Research On The Improvement Of Analogy Reasoning Ability In Sequence Of Number Teaching

Analogical reasoning is an indispensable part of mathematical reasoning.It is also an important way to discover and make conjectures.The basis for the emergence of many new ideas,discoveries,and achievements in ancient and modern time is analogical reasoning.The improvement of analogical reasoning ability is a vital goal of mathematics teaching.Focusing on cultivating students' analogical reasoning skills is a necessary aspect of the new curriculum standards.The series is an important content of high school mathematics.Combined with the series learning situation,the following problems have been found by testing senior high students' analogical reasoning ability:(1)The level of analogical reasoning of high school students is generally low,and there is a narrow gap between boys and girls in the level of analogical reasoning,but there are still differences.When performing simple analogies,girls outperform boys.However,boys accomplish better than girls when performing analogies which are slightly more complex.(2)The analogical reasoning ability of the high school students in number sequence is influenced to a certain extent by students' learning basis,flexibility of thinking,active learning attitude,good cognitive structure,and the ability to summarize.It seems that teaching more analogical reasoning knowledge is quite important.(3)In the course of teaching analogical inference knowledge,teachers always treat problems in an isolated,static way.The problems are combined together in a simple single form.Teachers rarely link the subjects together while teaching,and they hardly compare relevant series analogous reasoning so as to find the similarities and differences between them,seldomly conclude the principle of the same type of analogous reasoning.The improvement of analogical reasoning ability can be achieved by teachers' emphasis on cultivating students' analogical reasoning abilities,strengthening the teaching of digital representations to deepen understanding,focusing on forming the system structure of knowledge,summarizing general analogous approaches in solving problems,and grasping analogy key points,combining theory with reality and other aspects.This thesis is divided into five chapters: Chapter one mainly discusses the background of the research from the three aspects:the objectives of new math curriculum standards,the requirements of the new era of innovative thinking ability,and the current situation of high school students' analogical reasoning ability.The research direction of this thesis is based on teacher's as well as students' poor performances in analogical reasoning.Chapter two includes the definition of analogy and analogical reasoning,the author also analyzes the types of analogical reasoning,and theories related to analogical reasoning;then it reviews the researches on analogical reasoning and its present status from both domestic and international perspectives.The third chapter is an empirical study.Through questionnaires,interviews and other methods,the author had a deep understanding of the current situation of analogical reasoning ability in the series of high school students.According to the survey results,the current level of mathematical analogical reasoning ability of high school students is overall low.Combined with the results of interviews,the analysis found that the level of students' analogical reasoning ability is mainly decided by the students' previous learning level,the initiative and enthusiasm of learning,the flexibility of thinking,etc,what's more,teachers' emphasis on analogical reasoning is also a related factor.Based on the survey results,along with analyzing the basic approaches of analogical reasoning in mathematics.In the fourth chapter,the author proposes corresponding strategies for analogical reasoning teaching,to motivate high school mathematics teachers to have a more profound understanding in teaching and to push students to learn analogical reasoning better.The last chapter is a summing-up.To summarize the conclusions of the above research,and forecasts the deficiencies in the study.