| In math learning,the importance of "understanding" is self-evident."Understanding learning and teaching of mathematics "has become a hot topic in mathematics education research.In order for teachers to help students to achieve in-depth understanding through effective teaching.The seven dimensions of"understanding" cognitive process in bloom’s new objective taxonomy: explanation,example,classification,summary,inference,comparison and explanation are taken as the theoretical basis,the author carried out "research on teaching of trigonometric function based on deep understanding”.This study mainly discusses three issues :(1)Investigate the cognitive dimensions of students’ understanding of trigonometric function and the implementation of teachers’ understanding in the teaching process;(2)Instructional design of trigonometric function based on deep understanding;(3)Instructional strategies based on deep understanding.The research adopts several scientific methods,including literature research,questionnaires,interview,and case studies.Firstly,There are four parts of trigonometric function that are required to be understood in Curriculum Standards.Through questionnaires and interviews,the author can understand the current status of students’ understanding of trigonometric function,and the difficulties and corresponding breakthrough ways in the teaching process of teachers.Secondly,This paper discusses the generalized model of deep understanding instructional design.Combined with the teaching status of trigonometric function,the study forms five teaching designs that promote students’ deep understanding.Finally,based on the implementation of instructional designs,the study proposes the teaching strategies of deep understanding.The conclusions consists of three parts:Firstly,The current situation of students’ understanding of the cognitive dimensions of "Arbitrary Angle Trigonometric function","The fundamental relationship with the same Angle trigonometric function","Images and properties of trigonometric function","the image of y=Asin(ωx+ψ)".Secondly,The instructional design model based on deep understanding:focus on curriculum standards→analysis of teaching tasks→analysis of learning → present specific teaching objectives → design target detection → arrange teaching activities → revised instructional design,the specific knowledge of different trigonometric function presents different arrangement in teaching activities.Thirdly,three characteristics based on depth of understanding:depth,breadth,penetration,the study forms the teaching strategies of deep understanding.(1)Situation creation realizes the mutual transformation of multiple representations;(2)The combination of Numbers and shapes improves the ability of abstraction and generalization;(3)Explore generalization and generate general conclusions;(4)Assimilation learning,enrich the construction of mathematical knowledge system;(5)Reveal the essence and establish causality correctly. |
