Research Of Mathematical Inductive Reasoning Level Of Junior Middle School Students

Mathematical inductive reasoning is an important component of mathematical core accomplishment.It is an inference that follows a rule and has a non-necessary connection between the premises and the conclusion.Here,"rule" refers to the fact that there is a transitivity between the premise and conclusion of mathematical inductive reasoning and it conforms to the three laws of logical thinking,namely the law of identity,the law of contradiction and the law of excluded middle.The essence of mathematical inductive reasoning is to infer what has not been experienced from what has been experienced.It is the basis of getting mathematical propositions and the main reasoning form of getting mathematical conclusions.In scientific research,both finding and solving problems depend on inductive reasoning.Therefore,it is often said that inductive reasoning is the basis of creation.Mathematics is a science that studies quantitative relations and spatial forms.Mathematics originates from the abstraction of the real world.Based on the abstract structure,it understands and expresses the concepts,properties,relations and laws of things in the real world through symbolic operation,formal reasoning,model construction and other ways.Therefore,the expressive form of mathematics teaching content can be divided into the concept,nature,relationship and law of mathematics.This conclusion has been proved by real data analysis in this paper.According to this conclusion,the content of mathematical inductive reasoning can be classified from the perspective of mathematics teaching content form,and “the content dimensions of the level analysis of junior middle school students' mathematical inductive reasoning” can be obtained,namely,“concept” inductive reasoning,“nature” inductive reasoning,“relationship” inductive reasoning and “rule” inductive reasoning.According to different methods of mathematical inductive reasoning(thinking modes),the mathematical inductive reasoning methods are divided into three kinds: inductive reasoning methods(excluding complete inductive reasoning),analogical method and statistical inference method.This classification constitutes “the method dimension of mathematical inductive reasoning level analysis for junior high school students”.According to the research conclusions of cognitive psychology and the requirements of the compulsory education mathematics curriculum standard(2011 edition)on students' logical reasoning,and referring to the theory of “hermeneutics” and the suggestions of front-line teachers and education experts,the thinking stage of mathematical inductive reasoning is divided into three levels.Thus,“three levels of mathematical inductive reasoning and analysis for junior middle school students” is established.Finally,a three-level analytical framework of junior middle school students' mathematical inductive reasoning level is obtained based on “the content dimension of mathematical inductive reasoning” and “the method dimension of mathematical inductive reasoning”.According to the “analysis framework of junior middle school students' mathematical inductive reasoning level”,the test questions of junior middle school students' mathematical inductive reasoning level are compiled,and four schools in four provinces are tested.The test data are analyzed by two methods.One is to analyze the students' mathematical inductive reasoning ability by using the multidimensional and polytomous item response theory model.Alternatively,descriptive statistics are used to compare the percentages at each level of each dimension.Based on data analysis,it is found that the mathematical inductive reasoning ability of junior middle school students is gradually improved with the increase of grade.The induction ability is stronger than the analogy ability and the statistical inference ability.The analogy ability and statistical inference ability are relatively weak;The percentage of each level of each dimension increase with the increase of grade,among which the percentage of each grade level of analogy is lower than the other two categories.The percentage of induction in all grades and levels is higher than the other two categories.The percentage of rule content in all grades and levels is lower than the other three categories.The percentage of concept content in all grades and levels is higher than the other three categories.The following conclusions are drawn from this study:1.The forms of mathematical teaching content can be divided into four categories: concept,nature,relationship and law.Such classification is necessary for the teaching of mathematics core literacy.2.According to different methods,inductive reasoning can be divided into induction,analogy and statistical inference.This classification is not only in line with the logic theory,but also in line with the junior middle school mathematics teaching practice.3.The division of three levels of inductive reasoning thinking stage of junior middle school students better reflects the process of inductive reasoning thinking of junior middle school students and conforms to the reality of mathematics teaching in junior middle school.4.The analogy ability and statistical inference ability of junior middle school students need to be improved.Especially in the teaching of statistical content,we should pay attention to the thinking process of inductive reasoning instead of solving statistical problems in a deductive way.