Research On The Application Of Plausible Reasoning In Teaching Of Sequence

With the rapid development of science and technology,the demand for innovative talents is increasing.Therefore,the cultivation of reasoning ability in mathematics education is becoming more and more important.Firstly,this thesis make notes on the background and research significance of the plausible reasoning,and indicates the current research situation at home and abroad,and the related theories in the application of teaching of sequence,which are Polya Mathematics Education Theory,Constructivism theory,H.Freudenthal's re-creation education theory.It analyzes the two kinds of common patterns of the plausible reasoning,which are inductive reasoning and analogical reasoning.On the basis of integration of inductive reasoning,the induction reasoning is divided into five basic cognitive stages.This thesis creates a teaching case of“the sum of the first n terms of an arithmetic progression”,based on the contents of the sequence in High School Compulsory Five,published by PEP(People's Education Press).And then,from the conformity in research results of analogical reasoning,it is composed of three basic cognitive stages.This thesis probes into the wide application of inductive reasoning and analogical reasoning in solving problems by combining the sequence questions of National College Entrance Examination in recent years.This thesis analyzes the three aspects: teaching materials,teaching,solving problems based on the contents of series,and present some suggestions on how to cultivate the students ability of plausible reasoning in the process of sequence teaching:Firstly,creating problem situations,and focus on the occurrence and development of knowledge;Secondly,dig and make good use of materials in plausible reasoning;Thirdly,contact actual life and encourage students to guess.