Research On Cognitive Development Of Statistical Reasoning In12-15Years Old

As Statistics and our daily life becoming increasingly close, people are likely to face a large amount of data every day. One necessary question is that how to deal with large mount of data (such as statistic, analysis and inference, etc.) with efficient methods. As a result, knowledge on statistics are increasingly used in compulsory education, especially in math teaching. However, according to related references, the development of children’s cognition of statistical inference is still not clarified.In this thesis, two main problems are investigated:1)the periods and features of cognitive development on Statistical inference and basic knowledge of children aging at12to15years old.2) their problems in the period of the cognitive development of Statistical inference and basic knowledge.The research is carried forward in the following way:firstly two schools in Hangzhou area are selected. These schools’grades are ranging from6to9with its students are at the age from12to15, only one class is chosen in each grade, and there are totally263children in8classes. Secondly the questionnaire were tested, and only a few of them were interviewed in each class. Lastly the questionnaires are to be sorted and analyzed. The main results are as following:(1) Children’s basic knowledge of statistics cognitive reasoning is showing upward tendency. There are3periods in the cognitive development of Basic knowledge of statistical inference for the children from12to15:the slow period (12≤age≤13), the fast period(13<age≤14), and the backward development period (14<age≤15).(2) Children’s statistics cognitive reasoning is showing upward tendency, which can be devided into4levels:subjective level, transition level(aging12or13), quantification level(aging14or15) and analysis level. There are3periods in the cognitive development of statistics reasoning for the children from12to15:the slow period (12≤age≤13), the fast period(13<age≤14), and the backward development period (14<age≤15). (3) The cognitive development of children’s data comparative analysis is showing upward tendency, which can be devided into4periods:subjective level(aging12), transition level(aging12), quantification level(aging13to15) and analysis level (aging14). There are3periods in the cognitive development of data comparative analysis for the children from12to15:the slow period (12<age<13), the fast period (13<age<14), and the Backward development period (14<age<15).(4) The cognitive development of children’s data inference is showing upward tendency which can be devided into4periods:subjective level and transition level, showing positive correlation with age, as well as quantification level and analysis level, showing negetive correlation with age. There are3periods in the cognitive development of data inference for the children from12to15:the fast period (12<age<13), the slow period (13<age<14), and the backward development period (14<age<15).(5) The primal problem in the children’s basic knowledge of statistics cognitive reasoning is that children not knowing how to select cartogram and the statistical graphs are not complete and representative.(6) he primal problems in Children’s statistics cognitive reasoning from12years to15years are as follow:depending on subjective sense, focusing on invalid information; misunderstanding the proposition, incompletely considering the problem; not considering the variation of the amplitude, mistakenly thinking that the median can represent the extreme values, mistakenly thinking that extremes, modes can represent the general level, mechanically using averages, neglecting the extreme values of the mean, misunderstanding the definition of variances.