ABSTRACT

Employing a statistical modeling inspired pedagogy is becoming a widespread practice in the statistics education community. Many have incorporated the practice of formulating conjectures in their modeling-enhanced educational designs and have reported on its benefits. We further elucidate the mechanism through which students’ conjecturing may be beneficial, in particular to their emergent reasoning with informal statistical models and modeling, as well as examine what challenges it may entail – the double-edged sword of conjecturing. We introduce a framework to describe young learners’ reasoning with informal statistical models and modeling (RISM), in which students’ conjecturing is represented as one of two parallel planes of model creation and refinement. We offer a case study of a pair of students’ participation in an integrated modeling learning sequence, including both real-world modeling tasks and probability-world modeling tasks. The pair was chosen as both students held strong, opposing real-world conjectures. Our goal is to elucidate the roles these conjectures can play, for better or for worse, to fully harvest the pedagogical potential of conjecturing.

摘要

采用受统计模型启发的教学法正在成为统计教育界的普遍做法。许多人已将提出猜想的做法纳入其增强建模的教育设计中，并报告了其好处。我们进一步阐明了学生的推测可能有益的机制，特别是对他们使用非正式统计模型和建模进行的新兴推理，并研究了它可能带来的挑战——推测这把双刃剑。我们引入了一个框架来描述年轻学习者使用非正式统计模型和建模 (RISM) 的推理，其中学生的猜想被表示为模型创建和改进的两个平行平面之一。我们提供了一对学生参与集成建模学习序列的案例研究，包括现实世界建模任务和概率世界建模任务。两人之所以被选中，是因为这两名学生都持有强烈的、反对现实世界的猜想。我们的目标是阐明这些猜想可以发挥的作用，无论是好是坏，以充分收获猜想的教学潜力。