Research On Design And Teaching Of Ill-structured Problems In High School Mathematics

With the progressive development of the domestic politics,economy,and culture,it requires the education system to have quick responds to adapt the current demand.Under the circumstance of the reformation of education,the ill-structured problem appears as new question type in mathematics college entrance examination,and receives attentions gradually.As a good carrier for testing students’ literacy,this type of question can not only implement students’ interpretation of the basic knowledge and skill training,but also help to test students’ thinking ability.Additionally,it is beneficial to the improvement of core literacy of mathematics disciplines,so as to realize the change from the concept of knowledge and ability towards its literacy.Based on the above analysis,this dissertation is based on the theory of cognitive resilience,the theory of discovery learning and the theory of the recent development zone,and is conducted through the literature research method,questionnaire survey method and experimental research method.The research is divided into five parts.The first part summarizes the relevant literature domestically and abroad.It summarizes the existing research on problems with ill-structure in the field of mathematics,clarifies the conceptive definition and characteristics of the problems with good structure,ill-structure,and open-ended problems,and lays a theoretical foundation.In the second part,a questionnaire survey was conducted for high school math teachers.The survey concluded that most teachers had an understanding of ill-structured problems,but not in depth.Another conclusion is that most teachers recognize the value of ill-structured problems and the necessity of design and teaching;however,there are still some difficulties on designing and teaching.In the third part,according to analysis outcomes mentioned above,following the basis and principles of problem design,this part of the study takes the methods of reorganizing well-structured questions and new ill-structured questions,and presents the design process with specific problems in combination with the content of high school mathematics as examples,in order to provide a certain reference for the design of illstructured problems for high school mathematics teachers.In the fourth part,the study is based on the results of a questionnaire survey,following the principles of teaching,proposing and elaborating on the teaching strategies applicable to ill-structured problems.The teaching strategies include: encouraging students to brainstorm;guiding students to characterize diversity;selecting typical cases of problems;providing a structural framework for problems;and encouraging students to summarize.In the fifth part,based on the above design and teaching research content,with the purpose of the influence of ill-structured problems permeating teaching,experiments are carried out.The experimental set up control group and experimental group.The experiment collected data,analyzed the results and concluded that to what certain extent,ill-structured problems permeating teaching can improve students’ academic performance and has a positive role in promoting students’ classroom concentration,learning interest and learning attitude to varying degrees.This study aims to provide some assistance to high school mathematics teachers in the practice of ill-structured problems permeating teaching.