Research On The "Three Methods" Of Problem-solving Teaching Based On The Theory Of Zone Of Proximal Development

Cultivating students' core literacy of mathematics is an inevitable trend in the development of mathematics teaching under the background of the new curriculum standard.Problem-solving teaching is an inseparable and important part of mathematics classroom instruction,while it is also the main way to cultivate students' core literacy in mathematics.This thesis first gives the new definition of the problem-solving “ three methods(normal method,applicable method and clever method)”.Comparing the problem-solving teaching and the theory of zone of proximal development,this thesis then explores the research on “ three methods ” problem-solving teaching under the theory of zone of proximal development via the literature research,questionnaire survey,test method,classroom observation,teaching design and some other research methods.Three main contributions are as follows.Firstly,through a questionnaire survey of high school mathematics teachers in a certain area,a record of teaching in a high school mathematics teaching,and a mathematics test on students,the investigation on the current use of “ normal methods ”,“ applicable methods ” and “ clever methods ” in high school problem-solving teaching are made.The results about teacher: They are inclined to teach normal methods and applicable methods in problem-solving teaching to their students,and most teachers can combine the student's zone of proximal development when they teach the solution of problem.The results about student: The “ three methods ” are widely used in solving problems in each module of mathematics,and students' choice of problem-solving methods is closely related to the methods taught by their teachers in problem-solving teaching.Some additional problems have been discovered from our investigation: On the one hand,some teachers need to improve their own skills of solving problem,and they are lack of the training of students' core literacy in problem-solving teaching;On the other hand,the students' core mathematics literacy and innovation ability need to be improved.Secondly,based on the results of the questionnaire,teaching records and the students' test,we propose the principle of “ three methods ” problem-solving teaching under the theory of zone of proximal development via combining the some basic theories with the high school mathematics problem-solving teaching.On the basis of the principles of purpose,heuristic,demonstrative,and acceptability of problem-solving teaching,we propose some principles according to the different characteristics of three problem-solving methods: the “ normal method ” must follow the essential principle to consolidate the foundation and cultivate the students' core literacy of mathematics;the“ applicable method ” must follow the principle of high efficiency to cultivate thinking ability and improve the students' core literacy of mathematics;the “ subtle method ” must follow the principle of innovation to improve skills and sublimate the students' core literacy of mathematics.Thirdly,combining some theories in our thesis and the proposed principles of problem-solving teaching,we present the specific fragment design of problem-solving teaching.We first give a feasibility analysis of the integration of teaching principles and problem-solving teaching design,and propose some ways to implement the principles in problem-solving teaching and the basic mode of teaching design.We then present three detailed teaching fragment designs of problem-solving including analytic geometry,function inequality,and seeking the maximum and minimum value.Finally,in combination with the teaching principles proposed in Chapter 3,we give the detailed analysis of each teaching fragment design from view of the theory of zone of proximal development,student learning theory,and problem-solving theory.