Study On The Development Of Students’ Randomness Concept Cognition

Nowadays,the modern society becomes information gradually,the applications of statistics and probability are also constantly diversified.The school attaches great importance to students on the learning of statistics and probability,but it often ignores the teaching of the randomness event,which is the basic concept of the probability.And it lacks the training of students’ randomness concept cognition.There are relatively few studies on the development of students’ randomness concept cognition in the domestic and overseas,and the targeted studies of students’ mathematics education is less.Therefore,this study conducts pertinent and in-depth research on the cognitive development of students’ randomness concept.The research questions of this study are as follows.(1)The development of students’ randomness cognitive study on two aspects: First,research on the developmental stage and level of students’ randomness cognitive.Second,research on the level of cognitive and the important period of development of students in the cognitive dimension,such as random selection,random distribution and random mixture.(2)The cognitive errors of students’ randomness cognitive study on mainly including the following two aspects: First,what cognitive errors of students have.Second,the cognitive errors of students,when they are generated,which will disappear with age,which will not eliminate.The research processes of this study are as follows.(1)Find the literature based on the problems,design questionnaires,perform multiple modification and test.Through the questionnaire and interviews to carry out investigation and collect data.(2)Data quantitative analysis was performed by SPSS20.0 and Excel.Data qualitative analysis was performed by interview information,so as to get conclusions and give suggestion.The conclusions of this study are as follows.(1)The general process of students’ randomness concept cognition: the level of students’ randomness cognitive is gradually increased at the age of 7-9 and 14-16,and it is gradually decreased at theage of 9-14 and 16-18.(2)The developmental stage of students’ randomness concept cognitive: 7-9 years old is rising development stageⅠ,9-14 years old is falling development stage Ⅰ,14-16 years old is rising development stage 1Ⅱ,16-18 years old is falling development stageⅡ.9 and 16 years old are the critical period of randomness cognitive development.(3)There are differences in the cognitive level of students under different cognitive dimensions,such as random selection,random distribution and random mixture.(4)Students have cognitive errors,such as giving up judgment,subjective judgment,creating the deviation of understanding question and using fuzzy(error)probabilistic knowledge.(5)The cognitive errors in students’ randomness concept cognition,it will gradually eliminate,such as giving up judgments and creating the deviation of understanding question;it will gradually generate,such as using fuzzy(error)probabilistic knowledge;it will always exist,such as subjective judgment.The suggestions for the curriculum standards,class teaching and teaching material are as follows.(1)For the curriculum,it should consider how to distinguish between the randomness of the random phenomenon and the likelihood of a random phenomenon.So that students learn the probability,at the same time,they will not forget the uncertain results of the random event,they are randomly occurring.(2)For the class teaching,teachers don’t teach students the formal results at the beginning.Teachers can guide students to test,and based on the test results,teacher summarize the law in the random event.(3)For teaching material,it should be simple to show the knowledge.