Research On The Current Situation And Cultivation Strategy Of High School Students' Mathematical Rational Thinking

Rational thinking is the core of the core literacy of mathematics.Paying attention to cultivating students' rational thinking is the requirement of the high school mathematics education goal.Cultivating mathematical rational thinking is the need of students' development and also the need of educational development in China.At present,although the status of mathematics is relatively high,it is usually evaluated from the perspective of examination.The important value of mathematics itself for the development of students' thinking is still easy to be ignored in the actual teaching process.With the gradual advancement and deepening of education reform,the value of mathematics has been gradually gained attention.Teachers begin to try to cut into the core competence of mathematics and think about the significant advantages of mathematics for the cultivation of thinking.Firstly,this thesis analyzes the relevant theories of rational thinking through the literature analysis method,the main contents are as follows:(1)Define the concept of rational thinking,and believe that rational thinking must be flexible and orderly when considering problems,organizing and researching information from an overall perspective,and solving problems and making wise decisions in a logical way;(2)Expound the understanding and analysis of the characteristics of high school mathematical rational thinking,and hold that the abstract thinking of high school students is in the primary position of thinking mode in the process of mathematical learning,and it is mutually promoted and inseparable with dialectical rational thinking,and rational thinking has the characteristics of generality,rigor,logic,flexibility and criticism;(3)Analyze the value and significance of cultivating rational thinking in mathematics of senior high school students,and hold that cultivating rational thinking can effectively enhance the guidance in the process of problem solving,increase the scientific rigor in the process of analysis and testing,and increase the speculative nature in the process of mathematics learning communication and discussion.Secondly,designed from six dimensions of thinking purpose,thinking process,material representation,self-monitoring and adjustment,thinking quality,and non-cognitive factors,a questionnaire was distributed to a total of 571 students in 12 classes in two ordinary high schools,to understand the mathematical rational thinking of high school students,statistical analysis of the survey data,the following conclusions are obtained:(1)From the perspective of grades,there are significant differences between students' level and grade in the five elements of thinking process,material representation,self-monitoring and regulation,thinking quality and non-cognitive factors.In the second and third grades of senior high school,students' mathematical rational thinking is basically mature;the development space of mathematical rational thinking in the first grade of senior high school is broader and more plastic,therefore,it can be regarded as the critical period to cultivate mathematical rational thinking;(2)From the perspective of gender,there is no significant difference between the overall situation of mathematical rational thinking and gender,but two elements of thinking purpose and self-monitoring and adjustment are significantly different from gender.The average level of male students is lower than that of female students only in self-monitoring and regulation;(3)From the perspective of elements,students perform well in the three elements of thinking purpose,material representation and non-cognitive factors,while they perform poorly in the process of mathematical rational thinking,self-monitoring and adjustment,and thinking quality,and their performance in the critical aspect of thinking quality is not ideal.Finally,on the basis of the theoretical analysis in Chapter 2 and combined with the results of the questionnaire survey in Chapter 3,four strategies are proposed for the cultivation of high school students' mathematical rational thinking,which are illustrated in combination with individual teaching situations or course contents:(1)Guide students to clarify the purpose of thinking and develop the overall observation ability;(2)Pay attention to the cultivation of students' abstract logical thinking ability;(3)Develop students' potential and improve their quality of rational thinking;(4)Conscientiously construct mathematics concepts.At the same time,combining with the training strategies proposed in this paper,the teaching case analysis about the training of mathematical rational thinking is given by taking the course of "the image and properties of logarithm function" as an example.