标题： 上下文无关语言构造作业的难度生成因素 显示英文标题

标题： Difficulty Generating Factors for Context-free Language Construction Assignments

摘要： 计算机科学学生常常在抽象理论概念上遇到困难，尤其是在理论计算机科学的入门课程中。 其中一个挑战是理解上下文无关语言及其各种表示方法。 在本研究中，我们调查了影响学生构建上下文无关文法和下推自动机的因素。 我们提出了两个可能导致难度的因素，针对语言呈现给学生的方式：自然语言表示和冗长的集合符号表示。 此外，我们提出了两个针对给定上下文无关语言结构的因素：结构的嵌套和多重性的插入。 我们使用了交互式学习系统中的被试内随机化进行了一项控制实验，测试了构建上下文无关文法和下推自动机的难度因素。 我们的结果表明，四个因素中有三个显著影响学生在解决构建上下文无关文法练习中的客观表现，而学生的主观困难程度仅部分与客观表现指标一致。 对于下推自动机任务的结果与上下文无关文法任务的结果有明显差异。 我们的变化要么影响微乎其微，要么在某些情况下甚至降低了难度。 因此，无法对下推自动机任务做出可靠的统计结论。 这些结果为能够自适应地为个别学生选择适当练习的学习系统奠定了基础。 显示英文摘要

摘要： Computer science students often struggle with abstract theoretical concepts, particularly in introductory courses on theoretical computer science. One such challenge is understanding context-free languages and their various representations. In this study we investigate factors that influence the difficulty of constructing context-free grammars and pushdown automata for context-free languages. We propose two potential difficulty generating factors targeting how a language is presented to students: representation in natural language and as a verbose set notation. Furthermore, we propose two factors targeting the structure of the given context-free language: nesting of constructs and insertion of multiplicities. We conducted a controlled experiment using within-subject randomization in an interactive learning system, testing the proposed difficulty factors for constructing context-free grammars and pushdown automata. Our results suggest that three of the four factors significantly influence students' objective performance in solving exercises for constructing context-free grammars, while students' perceived difficulties only partly align with the objective performance measures. The findings for pushdown automata tasks differed markedly from those for context-free grammar tasks. Our variations either had negligible effects or, in some cases, even reduced difficulty. Thus, no robust statistical conclusions can be made for pushdown automata tasks. The results lay foundations for learning systems that adaptively choose appropriate exercises for individual students.