This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the relationships between predicates within the conditional statements and inference structures among various proofs (in number theory and geometry). We document the progression of Theo’s set-based emergent model (Gravemeijer, 1999) from a model-of the truth of statements to a model-for logical relationships. This constitutes some of the first evidence for how students can abstract such logical concepts in this way and provides evidence for the viability of the learning progression that guided the instructional design.

这份报告记录了一名本科生如何使用基于集合的推理来重新发明与条件语句及其证明相关的逻辑原则。这种学习发生在一个教学实验中，旨在通过比较条件语句中的谓词之间的关系和各种证明（数论和几何）中的推理结构来促进这些逻辑关系的抽象。我们记录了 Theo 基于集合的涌现模型 (Gravemeijer, 1999) 从陈述真实性模型到逻辑关系模型的进展。这构成了学生如何以这种方式抽象出这些逻辑概念的一些初步证据，并为指导教学设计的学习进程的可行性提供了证据。