods. |
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