发表机构
Key Laboratory of Magnetism and Magnetic Functional Materials, Ministry of Education, Lanzhou University（兰州大学教育部磁性功能材料重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出剂量与精度交互影响教学有效性的框架，将精度分解为三成分并推导出精度可补偿剂量的可量化替代关系，以固态物理案例说明。
AI 中文摘要
我们提出，教学有效性可能取决于两个设计维度之间的交互作用：剂量（即分配给某个主题的以学生为中心的主动学习总时长）和精度（即干预措施针对特定、有记录在案的认知瓶颈，并采用与机制匹配的表征工具的程度）。本文将该框架形式化，将其锚定在认知负荷理论中，推导出其可证伪的预测，并阐明其相对于现有教学设计文献的增量贡献。核心理论步骤是将精度分解为三个组成部分——靶向性（$P_t$）、表征匹配（$P_r$）和范围限制（$P_s$）——并论证只有表征匹配直接作用于外部负荷。这一分解产生了一个紧凑的模型，其中有效剂量为 $D_{\mathrm{eff}}=D P_s$，相关加工为 $G=D P_s\eta(P_r)$，其中 $\eta$ 为表征效率，学习为 $E=g(G)$，其中 $g$ 为递增且凹的函数（此处 $E$ 为目标构念上的累积学习结果，而非速率）。该框架的核心命题（P3）——即精度可以补偿剂量——因此成为一个可量化的替代性主张，即 $\mathrm{d}D/\mathrm{d}P_r=-\eta/\eta'$，而非仅仅是一个存在性陈述；其范围受精度上限和最小剂量阈值的约束。我们将该框架与卡罗尔的经典时间需求模型区分开来，依据是精度的方向性特征和替代率的可估计性，并与ICAP框架区分开来，依据是区分“参与内容与瓶颈的匹配”和“参与模式”。作为一个示例（而非对该框架的检验），
英文摘要
We propose that instructional effectiveness may depend on an interaction between two design dimensions: dosage---the total duration of student-centered active learning allocated to a topic---and precision---the degree to which an intervention targets a specific, documented cognitive bottleneck with a mechanism-matched representational tool. This paper formalizes the framework, anchors it in cognitive load theory, derives its falsifiable predictions, and clarifies its incremental contribution relative to existing instructional-design literature. The central theoretical move is to decompose precision into three components---targeting ($P_t$), representational match ($P_r$), and scope restriction ($P_s$)---and to argue that only representational match acts directly on extraneous load. This decomposition yields a compact model in which the effective dosage is $D_{\mathrm{eff}}=D P_s$, the germane processing is $G=D P_sη(P_r)$ with $η$ the representational efficiency, and learning is $E=g(G)$ with $g$ increasing and concave \rev{(here $E$ is the cumulative learning outcome on the target construct, not a rate)}. The framework's core proposition (P3)---that precision can compensate for dosage---then becomes a quantifiable substitutability claim, $\mathrm{d}D/\mathrm{d}P_r=-η/η'$, rather than a mere existence statement; its scope is bounded by a precision ceiling and a minimum dosage threshold. We distinguish the framework from Carroll's classic time-needed model by the directional character of precision and by the estimability of the substitution rate, and from the ICAP framework by distinguishing ``matching of participation content to the bottleneck'' from ``mode of participation.'' As an illustrative case (not a test of the framework),
Comments27 pages, 3 figures
