The Development Of Pupils' Statistical Thinking And Its Teaching Research

With the coming the era of big data,statistical literacy has become an important capability for future citizens.To reflect this need,statistical courses for improving students' statistical thinking,reasoning and literacy are becoming a part of mathematics curricula in many countries,and evaluating students' cognitive development of statistical thinking has also become one of the hotsopts in recent years.Considering that the statistical contents and requirements of the primary school stage have been greatly adjusted in Standard for compulsive education of mathematics curriculum(2011),and there is not sufficient research made on the statistical thinking of pup ils in the literature.Our research focuses on cognitive development of pupils' statistical thinking,explores the development level,the stage,the characteristic and the wrong cognition of the students' statistical thinking,and combines statistical thinking with specific curriculum teaching through a short teaching experiment Specifically,the research includes the following three questions:Question 1:what is the current situation of the development level of pupils'statistical thinking?Question 2:what is the cognitive development process of pupils' statistical thinking?Question 3:can short term teaching activities guided by the characterization framework of pupils' statistical thinking enhance the statistical thinking of Grade 3 students?Through researching on the connotation of statistical thinking in literature,our research selects 12 elements under 4 dimensions(including "statistical process","variation","need for data" and "question about data")of statistical thinking to explore the development of students' statistical thinking.Based on a questionnaire survey of 1541 students of Grades 1-6 in Anhui and Jiangsu Provinces and interviews with 23 students,our study chooses SOLO Taxonomy as the model marking the cognitive level to analyze the student' answers,describes the cognitive development of students' statistical thinking from quality and quantity aspects,and constructs a set of framework for characterizing pupils' statistical thinking that can be used to evaluate the level of students' statistical thinking.At the same time,taking into account that the framework also has a role in course preparation and teaching guidance,this paper,under the guidance of the idea of developmental research,designs 8 learning activities based on the characterization framework of pupils' statistical thinking.We choose a class of Grade 3 in a city school and carry out a short-term teaching experiment.The purpose of this teaching experiment is to explore the influence of teaching experiment on the development of students' statistical thinking,as well as the forms and characteristics of activities facilitating students" change.Through the research the following conclusions are obtained:(1)Using SOLO Taxonomy to analyze students' answers.The cognition of pupils'statistical thinking can be divided into four levels,namely idiosyncratic level(I),transitional level(T),quantitative level(Q),and analytical level(A).From the perspective of statistical thinking,the level of Grade 1 is relatively low,mainly at the idiosyncratic level(I)and transitional level(T),the level of Grade 2 and Grade 4 are mainly at the transitional level(T),and the levels of Grades 5 to 6 are at the quantitative level(Q).As to each dimension,the students' level of "statistical process" is obviously higher than the other three dimensions.(2)Through a systematic description of the pupils' cognitive development rules of statistical thinking as well as its dimensions.layers.and elements,we can find that the pupils show imbalance of development speed in different elements,but the same is that the students in the stage of Grades 5-6 show a state of gentle development or stagnation.(3)In terms of the level of statistical thinking,there is no significant difference between males and females,but the statistical thinking level of urban school students is obviously higher than that of rural school students.Specific to each dimension and layer,there is a significant difference in gender and school type in the statistical thinking level of the students in some stages or grades.(4)The situation type of a test question has a significant influence on students'performance in the same elements of statistical thinking,and different types of data also affect the performance of students in "classifying and representing data".(5)There are 9 kinds of common erroneous cognition in the statistical thinking of pupils,wherein one of the most common types of errors in the primary school is "the lack of title awareness when reading the data".Through the interviews,it is discovered that the improper reading method of the students is the main contributing factor of many errors.(6)The short term teaching activities based on the framework for characterizing pupils' statistical thinking can enhance the cognitive level of Grade 3 students'statistical thinking.But specific to each dimension,there is no significant improvement in "classifying and representing data" as well as "variation".Short term teaching experiment can help students overcome some erroneous cognition,and the students also show good emotion and attitude in this process.According to the results of the study,the author separately puts forward four suggestions for primary school statistical curriculum and teaching.For statistical curriculum design,it is suggested to the curriculum designers that:(1)grasp the rapid period of students' cognitive development,and design the course content rationally and evenly;(2)recognize the fundamentality of reading data and design related activities from multiple perspectives;(3)use real data and context,and design statistical learning activities around specific tasks;(4)base on the original idea of students,and globally construct the curriculum of statistics.For statistical teaching,it is suggested to the teachers that:(1)enrich the teaching knowledge of statistics,and carry out statistical activities scientifically and effectively;(2)grasp the contents of textbooks thoroughly,and promote students to apperceive statistics from various angles;(3)carefully design statistical tasks that students are interested in,and cultivate students'intimacy for statistics;(4)emphasize the connection between data and circumstances,and improve students' cognitive level of statistical thinking.