Developing and Assessing a Conceptual Approach to an Algebra-based Second Course in Statistics

对统计素养社会的需求正在增加，基于代数的统计入门课程仍然是大多数高中生和本科生学习统计的主要场所。然而，典型的统计学入门课程并没有给学生提供多变量统计方法的经验，而多变量统计方法是当今劳动力中使用的主要方法。学生在完成第一门统计学课程后的主要障碍是，他们还没有（或不打算学习）概率、微积分和/或线性代数的先决课程。为了增加选修以多变量方法为重点的统计学课程的学生人数，本项目将开发、试点测试和研究基于代数的第二门课程材料的使用。这些材料将(1)强调多变量假设背景下的总体统计过程，(2)从简单的多变量研究设计和探索性数据分析概念开始，以学生的直觉和理解为基础，(3)利用为典型本科生设计的写作风格和教学方法，(4)开发和整合技术工具以促进学生的探索和发现，(5)通过评估结果获得信息。拟议的项目将向大学教员提供一套完全综合的课程材料，以教授统计学第二门课程的一套完全不同的课程，其目标是重要的多变量统计概念。这些概念包括最小化无法解释的可变性，规划和控制混杂变量，以及探索和模拟变量之间的相互作用。这些材料将利用先前的支持，这些支持产生了以基于模拟的推理为中心的入门统计资料。该项目附带的评估活动、新评估工具（多变量统计概念清单）的开发以及学生评估结果的检查将解决以下研究问题：(1)使用新课程，多变量统计思维的哪些领域在概念理解方面有显著的收获？(2)学生对关键推论和描述性统计概念的学习轨迹有何特点？

Demands for a statistically literate society are increasing, and the algebra-based introductory statistics course remains the primary venue for learning statistics for the majority of high school and undergraduate students. However, the typical introductory statistics course does not give students experience with multivariable statistical methods, which are the primary methods used in the workforce today. The primary barrier to students' progressing beyond their first statistics course is that they have not yet taken (or do not intend to take) prerequisite courses in probability, calculus, and/or linear algebra. Toward increasing the number of students who take a statistics course that focuses on multivariable methods, this project will develop, pilot-test, and study the use of materials for an algebra-based second course. These materials will (1) emphasize the overarching statistical process in the context of multivariable hypotheses, (2) start with straightforward multivariable study design and exploratory data analysis concepts to build on student intuition and understanding, (3) utilize a writing style and pedagogical approach designed for the typical undergraduate student, (4) develop and integrate technology tools for facilitating student exploration and discovery, and (5) be informed by assessment results. The proposed project will provide college faculty with a fully integrated set of curriculum materials to teach a substantially different curriculum for a second course in statistics, aimed at important multivariable statistical concepts. Such concepts include minimizing unexplained variability, planning and controlling for confounding variables, and exploring and modelling interactions between variables. These materials will leverage prior support that produced materials for introductory statistics centered on simulation-based inference. The project's accompanying assessment activities, development of a new assessment tool (a Multivariable Statistics Concept Inventory), and examination of student assessment results, will address research questions such as (1) In which areas of multivariable statistical thinking are there significant gains in conceptual understanding using this new curriculum? and (2) What are the characteristics of students' learning trajectories for key inferential and descriptive statistics concepts?