A Novel Problem-Driven Teaching Method Based On The Problem Decomposition And Its Application Research

The basic idea of the Problem-driven teaching(PDT)method,also called problem-based Learning(PBL)method,is introduced in this master's thesis.Combining our practice of‘teaching' and ‘learning',a novel PBL method is proposed based on the problem-decomposition.The new method decomposes the problem,which is also called the main problem,to be solved into some sub-problems,the logical relation between the main problem and sub-problems and among all sub-problems is presented,the knowledge points attached to each sub-problem are explored and the corresponding knowledge base of each sub-problem is also created.Solving some sub-problems in proper order arrives at the solution of the main problem.Three methods of literature research,case analysis and theoretical analysis are tried to bring together in this paper.The research status and the essence of problem-driven teaching method is gradually getting clear.The novel problem-driven teaching method based on the problem decomposition is applied to deal with the teaching design and teaching process of mathematical teaching contents of all sorts of different grades in primary schools,junior high schools and senior high schools.The paper consists of four chapters,which are as follows.The first chapter is about the introduction.The background,significance and research history are presented by reading literatures of problem-driven teaching at home and abroad.The second chapter is about novel problem-driven teaching method based on the problem decomposition.Some understandings and theoretical basis of original problem-driven teaching method are introduced,and a new problem-driven teaching method based on the decomposition of problems is proposed.The theoretical basis such as the proximal development zone(ZPD),the constructivism theory and Kohler's Epiphany theory of the new problem-driven teaching method is introduced.The five advantages of the new problem-driven teaching method are analyzed.The two methods,i.e.,linear decomposition and nonlinear decomposition for decomposing the main problem into some sub-problems and the implementation steps of the new method are presented,respectively.In order to highlight the importance of the problem-driven teaching,the similarities to and differences of the heuristic teaching method from the problem-driven teaching are introduced.The third chapter is about the description and construction of mathematical knowledge base associated with all sorts of different grades in primary schools,junior and senior high schools,and the knowledge base needed for the new problem-driven teaching method based on the problem decomposition is constructed based on the mathematics textbooks published by Beijing Normal University Press.It is found that when using the problem-driven teaching method,the problem structure of problem-driven teaching should be hierarchical in practice,the problem design should be objective in different learning phases and based on the theory of the zone of proximal development and the sub-problems constructed should be strategic and systematic.The fourth chapter is about the practice of the novel problem-driven teaching based on problem decomposition.Taking junior and senior high school mathematics as the research object,the new problem-driven teaching method is applied to carry out new courses and exercise class,and research cases are selected for each type of class.