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

对一个有统计知识的社会的需求正在增加，以代数为基础的统计学入门课程仍然是大多数高中生和本科生学习统计学的主要场所。然而，典型的统计学入门课程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。学生在第一门统计学课程之后取得进步的主要障碍是，他们还没有(或不打算)选修概率、微积分和/或线性代数的必修课。为了增加选修多元统计方法课程的学生人数，该项目将开发、试行和研究基于代数的第二门课程的材料使用。这些材料将(1)强调在多变量假设的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，以建立学生的直觉和理解，(3)利用为典型本科生设计的写作风格和教学方法，(4)开发和整合促进学生探索和发现的技术工具，以及(5)从评估结果中获得信息。拟议的项目将为大学教职员工提供一套完全综合的课程材料，以教授针对重要的多变量统计概念的第二门统计学课程，该课程与以往有很大不同。这些概念包括最大限度地减少无法解释的变异性，计划和控制混淆变量，探索变量之间的相互作用并建立模型。这些材料将利用以前的支持，为以模拟为基础的推理为中心的介绍性统计提供材料。该项目伴随的评估活动、新评估工具的开发(多变量统计概念清单)以及对学生评估结果的检查，将涉及以下研究问题：(1)使用这一新课程，在多变量统计思维的哪些领域有显著的概念理解？以及(2)学生对关键的推论和描述性统计概念的学习轨迹有什么特点？

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?