Understanding And Analysis On The False Understanding Of Probability And Statistics Learning Of Senior High School Students

With the rapid development of science and technology,we have entered the era of big data.The theory and application of probability and statistics are becoming indispensable parts of our life.As a branch of mathematics with the characteristics of "uncertainty",probability and statistics require students to change the thinking and understanding mode in learning.If the students can not adjust their thinking mode in time,they will form false understanding in learning.Based on the constructivism theory,we analyze the false understanding phenomenon in probability and statistics learning from the cognitive development level of senior high school students and the characteristics of probability statistics education.The first part of this paper includes the background,main content,significance and method of the study.False understanding widely presents in probability and statistics learning,which is an important obstacle for students to understand concepts and transfer theoretical knowledge.However,in the front-line teaching and education research,this phenomenon has not been paid enough attention to.Therefore,there is theoretical and practical significance to study the false understanding phenomenon in probability statistics learning.The second part is the theoretical basis of this thesis,in this part,we define the basic concept of false understanding,summarize the research status of the phenomenon of mathematical false understanding by consulting the relevant literature at home and abroad,analyze the characteristics of high school probability and statistics subject content from the perspective of mathematical false understanding,and summarize five significant characteristics of students under the state of false understanding according to the relevant theories of learning psychology.On this basis,according to the mathematical learning process model under the view of modern cognitive theory,we make a theoretical analysis of the causes of false understanding,and hold that perceptual knowledge,mathematical thinking activities and original mathematical knowledge structure are the important factors influencing the formation of false understanding.The third part of this paper includes the status of false understanding in the probability statistics learning of senior high school students through questionnaire survey and individual interview.Based on the analysis of the questionnaire and false understanding self-evaluation,the main reason for the formation of false understanding in the learning of probability statistics is the lack of metacognitive ability.The results of the two parts of the questionnaire are analyzed comprehensively.It is found that the false understanding of senior high school students is lower than that of senior high school students,and there is significant difference in the false understanding among the students in different grades.However,there is no significant difference in the false understanding of senior high school students of different genders in probability statistics learning.In order to effectively prevent students from forming false understanding in probability and statistics learning,in the fourth part,based on constructivism theory,we put forward training strategies to overcome false understanding from the perspective of teachers and students,give teaching fragments and teaching cases to implement these training strategies in practice.Teachers: actively carry out "case teaching" to provide students with rich and real perceptual materials;pay attention to counter example teaching to guide students to think about concepts and formulas from multiple perspectives;carry out personalized teaching according to the differences of students’ thinking;strengthen reflective learning to improve students’ metacognitive ability.Students: improve learning initiative,pay attention to multi angle representation and application of knowledge;pay attention to details,improve the quality of mathematical thinking;cultivate problem awareness,improve questioning ability.The fifth part is the conclusion and prospect of the research,in which we summarize the five conclusions of this research work,and provide the improvement direction for the follow-up investigation and research.