Research On Unit Over All Teaching Design Based On Problem-driven

Solving triangles is an important part of middle school mathematics,but also the hot spot of the college entrance examination.2019 renjiao A version textbook fully incorporated the sine theorem,cosine theorem and other solving triangles knowledge into the plane vector knowledge system.It proves the sine and cosine theorems using plane vectors,highlighting the functions of the plane vector to study geometric problems.A general approach for the study of geometric problems by plane vectors is also shown.But at the same time,this textbook processing method also masks the geometric background of sine theorem and cosine theorem.The students lack a comprehensive and overall understanding of them.It is not conducive to students to understand the essence of sine theorem and cosine theorem and the comprehensive application ability of forming the two theorems.The author bases on the problem driven theory and unit overall teaching theory,to get through the middle and high school knowledge context as the goal,construct a whole solving triangles knowledge teaching scheme.On the basis of the study of sine theorem and cosine theorem by vector method,the author adds plane proof method and the corresponding problem chain,as the reference of high school mathematics school-based curriculum.Aim to make students have a more comprehensive and systematic understanding of solving triangles in high school.This study also analyzes the basic characteristics and effective application of problem-driven unit overall teaching design.This study first uses literature research method to analyze and comb relevant teaching theory and triangle knowledge to form their own understanding: Problem-driven teaching theory aims to enable students to "recreate" mathematical knowledge in the process of mathematics learning and understand the essence of knowledge;Unit teaching theory aims to pay attention to the integrity and relevance of knowledge,and promote students to form a complete and clear cognitive structure.This study further analyzes the historical development context of solution triangle and the content system of solution triangle in different textbooks to find the development core and essence of sine theorem and cosine theorem,and integrate it into the teaching.Further,this study used the empirical research method to investigate the psychological characteristics of students in the formation of solving triangles knowledge,and interviewed the understanding and understanding of the front-line teachers to analyze the key points of the relevant teaching design.Finally,the problem-based unit overall teaching design scheme of sine theorem and cosine theorem is formed,as a school-based course to solve triangles,and its promoting effect on students’ overall understanding of relevant knowledge is obtained.This study takes students’ existing geometry knowledge of "the equality of triangles","solving right angled triangle" and " the Pythagorean theorem" as the starting point of cognition to design the overall teaching scheme of solving triangles topic.In line with the cognitive characteristics of students and in line with the context of the development of knowledge;In the teaching of the sine theorem and the cosine theorem proof,Based on a problem-driven teaching theory,with the help of the mathematical history elements of the relevant knowledge,Building a more comprehensive teaching system,It is beneficial for students to understand the nature of the theorem;With "how to determine a triangle" as the core to build a holistic unit teaching program,construct a clear knowledge structure;At the same time,this study attempts to connect the context of the relevant teaching content of middle and high school,let the students build a more perfect and clear cognitive structure.It also has a certain reference significance for the development of middle school mathematics school-based curriculum.