The frame concept from linguistics, cognitive science and artificial intelligence is a theoretical tool to model how explicitly given information is combined with expectations deriving from background knowledge. In this paper, we show how the frame concept can be fruitfully applied to analyze the notion of mathematical understanding. Our analysis additionally integrates insights from the hermeneutic tradition of philosophy as well as Schmid’s ideal genetic model of narrative constitution. We illustrate the practical applicability of our theoretical analysis through a case study on extremal proofs. Based on this case study, we compare our analysis of proof understanding to Avigad’s ability-based analysis of proof understanding.

来自语言学，认知科学和人工智能的框架概念是一种理论工具，用于建模如何明确地将给定的信息与源自背景知识的期望相结合。在本文中，我们展示了如何将框架概念有效地应用于分析数学理解的概念。我们的分析还整合了来自哲学诠释学传统以及施密德理想的叙事构成遗传模型的见解。我们通过对极端证据的案例研究来说明我们的理论分析的实际适用性。基于此案例研究，我们将对证明理解的分析与对Avigad基于能力的证明理解的分析进行比较。