[This paper is part of the Focused Collection on Instructional labs: Improving traditions and new directions.] Uncertainty is an important concept in physics laboratory instruction. However, little work has examined how students reason about uncertainty beyond the introductory (intro) level. In this work we aimed to compare intro and beyond-intro students’ ideas about uncertainty. We administered a survey to students at 10 different universities with questions probing procedural reasoning about measurement, student-identified sources of uncertainty, and predictive reasoning about data distributions. We found that intro and beyond-intro students answered similarly on questions where intro students already exhibited expert-level reasoning, such as in comparing two data sets with the same mean but different spreads, identifying limitations in an experimental setup, and predicting how a data distribution would change if more data were collected. For other questions, beyond-intro students generally exhibited more expertlike reasoning than intro students, such as when determining whether two sets of data agree, identifying principles of measurement that contribute to spread, and predicting how a data distribution would change if better data were collected. Neither differences in institutions, student majors, lab courses taken, nor research experience were able to fully explain the variability between intro and beyond-intro student responses. These results call for further research to better understand how students’ ideas about uncertainty develop beyond the intro level.

中文翻译：

---

比较入门学生和非入门学生对不确定性的推理

[本文是教学实验室重点集锦的一部分：改进传统和新方向。] 不确定性是物理实验室教学中的一个重要概念。然而，很少有人研究学生如何推理超出入门水平的不确定性。在这项工作中，我们的目的是比较入门学生和超越入门学生对不确定性的看法。我们对 10 所不同大学的学生进行了一项调查，问题涉及测量的程序推理、学生识别的不确定性来源以及数据分布的预测推理。我们发现，入门学生和超越入门学生在入门学生已经表现出专家级推理能力的问题上的回答类似，例如比较具有相同均值但分布不同的两个数据集、识别实验设置中的局限性以及预测数据如何如果收集更多数据，分布将会改变。对于其他问题，超越入门学生通常比入门学生表现出更专业的推理能力，例如确定两组数据是否一致、确定有助于传播的测量原则以及预测如果收集到更好的数据，数据分布将如何变化。 。机构、学生专业、所修实验课程或研究经验的差异都无法充分解释介绍性和非介绍性学生反应之间的差异。这些结果需要进一步的研究，以更好地了解学生关于不确定性的想法是如何发展到入门水平之外的。