Research On The Application Of Subject-based Teaching Method In The Teaching Of Acute Angle Trigonometric Functions In Junior High School

Subject-based teaching is a teaching mode formed gradually under the influence of the concept of "unity of teaching and research" put forward by Humboldt in Germany in the early19 th century.It is widely used in the field of higher education and vocational and technical education,so that its application value is self-evident.In recent years,a new definition of subject-based teaching has appeared in the research of mathematics’ teaching.It is different from the previous subject-based teaching in that the former is similar to the current small subject research in middle school which emphasizes that students experience a certain research process.The latter requires teaching design and teaching to focus on the essential content — problems,ideas and methods,so that students can understand what problems to solve,how to solve them and what is the value of problem solving.In this study,the subject-based teaching requires teachers to grasp the knowledge connection and dig the core problems from the perspective of mathematical knowledge development research.In the teaching design,the overall design highlights the knowledge connection of the subject.In the local instructional design,we create the situation around the core issues,and design the guided question chain to lead the class together,so that teachers and students can carry out "hot thinking" in the teaching activities.Through the process of thinking,students "re-create" knowledge,grasp the mathematical ideas and methods,and establish a related knowledge framework.Based on the investigation to grasp the teaching situation of "acute Angle trigonometric function",this research carries out the design of the teaching reconstruction of "acute Angle Trigonometric function" under the guidance of the subject-based teaching mode.In the historical research of trigonometric knowledge,it is concluded that trigonometric knowledge can be studied in two lines—the calculation route and the function route,thus we form two projects — the triangle solving project and the trigonometric function project.The acute Angle trigonometric function in junior high school belongs to the triangle solving project.In the whole teaching design of the triangle solving project,we strengthen the knowledge connection of the project by creating a unified unmeasurable problem as the research situation,using the triangle equality to judge whether the triangle can be solved and its solution situation,and using the geometric method to prove the sine and cosine theorem.The acute Angle trigonometric function teaching design developed under the guidance of the subject-based teaching mode has the following distinct characteristics:1、Clear knowledge orientation.In the triangle solving project,the acute trigonometric function is defined as the geometric knowledge,which reflects the aspect ratio of the Angle relationship of right triangle,and the situation is created under the background of the unmeasurable problem,which highlights the application value of the acute trigonometric function knowledge.2、Knowledge is closely connected.The use of triangle congruence to determine whether a triangle is solvable can naturally lead students to pay attention to solving triangle problems."Making a high method" can realize the transformation of solving general triangle problems into solving right triangle problems,promote students to grasp related content and important methods in learning,and help students to build a meaningful knowledge system.3、Realize knowledge "re-creation" naturally.Centering on solving the core problem of right triangle,the guided problem chain is designed to guide students to find the law of "constant side length ratio of acute Angle" in similar right triangle,so as to deepen students’ essential understanding of the relationship between sides and angles by solving right triangle problems,and complete knowledge construction.Finally,teaching practice activities were conducted to test the effect of teaching reconstruction.Teachers who participated in course evaluation all believed that the "acute Angle trigonometric function" teaching design developed under the guidance of the subject-based teaching mode was feasible,and they also showed strong interest in the subject-based teaching mode.