发展学生统计推理能力，不仅契合了大数据时代对现代公民的素养要求，也是个体适应信息社会的必备能力。在时代的诉求之下，包括我国在内的许多国家，如美国、日本、新加坡等的课程标准或教学大纲都充分重视小学生的统计推理能力。国内外数学教育研究者们围绕统计推理的内涵、理论框架、评价等问题展开了一系列研究，但已有研究尚未形成指向统计推理能力构念的系统化评价框架和测评工具，且我国统计课程和教学背景下的小学生统计推理能力“是什么”“评什么”“怎么评”“表现如何”等问题依旧有待解决。
对此，本研究以小学六年级学生为研究对象，通过量化研究方法和质性研究方法相结合的混合研究方法来开展统计推理能力的测评研究，共包含三个研究问题：小学生统计推理能力的评价指标是怎样的？六年级学生统计推理能力的评价等级及测评工具是怎样的？六年级学生统计推理能力的表现是怎样的？围绕上述研究问题，主要得到以下研究结果：
（1）基于推理认知过程，结合我国小学统计教学背景下的实际情况和话语体系，通过文献分析、专家访谈等环节对Makar和Rubin三维理论框架进行“本土化”，最终构建的小学生统计推理能力评价指标包含“推测数据之外信息”“运用数据解释推测”“反思推测不确定性”。
（2）结合SOLO分类理论，通过文献分析，针对统计推理能力的三个评价指标分别初步构建“前结构水平、单一结构水平、多元结构水平、关联水平”四个评价等级，并基于此初步编制现实情境视角下的统计推理测评工具（含测试题及评分标准）。经过专家访谈、6人学生出声思维、第一轮预测试、第二轮预测试等环节，运用经典测量理论和项目反应理论，六年级学生统计推理能力的评价等级和测评工具得以确立。其中，该套测评工具共包含12道题，内部一致性系数为0.814，验证性因素分析结果为χ2/df=1.41, RMSEA=0.062<0.08, SRMR=0.062<0.08, CFI=0.928, TLI=0.903，具有良好的信效度，整体质量较好，可应用于大规模测评。
（3）采取方便抽样法和整群抽样法，选取1所普通公办小学的322名六年级学生开展测试调查，运用描述性统计、Rasch分析法、案例分析法刻画学生的总体表现和具体表现案例。结果显示，在总体表现上：近九成六年级学生的统计推理能力处于单一结构水平和多元结构水平，其中有超过五成的学生处于单一结构水平；少数学生仍处于前结构水平，极少数能达关联水平。在具体表现特征上：86%的六年级学生能推测数据之外的信息；90.1%的六年级能运用数据作为证据来初步解释推测；61.1%的六年级学生会认为统计所得推测是确定的或大概率确定，32.1%的学生能真正反思到推测的不确定性。同时，针对每个评价指标，挖掘和分析了学生典型作答策略和学习迷思。
综上，本研究开发了由“三个评价指标×四个评价等级”构成的六年级学生统计推理能力评价框架，并基于此深度刻画了学生的表现特征。基于Makar和Rubin三维理论框架并扎根我国小学生思维特点，以评价为切入口推动着统计推理培养在课堂教学中的落地，也拓展了SOLO分类理论在小学数学教育评价领域的应用。该套评价体系及对应学生案例不仅可通过测试等形式用于统计推理能力的结果性评价，也可在课堂教学中用于表现性评价、过程性评价等。此外，本研究所开发的可反映统计推理能力构念的、经得起信效度检验的六年级学生统计推理能力测评工具，可为数学开放题评分难问题的解决和数学开放题融入大规模测评提供启示。尽管如此，本研究还存在一些局限性，如测试抽样的代表性有限，测试题的评分相对繁琐等。在未来研究中，可进一步扩大学生样本的数量和区域覆盖性，以及通过在线测评研究逐步实现开放题的自动化评分等。

Developing students' statistical reasoning (SR) ability not only meets the literacy requirements of modern citizens in the era of big data, but also is an essential ability for individuals to adapt to the information society. Under the demands of the times, the curriculum standards or syllabus of many countries, such as China, the United States, Japan, and Singapore, fully pay attention to the statistical reasoning ability of primary school students. Mathematical education researchers have carried out a series of studies on the definition, theoretical framework and assessment of statistical reasoning. However, the existing research has not yet formed a systematic assessment framework and tools for statistical reasoning ability. Under the background of statistics curriculum and teaching in China, problems such as "what is SR", "what to assess SR", "how to assess SR” and “what is the students’ performances” still need to be solved.
The current study takes sixth-grade students as the research object, and carries out the assessment of statistical reasoning ability through the mixed method. There are three research questions: What are the assessment indicators for primary students' statistical reasoning ability ? What are the assessment levels and tools for sixth-grade students' statistical reasoning ability? How do sixth graders perform in statistical reasoning? Focusing on the above questions, the following results are mainly obtained:
(1) Based on the cognitive process of reasoning, combined with the actual situations and discourse system of statistical teaching in China, the three-dimensional theoretical framework of Makar and Rubin is "localized" through literature analysis and expert interviews. And primary school students’ statistical reasoning is constructed. The assessment indicators include "Inference beyond the data", "Use data to explain inference" and "Reflect on the uncertainty of inference".
(2) Combined with the SOLO taxonomy, four assessment levels of " Prestructural level, Uni-structural level, Multi-structural level and Relational level" are initially constructed for the three assessment indicators of SR through literature analysis. From the perspective of realistic context, the SR assessment tool (including test items and grading standards) has been preliminarily compiled on the ground of assessment framework. And then, after the phases that including expert interviews, students' thinking aloud, and two round of pre-testing, the assessment level and tool of the sixth-grade students' SR are established by the help of CTT and IRT. Among them, this assessment tool contains a total of 12 questions, the internal consistency coefficient is 0.814, the confirmatory factor analysis results are χ2/df=1.41, RMSEA=0.062<0.08, SRMR=0.062<0.08, CFI=0.928, TLI=0.903. These show that the tool is of good quality and can be applied to the large-scale test.
(3) Convenience sampling method and cluster sampling method were adopted to select 322 sixth-grade students from an ordinary public primary school to carry out a test survey. Using descriptive statistics, Rasch analysis method, and case analysis method, this study describes the overall performance and specific performance cases of sixth graders. The results show that, in terms of overall performance, nearly 90% of the sixth grade students' statistical reasoning ability is at the Uni-structural level and multi-structure level, and more than 50% of the students are at the Uni-structural level; a few students are still at the pre-structure level, and very few can to the Relational level. In terms of specific performance characteristics, 86% of sixth graders can infer information beyond the data; 90.1% can use data as evidence to preliminarily explain the inference; 61.1% think that the inference is certain or almost certain, and 32.1% can really reflect on the uncertainty of inference. At the same time, the typical answering strategies and learning myths of students are excavated and analyzed for each assessment indicator.
To sum up, this study has developed an assessment framework for sixth graders  statistical reasoning ability composed of "three assessment indicators × four assessment levels". Based on it, the performance characteristics of students are deeply described. This assessment system and corresponding student cases can not only be used for the summative assessment of SR through tests, and it can also be used for performance-based assessment and formative assessment. Besides, based on the Makar and Rubin's three-dimensional theoretical framework and rooted in the thinking characteristics of Chinese primary school students, this assessment system takes “assessment” as the entry point to promote the teaching of statistical reasoning in school. And it also expands the application of SOLO taxonomy in the field of primary school mathematics education assessment. In addition, the SR assessment tool developed in this study can reflect the concept of SR and stand the test of reliability and validity. It can provide inspiration for the solution of difficult scoring problems of mathematics open-ended questions and the integration of mathematics open-ended questions into large-scale test. Nonetheless, this study has some limitations, such as the limited representativeness of the test sample and the relatively cumbersome scoring of the test. In future research, the number and regional coverage of student samples can be further expanded, and automatic scoring of open-ended questions can be gradually realized through online assessment research.