随着大数据时代的到来,收集,提取,整理,分析,应用数据的能力成为每个公民适应社会的必备技能,因此在普通高中数学课程标准和义务教育数学课程标准中都将‘数据分析观念’列为学生在学习数学过程中需要被逐渐培养起来并得到一定发展的核心素养之一,而‘平均数’又是人们在日常生活中经常会提及并用到的一个概念,它是小学阶段统计与概率领域内非常重要,而学生又比较难理解,还第一个学习的,比较抽象的一个‘统计量’。因此,本研究在了解学生对‘平均数’的认识现状存在局限性的基础上,致力于对‘平均数’内容的教学实施的改进和优化,过程中进行了参与式调查,分析,讨论并尝试进行教学实践,共分为三个子研究,第一,编制了小学生平均数认识的诊断测验,内容包括平均数概念理解,算法应用及统计意义理解三方面,并对实验学校的三-六年级学生进行调查分析;第二,根据查阅以往研究文献及访谈一线教师,结合学生的测验结果,根据学生的问题,分析教学原因,提出改进建议;第三,实施教学改进,针对部分教师展开学生学习平均数教学过程的持续性跟进指导,从而深化学生对‘平均数’这一统计量的认识和理解,进而提升其数据分析观念. 从调查研究结果能够得知:1,学生对平均数的算法理解及应用比较熟练,但缺少对平均数统计概念尤其是应用价值的深入理解.2,在平均数概念理解中,能够准确判断平均数与各数据之间关系,并提取出平均数,理解单个数据对平均数的影响,但是在实际情境中平均数所代表的真实意义理解会存在一定偏差.3,在对平均数的统计应用意义理解上,学生会在统计方法的选择上选择平均数这一统计量做出判断或推断,缺少对丰富数据的敏感性或选择的多样性.通过教师访谈对学生认识平均数的现状从教学原因入手,探究原因发现:教师和学生普遍认为平均数的学习比较简单,教学过程通常有一定路数,并且教学过程的关注点与学生的认识现状密切联系.因此提出建议:从源头入手认识平均数的特性;要放在统计全过程中,注重学生数据分析观念的引导培养,关注统计意识,数据的随机现象等;在教学的完整性和逻辑性中要设置适当关键的问题引导,关注它与日常生活的关系,情境要具有现实性,真实性,从而激发学生挖掘利用数据的兴趣.

With the advent of big data's time, the ability to collect, extract, collate, analyze and apply data has become a necessary skill for every citizen to adapt to society. Therefore, the concept of data analysis is included in the mathematics curriculum standard of high school and primary school as one of the core qualities of students' cultivation and development. And the average is a concept that people often use in their daily lives. It is very important in the field of statistical probability in primary school, and it is difficult for students to understand, and the first to learn , a relatively abstract statistic. So, this study focuses on the students' understanding of the average, the teaching improvement of the average, to do the investigation, analysis, discussion and teaching practice. This study is divided into three sub-studies. First, a diagnostic test of pupils' average cognition is compiled, which includes three aspects: the concept understanding of average, the application of algorithm and the understanding of statistical meaning. Second, according to the previous research literature and interviews with front-line teachers, combined with the results of the students' tests, according to the students' problems, the teaching reasons are analyzed, and suggestions for improvement are put forward. Third, we should carry out teaching improvement and carry out continuous follow-up guidance for some teachers in the teaching process of students' average learning, so as to promote students' understanding of the average and thus enhance students' concept of data analysis. The results of a survey of students' perception of averages show: 1. Generally speaking, the students are proficient in the arithmetic and application of average, but they lack a deep understanding of the statistical concept of average, especially the value of application. 2. In the conceptual understanding of averages, it is possible to accurately judge the relationship between averages and data, and extract averages to understand the impact of individual data on averages, But in the actual situation, there will be some deviation in the understanding of the true meaning represented by the average. 3. In the application of statistical significance of mean understanding, the average number of students in learning, and generally in the choice of statistical methods to choose the average number of the unified measurement to discriminate the diversity, lack of rich data sensitivity or choice. Through the teacher interview to the student cognition average present situation starting from the teaching reason, probes into the reason discovery: Teachers and students generally think that the average learning is relatively simple, the teaching process usually has a certain number of ways, and the focus of the teaching process is closely related to the understanding of the students. Therefore, we made some recommendations: understanding the characteristics of mean from the source. In the whole process of statistics, attention should be paid to the guidance and cultivation of students' concept of data analysis, to the awareness of statistics and the random phenomenon of data, etc. The proper key problem guidance should be set in the integrity and logicality of teaching. Attention should be paid to the relationship between it and daily life, and the situation should be realistic and authentic, thus stimulating students' interest in mining and using data.