An Investigation Of Mathematical Analogical Reasoning Ability Of High School Students

With the development of the times and the implementation of the new curriculum standards,the education sector is paying more and more attention to the cultivation of students’core literacy and overall development.Therefore,in order to meet the needs of the new college entrance examination for the overall development of talents,it is necessary to implement the new curriculum standards,expand students’ thinking,improve their reasoning ability,and strengthen their creative ability.The first year of high school is a crucial stage,when students have just left compulsory education and entered the high school mathematics curriculum,which is a critical period to help students build their knowledge system,develop good study habits and help them to develop better in mathematics.For this reason,it is necessary to study the analogical reasoning ability of senior high school students.Thesis focuses on the following two questions:1.What is the current situation of mathematical analogical reasoning ability of senior students;2.What are the factors that affect students’ mathematical analogical reasoning ability?Thesis analyzes the literature on analogical reasoning in four different fields:psychology,philosophy,logic,and mathematics.It also reviews the cognitive process of analogical reasoning,research on students’ ability to reason by analogy,research on teachers’ teaching of analogical reasoning,research on methods and ways of developing analogical reasoning,and research on teaching strategies based on analogical reasoning,and defines the concepts of"reasoning","analogy","analogical reasoning",and "mathematical analogical reasoning ability".In thesis,389 senior students were studied by means of questionnaires and test papers,20 mathematics teachers were surveyed,and 4 of them and 6 students were interviewed.The following conclusions were drawn:(1)The overall mathematical analogical reasoning ability of senior students was low,with senior students having the strongest conceptual analogical reasoning ability and arithmetic relationship analogical reasoning ability,the second strongest property analogical reasoning ability and method of thought analogical reasoning ability,and the worst structural analogical reasoning ability and ascending analogical reasoning ability;(2)The mathematical analogical reasoning ability of senior science students was higher than the mathematical analogical reasoning ability of senior arts students;(3)the mathematical analogical reasoning ability of senior boys was higher than that of senior girls;(4)the mathematical analogical reasoning ability of students in different schools was lower overall,and there was no significant difference between the mathematical analogical reasoning ability of students in the two schools;(5)The influencing factors affecting students’ mathematical analogical reasoning ability originated from two aspects.The influential factors affecting students’ ability to reason by analogy in mathematics originate from two sources.The influencing factors originating from the students are students’ poor basic knowledge and their inability to identify analogical sources to reason by analogy;poor problem solving habits;the influence of gender and different subject choices;students’ lack of interest in learning mathematics and negative learning attitudes;and students’ passive learning and inability to think and find out summaries.The main influencing factors from teachers are lack of theoretical knowledge about analogical reasoning,lack of attention to teaching analogical reasoning,and lack of guidance in the process of teaching analogical reasoning.Based on the study,suggestions for the development of students’ analogical reasoning ability are given.