A Case Study Of Cultivating The Ability Of Analogical Reasoning Of Junior High School Students

"High School Mathematics Curriculum Standards(2017 Edition)" clearly proposes logical reasoning as one of the six core qualities of mathematics.Analogical reasoning is an important part of logical reasoning.The "Four Basics" of "Compulsory Education Mathematics Curriculum Standards(2011Edition)" mentions that the basic ideas of mathematics include reasoning and other ideas.Analogical reasoning is a type of logical reasoning.Analogical reasoning runs through the middle school mathematics learning and teaching process.The students' analogical reasoning ability is one of the important tasks of middle school mathematics education.However,the teaching of deductive reasoning in middle school mathematics teaching often ignores the teaching of reasonable reasoning such as analogical reasoning,and students have insufficient analogical reasoning skills.This research focuses on exploring the process of analogical reasoning,understanding the current status of junior high school students' ability to use analogical reasoning,and designing teaching cases for some courses and different types of analogical reasoning.This article uses literature research method,questionnaire survey method,interview method and other methods for research.First,the literature research method is used to analyze the current status of domestic and international research on analogical reasoning and to explore the process of analogical reasoning,combining the analogical transfer process from the psychological perspective and the analogical reasoning process from the mathematical knowledge management perspective,and to summarize the reference model of the analogical reasoning process;second Through a questionnaire survey,taking the second and third grades of a middle school in Guang'an as an example,understand the analogy reasoning ability of junior high school students from three dimensions: the basic understanding of analogy reasoning,the attitude and frequency of using analogy reasoning,and the level of analogy reasoning ability.Propose relevant suggestions to promote the training of junior middle school students' analogical reasoning ability;In addition,use interview methods to understand the understanding of first-line mathematics teachers' analogical reasoning and the application of analogical reasoning in junior middle school mathematics teaching.The survey results show that:(1)Students have a certain sense and ability of logical reasoning,but they have insufficient understanding of the nature and characteristics of analogical reasoning.(2)Students with grades above the mid-range(84-95 points)often use analogical reasoning to explore problem-solving problems,accounting for more than 30%,while students below the mid-range are only about 10%,which indicates the use of analogy Reasoning to explore and solve mathematical problems requires a high level of students.(3)Students have a good grasp of the content of the knowledge they have learned,but on the basis of the existing knowledge,it is difficult to carry out analogical reasoning.The test results show that the conceptual analogy accuracy rate is 68%,the structural analogy accuracy rate is 38%,and the nature analogy and method analogy accuracy are low.Conceptual analogy and structural analogy are better than property analogy and method analogy.Through research and analysis,three suggestions are given to develop students' analogy reasoning ability.First,let students experience the process of analogical reasoning and strengthen the teaching of the basic nature of analogical reasoning,and deepen their experience and comprehension of sensible reasoning;second,start analogy teaching from simple logical reasoning,so that more students can understand and master the analogy reasoning.The third is to focus on the teaching of analogy such as concept analogy,nature analogy,thought method analogy,and structural analogy,which are common in analogy teaching.Finally,based on the status quo of analogical reasoning teaching,combining analogous teaching principles and teaching ideas,design analogous teaching cases of concept courses,unit summary courses and problem solving courses.