A Survey Of The Mathematical Analogy Reasoning Ability Of Junior High School Students

In 2011,The Ministry of Education formulated and promulgated the "Compulsory Education Mathematics curriculum standard".In this standard,it focused on developing students' reasoning ability in math class,and pointed out that the development of reasoning ability should exist in the process of mathematics learning in the whole compulsory education stage.Since then.both Master's thesis and doctoral dissertation started to turn their attention from studying the application of analogical reasoning to studying how to cultivate students ' analogical reasoning ability by teaching.For the moment.the research for the students' analogical reasoning ability concentrates mainly on high school students,junior middle school students regarded are few.This paper summarizes four important theories about analogical reasoning by finding and reading a lot of literature,namely Gentner's structure mapping theory,Holyoak's practical Diagram Theory,Ross's sample theory and Piaget's Structural stage theory.A literature review is made from four aspects:first researcher,implementation process,Implementation principles and classification.According to Gao Jiping's idea,this article divides analogies into five forms in terms of characteristics of similarity of two objects.The five forms are respectively the nature of analogy,Analogia relationis,Structural analogy,Method of analogy and Propositional analogy.This article focuses on the current situation of mathematical analogy reasoning ability of two school students in junior grade.Their ability for Analogia relationis,Method of analogy,Structural Analogy and Propositional analogy is low,but the nature of analog is the highest.Analogical reasoning ability for the minimum relationship is higher than that for computational relationship;Analogical reasoning ability for counting methods is stronger than that for the method of connecting number with shape.For the analogy of counting method,when facing easy questions,they can draw an analogy correctly,but if the questions are complex,larger numbers or demanding,there are only a small proportion whose integrated ability are stronger can get the exact answer by accurate observation and thinking.Yet,there are many students make blind mathematics mistakes and thorough study,lacking systematic analysis.After making an investigation and analysis to teachers'teaching of analogy reasoning through the form of questionnaire.This paper can deduce some conclusions:most of the teachers start to know analogical reasoning through participating in the new curriculum training.they think that the arrangement of analogical reasoning-related content on Current Textbooks is reasonable,and they can also using analogical reasoning consciously in teaching.The major of them consider that analogy teaching is more useful in teaching the new lesson and example discussion.Some more effective strategies for improving students' ability of analogical reasoning should also be found,explored and put into practice.Then this paper summarizes effective strategies about cultivating students' capacity of analogous inference from three aspects,namely teachers teaching,the students themselves and evaluation system,and formulates the application of analogical reasoning in mathematics teaching in junior high school,from two aspects that are drawing an analogy with instance and previous knowledge...