An Investigation Into High School Students' Understanding Level On Trigonometric Formulas For The Sum And Difference Of Two Angles

With a test based on SOLO classification theory and a questionnaire,this paper,taking191 high school students from two schools in Urumqi as the research object,makes an investigation into high school students' understanding level on trigonometric formulas for the sum and difference of two angles from three dimensions: cosine formula for the difference of two angles,transformation of formulas for the sum and difference of two angles,use of formulas for the sum and difference of two angles.The results are as follows :High school students' understanding level on trigonometric formulas for the sum and difference of two angles:(1)on the dimension of cosine formula for the difference of two angles,most students' understanding is at unistructural level and multistructural level,and there is some clear difference between understanding levels of different grade students,but no clear difference between understanding levels of different male and female students;(2)on the dimension of transformation of formulas for the sum and difference of two angles,most students' understanding is unistructural level while others' is multistructural level and relational the level,and there is no clear difference between different grade students' understanding levels,also between male and female studennts' understanding levels;(3)on the dimension of application of formulas for the sum and difference of two angles,most students' understanding is multistructural level level while others' is unistructural level and relational the level,and there is no clear difference between different grade students' understanding levels,also between male and female students' understanding levels.The factors that have effects on high school students' understanding level on trigonometric formulas for the sum and difference of two angles:(1)There are many trigonometric formulas,which are difficult to memorize,and students easily get confused when using these formulas;(2)Some students pay little attention to the ways of proving the formulas,examples and exercises on the textbooks;(3)Some teachers ignore the importance of proving formulas in class,and pay little attention to examples and exercises on the text books;(4)There are too many exercises and not enough examples on the text book.Some exercises are too difficult while examples are easy.Suggestions from the research are as follows:(1)Teachers should stress the importance of proving trigonometric formulas,and encourage students to prove the formulas in different ways by themselves;(2)The chapter of Trigonometric Functions and chapter of Trigonometric Formulas for the Sum and Difference of Two Angles should not be separated on the text book;(3)Text books should adjust the quantity and difficulty of examples and exercises,appropriately increasing the number of examples but cutting the number of exercises.