ABSTRACT

Growing scholarship on the pedagogical applications of statistical modeling is currently taking place to create adaptations of this practice to introduce novices to statistics. These are intended to promote novices’ reasoning, and are typically void of formal mathematical procedures and calculations. In this article, we define the potential product that novices can create as they engage in such informal implementations, Informal Statistical Models (ISM), as purposeful representations – with both deterministic and stochastic components – of how observed variability in data is generated. This definition reflects the potential connection between informal constructs that novices and young students can create and the formal view of statistical models, thereby suggesting how informal insights may be later cultivated into more mature understandings. We illustrate the usefulness of this definition by providing an in-depth account of the reasoning that a pair of sixth-grade students employed through their informal statistical modeling process. The findings illustrate a four-episode sequence where students created and developed an initial deterministic model before extending it with an informal stochastic component. This shows how starting with deterministic models can be a valuable precursor to develop initial ISMs.

摘要

目前正在对统计建模的教学应用进行越来越多的学术研究，以对这种做法进行改编，以向新手介绍统计数据。这些旨在促进新手的推理，并且通常没有正式的数学程序和计算。在本文中，我们定义了新手在参与此类非正式实施时可以创建的潜在产品，即非正式统计模型 (ISM)，作为有目的的表示 - 具有确定性和随机性组件 - 如何生成观察到的数据变异性。这个定义反映了新手和年轻学生可以创建的非正式结构与统计模型的正式观点之间的潜在联系，从而表明非正式的见解以后可以如何培养成更成熟的理解。我们通过深入说明一对六年级学生通过非正式统计建模过程采用的推理来说明该定义的有用性。调查结果说明了一个四集序列，其中学生创建并开发了一个初始确定性模型，然后使用非正式随机组件对其进行扩展。这表明从确定性模型开始如何成为开发初始 ISM 的宝贵先驱。