An Investigation On The Understanding Level Of Trigonometric Functions Among Senior High School Students

Mathematical understanding plays an important role in mathematical education,and the goal of mathematical learning is often to obtain a deep and conceptual understanding of mathematical phenomena.Trigonometric functions are a bridge between geometry and algebra,and students’ understanding of their images and properties can greatly improve their ability to apply them.Therefore,this study uses trigonometric function images and properties as knowledge carriers,using test methods and interview methods,to investigate the current situation and difficulties of understanding trigonometric functions among students of different grades,and provide suggestions.This study develops test questions based on the classification framework for mathematical understanding,and develops corresponding scoring standards based on Professor Cai Jinfa’s scoring standards for mathematical test questions,combining the content of this study and the classification framework.The research mainly answers the following three research questions:(1)At what level do high school students have a mathematical understanding of trigonometric functions?(2)What are the differences in understanding trigonometric functions among high school students of different grades?(3)What problems do students have when understanding trigonometric functions?In response to the research questions,a test was conducted on students in Grade 2and Grade 3 of a high school in Shanghai.Through quantitative analysis of the test data and qualitative analysis of the interview results using SPSS software,the following research conclusions were obtained: In terms of the current situation of students’ understanding of trigonometric functions,(1)the vast majority of students in Grade 3 can achieve high levels of memory and algorithmic understanding in the understanding and learning of trigonometric functions;(2)Senior three students can basically achieve the level of interpretive understanding,but not many students are at the level of exploratory understanding;(3)Senior two students can achieve algorithmic understanding level,but their memory understanding level still needs to be improved;(4)The level of interpretive understanding among senior two students is generally low,and fewer students are at the level of exploratory understanding.Moreover,in terms of grades,senior two students’ performance on various levels of test questions is somewhat worse than that of senior three students,especially in terms of memory understanding and explanatory understanding.Students have the following problems in understanding trigonometric functions: 1 Students do not have a good understanding of some basic knowledge points of trigonometric functions;2.Students have a mechanical understanding of image changes;3.Students cannot well combine the properties of trigonometric functions and images to think about problems.Based on the above conclusions,the author puts forward suggestions on three aspects: students’ learning strategies for trigonometric functions,teachers’ teaching of trigonometric functions,and research on students’ understanding of mathematical knowledge.