Investigation On The Cultivation Of Key Competency Of Mathematics In Senior High School Students Under “the Problem-solving Teaching”

With the promulgation of Mathematics Course's Standards for Ordinary Senior High Schools(2017 Edition),Chinese mathematics educators pay more attention to and join one after another to study key competencies of mathematics.Now the key competency of mathematics has become the center of the new round of course's reform.Mathematics teaching should be carried out around this central task.Mathematics teaching which takes the key competencies of mathematics as the teaching aim should propose creative and critical problems as teaching center,and carries out classroom activities around a series of mathematics or practical problems which have directivity.Under teachers' guidance,students obtain not only knowledge,but also extend new problems to explore and to experience the process of making a guess and giving assumptions.This requires us to use "problem-solving teaching" mode,and to combine the teaching methods and team cooperation inquiry method.This dissertation conducts mainly investigation and research by combining the problem-solving teaching with the key competencies of mathematics.From the perspective of theory,the problems raised by our mathematics teachers in the teaching process,the order of setting problems and the interval after asking problems are all finished designing in the stage of lesson preparation.The setting of problems should be creative and critical,and some mathematical conceptual problems that are right or wrong should be reduced appropriately.The setting order of the problems should follow the student's recent development area.Problems that some students cannot answer should not be put forward blindly.The pause of the problem should be appropriate.The simple problems may be in the way of rushing to answer.The larger open problems should give the student to some time for communication and thinking.The investigation objects are selected as 6 classes of grade 3 of high schools Y and E in city S,the internship units of author.By observing the teachers' problem-solving teaching in classrooms,current situation problems of teachers' application for this teaching model are analyzed and understand.On the basis of this,and combination of students' questionnaire investigation,the students' current ability of solving problems and their levels of students' key competencies of mathematics are analyzed and understand.The results show that the students' levels of key competencies of mathematics in the two high schools are low,and do not meet the requirements.When the teachers apply the problem-solving mode to classroom teaching activities,the following several phenomena appear: 1)the teaching mode fails to be used flexibly.Although the teachers introduce with problems,they do not solve problems generally;2)The difficulty and logic span of the problems proposed by the teachers are large and out of the students' immediate development area,resulting to the situation that teachers ask and answer the problem themselves;3)In the teaching course of concept,the teachers do not the relate closely enough the background of the concept;4)In teaching course of principle,the teachers can use the idea of analogy and induction to guide the students.Furthermore,basing on the investigation results and aiming to cultivate students' key competency of mathematics,we put forward some suggestions for improving the method of problem-solving teaching mainly from two aspects: the preparation of lesson preparation and the way of problem setting.Finally,we select three types of teaching lessons of concept,principle and exercises and design three teaching examples of the concept of complex number,the theorem of sine and the exercises of conic curve.