Instructional Design Of Solving Triangle Examples And Exercises

Solving triangles is an important content in high school mathematics,and its importance is also reflected in the college entrance examination.Solving triangle is a further extension of solving right triangle in junior high school.Students are just exposed to this kind of knowledge,especially there are difficulties in practical problems.In order to help students overcome difficulties and solve the situation of their limited knowledge,the author conducted the teaching design study of solving triangle examples and exercises in senior high school.Instructional design of solving triangle examples and exercises consist of three aspects: the choice?explanation and variation of exercises.This research mainly discusses three questions: 1.Students' current level and target level;2.The strategy of selecting problems and variant problems;3.Demonstration teaching case of solving triangle's recitation.This study focuses on the methods of literature research,interview survey,classroom observation and testing.First of all,through reading the references,it is confirmed that the first four of the six levels of the Bloom's taxonomy of educational objectives are used to evaluate the students' pretest and interview and analyze the errors in the students' pretest,then use the six levels to evaluate the students' post-test and interview.Secondly,the selection criteria of the basic application and practical application of triangle solution are determined through references and interviews with teachers.In addition,it would get the basic problem types and solution analysis of basic application and practical application of solving triangles through the recent eight years of the college entrance examination papers and the exercises of the unit of solving triangles in the teaching of A version,and finally determined the specific examples;Then,in order to mainly emphasize the key and difficult points of a set of problems,it could design the variant problem group by using some existing variant methods from the literature according to the determined examples;Finally,it would get the result of the teaching design of problem solving according to the selected examples,variant results and the students' current level and goal level.Through the above five steps of research,the following conclusions are finally obtained: At first,students' error types of solving triangles mainly include knowledge error,logic error,strategic error,potential hypothesis error and testable error,which are divided by using six levels of the Bloom's taxonomy of educational objectives.The target level of basic word problems is close to that of college entrance examination,while the actual target level of word problems is that students can independently design solutions.Secondly,the better standards of the basic word problems are that the problem set is simple and easy to understand and the exercises can be expanded further and variable;it could use one method to solve a class of problems.The better standards of measurement problems are the problem set is simple and easy to understand and there are various solutions;the exercises can be further developed and variable;the exercises need contain important mathematical thought.Thirdly,according to the analysis of college entrance examination and textbooks,the basic question types of solving triangles are divided into problems of solving the fundamental quantity,value range,shape judgment,proving problems and so on.Measurement problems are divided into problems of measuring distance,height and angle.Fourth,The variant is carried out on the basis of the basic question and then it is necessary to determine the core content of the examination in the light of the basic application of the question,and use the methods of solving basic quantities transforming conditions for variant problems;For the measurement problems,the method of simplifying conditions is mainly used to change from the simplest problem to the complex one,so as to master the core content.Fifth,considering the students' possible problem-solving ideas and the students' level and grasping the potential distance between variable exercises are necessary in order to get the teaching design.Sixth,pay attention to the openness and multiple solutions of practical problems and mainly from raising questions and thinking independently to cultivate students' innovative consciousness.