2001年《数学课程标准》颁布后，统计与概率成为一个单独的模块，作为四个学习领域之一被纳入小学课本，随着“统计与概率”在《数学课程标准》中被规定为义务教育阶段数学课程的4个学习领域之一，统计与概率的研究逐渐成为热点。2011年颁布的《数学课程标准》又对概率的内容和难度进行了调整。笔者通过对国内外学者有关概率教学研究的论文、著作的研读，发现学者们的研究主要集中在一个核心问题上，即在新课程理念下，如何采用合理的教学策略更有效地纠正学生的错误观念，进而提高师生之间教概率和学概率的效率。而针对概率学习规律与特征以及概率学习水平的研究还相对比较匮乏。由此，本研究将以约翰斯等人提出的学生概率推理发展框架为基础和依据，编制一份测试卷，对学生的概率学习进行调查。并根据SOLO分类法对学生的概率学习水平进行刻画。本研究中参加测试的是3个年级共24个班级的1137个四、五、六年级学生，回收有效测试卷1000份。测试卷回收后按统一标准进行批阅，利用Quest软件和SPSS统计软件对学生的得分情况进行分析。以此对小学生概率学习规律与特征进行描述和刻画，并对小学生概率学习水平进行分析。本研究中所界定的概率学习，指“统计与概率”这一领域中的概率学习。主要考查新课标中规定的小学生概率学习的内容。根据约翰斯等人的研究，这些内容可以被概括为六个主要概念：样本空间、实验概率、理论概率、概率比较、条件概率和独立事件。因为条件概率部分在小学阶段不作学习要求，所以本研究仅对其余的五个概念进行研究。通过分析，我们主要得出了如下结论：第一，从总体来讲，小学生概率的学习水平会随着年级的增长而逐渐提高。而且三个年级学生在概率学习的测试上存在着显著性差异。对于概率中几个不同概念而言，学生的掌握水平也有相同的趋势：六年级学生的掌握水平普遍高于五年级学生，五年级学生又都高于四年级学生。且几个概念间的难度水平满足这样的关系：实验概率＞独立事件＞概率比较＞理论概率＞样本空间。第二，四年级学生对样本空间、理论概率和概率比较三个概念掌握的比较好，但是在实验概率和独立事件这两个概念上的表现很不理想。五年级学生能够较好地掌握样本空间、理论概率和概率比较的相关内容，在实验概率和独立事件两个概念上的表现尚可。六年级学生对样本空间、理论概率、概率比较、实验概率和独立事件五个概念的理解和掌握都比较好，说明在六年级开始开设涉及这些概念的相关内容对六年级学生来说难度适当。

After the enactment of “Mathematics curriculum standards” in 2001, Statistics and Probability as one of the four learning Areas, are included in the primary school textbooks. Statistics and Probability has thus become the focus of research. Through the study of domestic and foreign scholars on the probability of teaching and learning papers, the author found that the research focuses on a core issue on how to correct the misconceptions of students more effectively using a reasonable amount of teaching strategies and how to improve the efficiency of teaching and learning of the probability. While, the research on the learning laws, characters and levels of probability is relatively scarce.Thus, the author will prepare an examination to investigate the students’ learning on the probability on the basis of “probabilistic reasoning development framework”, which proposed by Johns et al. Then, the author will depict the students’ learning on the probability according to the SOLO classification. The author selected a sampling of about 1000 pupils in Grades 4, 5 and 6 in eight schools of different levels as subjects for research. In order to find out the learning laws, characters and levels of probability, the author will mark the examinations according to uniform standards and analyze the scores of students by Quest Software and SPSS statistical software. The probability learning defined in this study is included in the Learning Areas of "Statistics and Probability". Johns divides the contents of Probability into six notions, namely, Sample space, Experimental probability, Theoretical probability, Comparison of probability, Conditional probability and Independent events. As the new curriculum standards doesn’t require the primary school students to master the contents of the Conditional probability, the author will analysis the rest of the five concepts in this study.The author arrived at the learning laws, characters and levels of probability from the results of these examinations and the statistical analysis. The major findings include: First of all, I have found that the learning level of probability of primary school students develops as grades grows in general. There is a significant difference in the learning levels between Grade 4 and Grade 5, Grade 5 and Grade 6.The same laws can be found in the analysis of each of the five notions, namely, the level of Grade 6 is generally higher than that of Grade 5, and Grade 5 is higher than that of Grade 4. The level of difficulty of the five notions (from high to low) in the order of this: Experimental probability, Independent events, Comparison of probability, Theoretical probability, Sample space.Secondly, the contents of the Sample space, Theoretical probability and Comparison of probability can be taught in Grade 4, but these students are unable to grasp the contents of Experimental probability and Independent events. Students in Grade 5 are able to master the contents of the Sample space, Theoretical probability, Comparison of probability, parts of the Experimental probability and Independent events. Students in Grade 6 are able to master all of these 5 notions.