Investigation And Research On The Actual Situation Of Junior High School Students' Mathematical Reasoning Abilit

The Mathematics Curriculum Standards for Compulsory Education(2022 edition)proposed the core competences of "three abilities" : being able to observe the real world with mathematical vision,think about the real world with mathematical thinking,and express the real world with mathematical language.Reasoning ability is one of the main performances of the core competences of "three abilities" in junior high school mathematics.Reasoning in mathematics has an important impact on students’ problem solving,argumentation and logical expression.To understand the status of students’ reasoning ability through assessment is an important task to implement the academic quality evaluation of the new curriculum standards and measure the achievement of students’ mathematical core competences.Therefore,the research questions are determined as follows:(1)How to build an assessment framework for junior high school mathematical reasoning ability based on curriculum standards and compile assessment tools?(2)What is the status of junior high school students’ mathematical reasoning ability?(3)How to effectively promote the development of junior high school students’ mathematical reasoning ability according to the status?Based on the Mathematics Curriculum Standards for Compulsory Education(2022 edition),a three-dimensional evaluation framework of junior high school students’ mathematical reasoning ability is constructed from the content dimension,performance dimension and level dimension.Secondly,the mathematical reasoning ability test questions and questionnaires of junior high school students were prepared based on the evaluation framework,the reliability and validity of the test were 0.856 and 0.748,and the reliability and validity of the questionnaire were 0.967 and0.950,respectively,and the overall reliability and validity were good.By adopting questionnaire survey method,280 students in the second and third grades of junior high school in three different schools was conducted and 220 valid questionnaires were obtained.Furthermore,statistical analysis is adopted to analyze.From the macro level,analyze students’ level of reasoning ability and four specific performance,the differences between reasoning ability and gender and grade,the correlation between reasoning ability and academic achievement,and the correlation between possible factors affecting reasoning ability.From the micro level,typical errors are analyzed to understand students’ cognitive problems in the performance dimension.From the micro level,analyze typical errors,and understand students’ cognitive problems in the performance dimension.The status and characteristics of junior high school students’ mathematical reasoning ability are as follows:(1)The overall mathematical reasoning ability of junior high school students reached level 2,mastering basic forms and rules of reasoning,inferring conclusions from special to general reached level 3,exploring and expressing argumentation process and understanding proposition system reached level 2;(2)The reasoning ability of junior high school students presents progressive development,and there are significant differences in the total reasoning ability of students of different grades;(3)The mathematical reasoning ability of junior high school students has no significant difference in gender,there is a significant difference in the performance of students of different genders in understanding the proposition system,and there is no significant difference of different genders in the content fields of "number and algebra" and "figure and geometry";(4)The mathematical logic reasoning ability of junior high school students has a significantly positively correlation with academic achievement,and has correlation with motivation,emotion,mathematical metacognition and problem raising ability.Typical problems of students’ reasoning ability are as follows: first,it is difficult to conduct clear and strict reasoning with mathematical symbolic language;second,it is difficult to generalize special conclusions to more general situations;third,many students have not formed a network connection to the proposition system;fourth,it is difficult to transition from arithmetic thinking to algebraic thinking;fifth,it is difficult to use counter-examples for reasoning.Based on the status of junior high school students’ reasoning ability,combined with the interview,this paper puts forward the cultivation strategies of junior high school students’ reasoning ability:(1)strengthen the foundation to consolidate the core knowledge and system of reasoning: gradually arrange the reasoning tasks,structure and integrate knowledge to promotes students to form a proposition system;(2)Complement each other to realize the coordinated development of reasoning ability and multiple capabilities: enable the collaborative development of mathematical reasoning ability and key mathematical competences,and the development of reasoning ability with problem proposing ability;(3)Outline and improve algebraic thinking and argumentation thinking: strengthen letter reasoning and strengthen reasoning training;(4)Activate motivation develop interest in reasoning: driven by real situation problems and design open-ended learning tasks.