发表机构
Osaka Kyoiku University（大阪教育大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该活动通过黑箱RC电路实验，引导学生从数据构建经验表征，并经历其失效与重构，强调表征需明确有效域，理论可事后引入以解释物理意义。
AI 中文摘要
在基础物理实验室中，一个核心教学目标是帮助学生从实验数据中构建、评估和修正数学表征，而非直接应用给定公式。我们提出了一项引导式的数据驱动活动，其中RC电路被视为一个通过可观测的输入-输出关系定义的黑箱。提供了实验和图形化操作步骤，而标准RC电路理论最初不予给出。学生首先检查在不同标称R和C值下获得的放电数据。他们使用T=t/RC重新标度时间，并比较不同电路条件下的归一化电压v=V/E，使放电数据更接近一条共同轨迹。通过绘制lnv对T的图形进行线性化，为提出经验表征提供了基础，并允许将RC解释为一个时间尺度，而非先验地赋予该含义。当针对放电提出的表征用充电数据进行检验时，尽管数据仍按T组织，但对数线性关系丧失。用距稳态的距离1-v替换v，线性关系得以恢复，由此产生的线性关系为提出修正的充电表征提供了基础。该活动利用一个熟悉的物理系统，使表征的构建、失效和重构在实验上变得明确。它还强调，经验表征必须附带指定的有效域，并且标准电路理论可以在事后引入，以解释从表征约束中涌现的物理意义。
英文摘要
In introductory physics laboratories, a central instructional goal is to help students construct, evaluate, and revise mathematical representations from experimental data rather than apply given formulas. We present a guided data-driven activity in which an RC circuit is treated as a black box defined through observable input-output relations. Experimental and graphical procedures are provided, while standard RC circuit theory is initially withheld. Students first examine discharging data obtained under different nominal values of R and C. They rescale time using T=t/RC and compare the normalized voltage v=V/E across circuit conditions, bringing the discharging data closer to a common trajectory. Graphical linearization through a plot of lnv versus T provides a basis for proposing an empirical representation and allows RC to be interpreted as a time scale rather than being assigned that meaning a priori. When the representation proposed for discharging is tested with charging data, logarithmic linearity is lost despite the continued organization of the data by T. Replacing v with the distance from the steady state, 1-v, restores linearity, and the resulting linear relation provides a basis for proposing a revised representation for charging. The activity thus uses a familiar physical system to make representation construction, breakdown, and reconstruction experimentally explicit. It also emphasizes that an empirical representation must be accompanied by a specified domain of validity and that standard circuit theory can be introduced a posteriori to interpret the physical meanings that emerge from representational constraints.
Comments38 pages, 3 figures. Substantially revised and retitled version of an earlier preprint posted on Jxiv (https://doi.org/10.51094/jxiv.4885). Expanded instructional framing and Supplementary Materials on implementation, instructor guidance, student outcomes, and informal classroom observations
