This paper proposes a novel application of knowledge space theory for identifying discrepancies between the knowledge structure that experts expect students to have and the real knowledge structure that students demonstrate on tests. The proposed approach combines two methods of constructing knowledge spaces. The expected knowledge space is constructed by analysing the problem-solving process, while the real knowledge space is identified by applying a data-analytic method. These two knowledge spaces are compared for graph difference and the discrepancies between the two are analysed. In this paper, the proposed approach is applied to the domain of stoichiometry. Although there was a decent agreement between expected and real knowledge spaces, a number of relations that were not present in the expected one appeared in the real knowledge space. The obtained results led to a general conclusion for teaching stoichiometry and pointed to some potential improvements in the existing methods for evaluating cognitive complexity.

中文翻译：

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使用知识空间理论比较学习化学计量中的预期知识空间和实际知识空间†

本文提出了一种知识空间理论的新应用，用于识别专家期望学生拥有的知识结构与学生在测试中展示的真实知识结构之间的差异。所提出的方法结合了两种构造知识空间的方法。通过分析解决问题的过程来构造期望的知识空间，而通过使用数据分析方法来识别实际的知识空间。比较这两个知识空间的图形差异，并分析两者之间的差异。在本文中，所提出的方法被应用于化学计量领域。尽管在预期知识空间和实际知识空间之间达成了不错的协议，但是在预期知识空间中不存在的许多关系出现在真实知识空间中。