Constructing Concepts of Average

这个项目的目标是研究人们如何发展、构建、解释和表现中心倾向或平均的概念。从这一认识出发，将为中小学统计的教与学提供更有效的方向。鉴于全民统计素养教育的主要推动力，以及明显缺乏关于儿童对统计学的理解的研究，这项研究代表着将研究与新兴的数学教学实践联系起来的重要一步。在项目的第一年，四年级、六年级和八年级的学生以及这些年级的老师将接受采访，以确定他们如何找到和解释平均数。参与者将使用各种材料来解决和表示涉及到引人入胜的、熟悉的量化数据的问题。对这些访谈的分析将确定这些年龄段的人所表现出的概念、方法、误解、陈述和规则。根据第一年的分析，我们将构建一个平均数概念的理论模型。在这个模式的基础上，将设计一系列的教学访谈，使用具体的和基于软件的表示法。第二年的研究将集中于调查平均水平不充分的认知模型如何变得更加完整和灵活。

The goal of this project is to examine how people develop, construct, interpret, and represent concepts of central tendency, or average. From this understanding, more effective directions for the teaching and learning of statistics at the elementary and middle school levels will be derived. Given the major educational thrust toward statistical literacy for all, and given the clear lack of research on what children understand about statistics, this study represents an important step in linking research to emerging mathematics teaching practices. During the first year of the project, fourth, sixth, and eighth graders as well as teachers of these grades will be interviewed to determine how they find and interpret average. Participants will use a variety of materials to solve and represent problems involving engaging, familiar quantitative data. Analysis of these interviews will identify the concepts, approaches, misconceptions, representations, and rules exhibited by individuals at these ages. A theoretical model of conceptions of average will be constructed from the first year's analysis. Based on this model, a series of teaching interviews, using concrete and software-based representations, will be devised. The second year's research will focus on investigating how inadequate cognitive models of average can become more complete and flexible.