大数据时代，面对随机现象及产生的数据做出合理判断和决策时，统计思维尤为重要。随着对统计及统计教育价值的认识，很多国家将统计内容作为基础教育数学课程的重要组成部分，统计思维以及如何发展学生统计思维是统计教育研究的热门话题之一。已有统计思维相关研究主要有两种视角：一是从统计学科角度给出要素，二是以数据分析过程为线索。不考虑随机性或将随机性单列为一个维度，缺少将其贯穿于统计思维的全过程，另外统计思维的建构缺少思维科学研究的指导。基于此，本研究聚焦三个研究问题：1.统计思维的内涵是什么？2.中学生统计思维发展水平是什么？3.中学生统计思维发展的现状如何？

通过概念演绎的方式，从统计学科、思维学科两个视角界定统计思维的内涵，尝试刻画统计思维的结构，划分统计概念、统计判断和统计推断三种思维形式。依据统计思维内涵的界定确定中学生统计思维评价框架，设计测试题目；采用目的抽样在北京四个区县各选择1所完中，每所学校初一、初二、高一、高二各选择1个平行班进行测试，参与测试的学生共535人；根据测试结果并综合已有研究，将学生在每个题目上不同水平的表现进行编码，进而提炼概括对统计概念、统计判断和统计推断分别划分为五个不同水平。根据水平划分完善测试题，形成中学生统计思维发展测试工具；采取目的抽样在北京某区选择两所不同水平的学校，每所学校初一、初二、高一、高二各选择1个平行班进行测试，参与测试的学生共287人，有效样本为278人；初步探究中学生统计思维发展水平的现状；并选择参与测试的6名初二年级学生进行学习个案研究。

本研究的主要结论如下：

1.统计思维的界定。统计思维是在解决统计问题、从事统计活动中对统计材料的概括、间接的反映，进而得到统计问题、统计活动本质和规律的认识；统计问题重要特征是统计研究的五种数据类型及其关系。统计思维是一个有系统的动态结构，包括统计思维目的、统计思维材料和结果、统计思维过程、统计思维品质、统计思维非认知因素、统计思维的自我意识和监控等要素；包括三个动态循环过程。统计思维形式包括统计概念、统计判断和统计推断。

2.中学生统计思维发展水平。统计概念理解划分为五个水平：确定的角度理解统计概念，概括的角度理解统计概念，关联的角度理解统计概念，随机性的角度理解统计概念，定量刻画统计概念的随机性。统计判断划分为五个水平：单一、确定角度判断数据，多个角度信息判断数据，关联角度判断数据，整体判断数据，联系背景判断数据。统计推断划分为五个水平：确定地认识样本推断总体这种不完全归纳推理；怀疑由样本推断总体的不完全归纳推理；理解样本随机性会影响不完全归纳推理的准确性；平衡样本随机性导致的不完全归纳推理的可靠性与风险性；定量刻画不完全归纳推理的可靠性。

3.中学生统计思维发展现状。调查结果表明（1）整体而言，统计概念方面，描述意义数字特征理解集中在水平2，随机抽样和频率解释理解集中在水平4；统计判断方面，频数分布直方图信息判断主要分布在水平1到水平3，多变量统计表信息判断主要分布在水平2到水平4；统计推断方面，抽样推断主要分布在水平3和水平4，机会推断从水平1到水平4都一定的人数百分比。（2）四个年级共同特点是多变量统计表信息判断好于频数分布直方图；随机抽样理解集中在水平4；统计推断水平低于相应概念理解，抽样推断表现好于机会推断。（3）不同年级差异而言，四个年级只在随机抽样理解差异不显著；相邻年级发展来看，初二年级在频率解释、频数分布直方图信息判断显著好于初一年级，高一年级在统计推断显著好于初二年级，高二年级在频率解释、统计判断、抽样推断显著好于高一年级。（4）每个年级整体而言，高二学生在抽样推断方面水平分布更加分散，近30%的学生在水平2。（5）学生学习个案研究，初步验证通过所设计的学习活动材料，一定程度上可以促进学生统计思维水平的提升，质疑的思维品质有很重要的作用。

Statistical thinking is of important in the reasonable judgments and decisions, especially in the era of big data. Because of the understanding of statistics and its value in education, many countries have made it as the important part in the primary and secondary school. Statistical thinking and how to develop it have been popular topics in the statistical education research. There are two perspectives in the research about it: giving the important dimensions from statistics, or expressing the behaviors of what students can do in the data analysis process. These researches did not consider randomness, or treat it as a independent dimension. The randomness，variation or the uncertainty should be in every aspect of statistical thinking，and the construction of statistical thinking should be guided by the cognitive science. On the basis of these, this study focuses on three contents: 1.what is statistical thinking and its construction? 2.What are the developmental levels of statistical thinking about middle-school student? 3.What are the developmental situations about middle-school student in it?

By deduction of conception, this study constructs the statistical thinking and its construction according statistics and cognition, and tries to give the form of statistical concept, statistical judgment, and statistical inference. And then it constructs the assessment framework of statistical thinking, design several items. Selecting 4 middle schools according purposive sampling in different districts in Beijing, and then selecting 1 in four grades in each school: grade one and two in junior middle school, grade one and two in high school, and there are 535 students in the tests totally. Recoding different behaviors on the basis of the tests and existing researches of each item, and summarizing all recodes and getting five different levels in statistical concept, statistical judgment and statistical inference respectively. Refining the items according the five levels, selecting 2 different middle schools in a district in Beijing by purposive sampling, there are 287 students in four classes and 278 effective samples. The purpose of the second test is to explore the developmental situations about middle-school student in statistical thinking. There 6 students in the case study in grade two of junior middle school who selected from the second test.

The conclusions of this study as following:

1. Definition and construction of statistical thinking. The statistical is cognition about statistical problems and statistical activities in the process of them by general and indirect reflection. The important feature of statistical problems or activities is the variations and their relationship. The construction of statistical thinking has six dimensions: aim, materials and results, procession, disposition, non-cognitive factors, self-awareness and monitoring. And the construction of statistical thinking is a dynamic system which has three dynamic cycles. The forms of statistical thinking are: statistical concept, statistical judgment, and statistical inference.

2. Developmental Levels of statistical thinking. There are five different levels in each form of statistical thinking. For the statistical concept：determinate understanding，summary understanding，relation understanding，random understanding and quantitative random understanding. For the statistical judgment: unique and determinate judgment, unique and determinate judgment, multiple judgments, relation judgments, aggregation judgments, aggregation and judgment with context. For the statistical inference: determinate conclusion, skeptical about the inference, understanding the inaccurate of inference because the randomness in sample, balancing the reliability and risk in inference, qualified the reliability of inference. 

3. Developmental situations about middle-school student. The Survey has following findings:1) Overall, understandings of numerical characteristics are mainly in the level 2, understandings of random sampling and frequency are mainly in level 4; for statistical judgment, frequency distribution histogram judgments are mainly distributed from level 1 to3, multivariable table judgments are mainly distributed from level 2 to4; for statistical inference, sampling inference is mainly distributed in level 3 and 4, chance inference is distributed from level 1 to 4. 2) Same features of 4 grades are: multivariable table judgments are better than frequency distribution histogram judgments, understandings of random sampling are mainly in level 4; inference level is lower than corresponding concept understandings; sampling inference is better than chance inference.3) For different grades: there are no significant differences in understandings of random sampling for the four grades only; grade two in junior middle school is better than grade one in frequency understandings and frequency distribution histogram judgments; grade one in high school is better than grade two in junior middle school in inference; grade two in high school is better than grade one in frequency understanding, statistical judgmentsand sampling inference.4) Grade one in high school has more differences in all the four grades in sampling inference, there is 30% in level 2. 5) The 6 cases study of grade two of junior middle school verified effectiveness of the materials, some of them develop to higher level under the materials, and the query or skeptical feature are important dispositions.