A Study On Development Of Probability Concept And Cognitive Strategy In Children Aged 11-15 Years

Domestic researches on the cognitive development of probability concept are mostly concentrated in primary schools or middle schools.This study USES three levels of probability cognitive tasks: probability comparison,sample space,and score to represent probability,which is referred to as "cognitive task".There are three types of probabilistic models: simple probabilistic model(one ball),complex probabilistic model(two balls),and independent repeat probabilistic model(one ball,put it back,and then one ball),which are referred to as "probabilistic model".The cognitive development of probability concept in children aged 11-15 years was studied.The research question of this study.(1)The general situation of cognitive development of children aged 11-15 years on three cognitive tasks under the three types of probability models.(2)How to develop the cognitive level of children aged11-15 in probability size comparison(sample space,score represents probability)under each type of probability model.(3)Under each type of probability model,how to develop the cognitive strategies of children aged 11-15 years in the comparison of probability size(sample space,score represents probability).(4)How to develop the cognitive strategies of children aged 11-15 years on the simple probability model(complex probability model,independent repetition probability model)under each cognitive task.The process of this study.First of all,since 11-year-old children had not learned the probability knowledge of events before,we conducted a one-month teaching experiment with 9 class hours of probability knowledge.To examine how 11-year-old children learn probability;To investigate the probabilistic cognitive development of children aged 11-15 years;To analyze the differences of probability cognition(level and strategy)between children aged 11 and 15 years;Answer questions about the probability of an 11-year-old being able to learn.Secondly,the questionnaire was designed and modified according to the research questions.The questionnaire was first tested on children aged 11-14 years old,and then on children aged 15 years old after 6 and a half months(at which time the probability content of children aged 15 years old had been learned).Thirdly,data analysis is carried out based on the results of the questionnaire survey.The quantitative analysis was based on Spss17.0 and Excel software,mainly used to calculate the average scores of children of all ages and the average number of children at all cognitive levels.Qualitative analysis is based on the reasons given in the questionnaire so as to know the reasons why children of all ages are at all levels of cognition and the development of various cognitive strategies.Finally,based on the research conclusions,the author puts forward Suggestions on curriculum standards and teachers’ teaching.The main conclusions of this study.(1)Development of probability concept cognitive level of children aged 11-15 years.Under the three types of probability models,11-year-olds scored higher on all three cognitive tasks on average.The mean scores of 12-to 14-year-olds on the three cognitive tasks were similar,but all were lower than those of 11-to 15-year-olds.Except that 15-year-olds scored lower on average than 11-year-olds in the sample space,the average scores on the other two cognitive tasks were about the same as those of 11-year-olds.Under the three types of probability models,children aged 11 and 15 years are mainly at level 4 in the three cognitive tasks(level 1 to level 4 are gradually improved).In terms of "possibility size comparison" and "sample space",children aged 12-14 years are mainly at level 1.In "score represents probability",children aged 12-14 years are mainly at level 3.This shows that children aged 11 and 15 can not only judge and calculate correctly on these three cognitive tasks,but also use correct methods and make a reasonable case.Even if children aged 12 to 14 were able to choose the right answers on all three cognitive tasks,most of the reasons given were low.(2)Development of probabilistic concept cognitive strategies in children aged11-15 years.Development route: in the case of different probability models of the same cognitive task,the main route adopted by children aged 11 and 15 on the three cognitive tasks is that the cognitive strategies used in each cognitive task under the three types of probability models reach the level of three levels.The main route used by children aged 12 to 14 in "likelihood comparison" was.In the case of "sample space" and "score representation probability",the main route used is.Under the sameprobabilistic model and different cognitive tasks: under the simple probabilistic model and the complex probabilistic model,the main route adopted by children aged 11-15 is that the cognitive strategies used by these two types of probabilistic models on the three cognitive tasks reach level 3.Under the independent repetition probability model,the routes used by children aged 11-15 years are relatively diverse.Speed of development: under the same cognitive task with different probability models,the cognitive strategies used by children aged 11-14 in the "probability size comparison" have the characteristics of first fast,then slow and then fast.The cognitive strategies used in "sample space" and "score represents probability" have maintained a rapid development rate.Under the same probabilistic model and different cognitive tasks:under the simple probabilistic model and the independent repetition probability model,the cognitive strategies used by children aged 11-15 on the three cognitive tasks have the characteristics of rapid development first,then slow and then fast.Under the complex probabilistic model,it keeps a fast development speed.This study provides suggestions for curriculum standards and teacher teaching.(1)It is suggested that in curriculum standards,the probability of simple events learned in the third learning paragraph should be appropriately learned in the senior grades of the second learning paragraph,but the related knowledge in the independent repetition probability model should be continued to be learned in the third learning paragraph,because this is a difficult point for children aged 11-15.(2)Teachers should pay more attention to the reasons why children answer questions in daily teaching,because even if children can make correct choices,the reasons why they make choices may be wrong.(3)Teachers should pay more attention to children’s understanding of "sample space" in daily teaching.According to the research,many children cannot accurately list the sample space of the two-step experiment,especially when there is a copy of the ball,it is easy to ignore the copy of the ball.(4)When teaching probability,teachers should pay attention to whether children can distinguish the complex probability model from the independent repetition probability.The study found that children responded to tasks in the independent repetition probability model as if they were complex probability models.