Problem-driven Research And Teaching Reconstruction Of Probability Teaching In High School

Probability theory has abundant thought methods,among which random thought and random method are its unique characteristics.It enriches our methods of understanding the world and changes the limitations of our deterministic thinking.This study takes the high school probability unit as an example,based on the roblem-driven reconstruction teaching,explores how to integrate the problem-driven teaching theory with mathematics teaching.The research mainly explains the following four aspects:(1)To analyze the present situation of senior high school teaching through classroom record and online interview,to further study high school probability teaching at home and abroad through literature analysis,to analyze the existing problems,and to analyze the problem-driven theory in depth from the connotation and significance.(2)Analysis of the historical development of probability to understand the probability of what causes the development? The development of probability through which several important stages,the root of the concept and the relationship between knowledge points,from the historical point of view of high school probability curriculum,re-examine the content of high school probability teaching,for teaching reconstruction to bring enlightenment.(3)Analyse the content of the current two-edition high school mathematics textbook probability unit,analyze the difference between the two-edition textbooks from the knowledge system,content arrangement,chapter introduction,concept expression and concrete content presentation,and analyze the characteristics and shortcomings of the textbook compilation.(4)Reconstructing the content and order of probabilistic teaching on the basis of problem-driven theory,proposing first probability and then statistics from the whole teaching order,focusing on the integrity and systematicness of knowledge,combining the whole high school probabilistic teaching content organically with the core concepts of sample space,classical probability type and random variable,reflecting the relationship between knowledge and realizing the problem-driven reconstruction of high school probabilistic teaching.The following conclusions are drawn:(1)Problem-driven reconstruction of high school probabilistic teaching content.Through the analysis of the present situation of probability teaching in senior high school and the literature analysis of probability teaching research in senior high school,this paper grasps that the root cause of the problems in teaching is the lack of teachers’ understanding of the essence of concept and the lack of understanding of the history of probability development.Teachers’ mathematical literacy and their understanding of probability knowledge are important influencing factors in teaching classroom.Through combing the history of probability,the development of probability has experienced three important periods,from the historical point of view of high school probability curriculum,re-examine the content of high school probability unit,deeply analyze the teaching materials,find out the shortcomings of the teaching materials.To solve three problems,(1)the integrity and systematization of the whole teaching structure: adopting the teaching order of probability and statistics;(2)adjusting the teaching according to the order of historical development to reflect the essential relation between knowledge.The teaching reconstruction is based on three core concepts:sample space,classical probability and random variable.(3)Introduction of strict definitions of key concepts.For example,the definition of probability,the definition of random variables.The reconstructed teaching is more conducive to students’ learning,knowledge mastery and ideological methods.(2)Read the teaching material deeply,excavating mathematics essence,forming high school probability teaching case design Combing history is helpful for us to analyze the content of teaching materials and reflect on the rationality of teaching content from the angle of history.Following the clue of historical development and the root of concept,the probability teaching is reorganized from the point of view of problem-driven,and the teaching case design of high school probability unit is formed,which can be used for the reference of front-line teachers.The mathematics teaching under the problem-driven teaching theory pays attention to the analysis of the essence of the concept and the positive thinking of the students through the real and effective problems.In order to change the concept of teaching is not clear,students passive thinking of the teaching situation.(3)To provide new thinking direction for middle school mathematics teachers to determine teaching contents The problem-driven mathematics teaching emphasizes combing and analyzing the historical context of subject development from the macro level and excavating the ideological methods contained in knowledge.To grasp the historical and logical order of subject development as a whole,to seek the most suitable teaching content and the general direction of teaching order for students to learn,and to reconstruct the unit teaching content in combination with the teaching material content,that is,to examine the teaching content from a historical perspective.The microcosmic level combines the student mathematics reality,reconstructs the concrete concept class or the principle class teaching content,determines the concrete class time to teach what.The problem-driven theory provides a new direction for teachers to grasp and determine the teaching content and the organization of teaching.To a certain extent,problem-driven teaching theory affects teachers’ re-understanding of mathematics teaching and better realizes student-centered teaching.