Research On The Evaluation Model Of Junior Middle School Students’ Mathematical Reasoning Ability

Mathematical reasoning ability is one of the core qualities of mathematics in junior middle school,which is clearly put forward in Mathematics Curriculum Standard for Compulsory Education（2022Edition）（hereinafter referred to as Standard 2022）.Many scholars have studied this,and the evaluation model can express something intuitively in a structured and quantitative way,but at present,there are few studies on the evaluation model of junior middle school students about mathematical reasoning ability education.It will gradually promote the cultivation and development of junior high school students’mathematical reasoning ability and provide reference for teachers and educational administrative institutions to carry out teaching in the future or formulate teaching strategies or policies to improve junior high school students’mathematical reasoning ability.Through the methods of literature research and investigation,based on combing the related research on mathematical reasoning ability and education evaluation,and combining with the opinions of experts,this paper constructs the operational definition of junior middle school students’mathematical reasoning ability（hereinafter referred to as research topic）by using behavior description method.Delphi method is used to determine the evaluation index system of research topic（W）,including three first-level indicators and their numbers,which are“Understanding facts and propositions（A）,analyzing problems according to facts and propositions（B）,expressing、explaining and communicating the results（C）”and the corresponding nine secondary indicators and their numbers are“understanding the basic facts of quantity and figure（A₁）,understanding the structure and relationship of mathematical concepts,propositions and theorems（A₂）,understanding the basic forms and rules of reasoning（A₃）;establishing the logical connection between mathematical concepts,propositions,theorems and facts（B₁）,inferring some results by induction and deduction based on facts and propositions（B₂）,proving and calculating according to the rules of logical reasoning based on facts and propositions（B₃）,explaining the ideas and methods of the analysis process in an orderly way（C₁）,explaining the practical significance of the mathematical results reasonably（C₂）,making reasonable judgments and predictions according to the mathematical results（C₃）”.With the help of confirmatory factor analysis,the weights of each index are determined,and a first-level linear evaluation model W=0.34A+0.35B+0.31C is constructed,in which the weights of the first-level index and its corresponding second-level index are as follows:A=0.33A₁+0.33A₂+0.33A_3,B=0.30B₁+0.37B₂+0.34B_3,C=0.35C₁+0.33C₂+0.32C_3,The comprehensive weight method is used to represent the evaluation model,which can also be written as:W=0.11A₁+0.11A₂+0.11A₃+0.11B₁+0.13B₂+0.12B₃+0.11C₁+0.10C₂+0.10C₃In order to make the evaluation model operable,after retaining one decimal place,the above-mentioned first-order linear evaluation model can be expressed as follows:W=0.3A+0.4B+0.3CFinally,the evaluation model is applied,and the test paper is compiled by the way of screening,translating and adapting the questions→evaluating the difficulty and readability of the test questions→evaluating the content validity of the test questions→composing the test paper”.The prediction results show that the Cronbach Alpha value of the reliability coefficient of the test paper is 0.716,which is above 0.7,indicating that the test paper has good internal consistency and the test results have certain credibility.To understand the current differences of students’mathematical reasoning ability under different school and gender conditions,according to the researcher’s academic and friendship,216 junior two students（including 30 predictions）from J school in the developed eastern region and G school in the underdeveloped western region were selected as subjects.According to the existing research results,it is estimated that the test scores of students in developed areas are better than those in underdeveloped areas,and there is little difference between boys and girls.The test results show that under different conditions,the total index score of J school is significantly higher than that of G school;The first-level index score,J school is significantly higher than G school in indicators A and B,but there is no significant difference in indicators C;The score of secondary indicators in J school is significantly higher than that in G school in indicators A₂,A₃,B₂,B₃and C₂,but there is no significant difference between the two schools in indicators A₁,B₁,C₁and C₃.Under different gender conditions,there is no significant difference between male and female students in total index score,first-class index score and second-class index score.The test results are basically consistent with the prediction,which shows that the test paper based on the evaluation model can reflect the practical level and basic characteristics of students’mathematical reasoning ability.As a tool to evaluate junior high school students’mathematical reasoning ability,the evaluation model has certain reliability and maneuverability,but the research depth is still not enough due to my own ability,and I look forward to further research.