Difficulty Generating Factors for Context-free Language Construction Assignments
Florian Schmalstieg, Marko Schmellenkamp, Jakob Schwerter, Thomas Zeume

TL;DR
This study identifies factors influencing the difficulty of constructing context-free grammars and pushdown automata, revealing that presentation and structural complexity significantly impact student performance in learning these concepts.
Contribution
It introduces and empirically tests four difficulty-generating factors affecting students' understanding of context-free languages, informing adaptive learning system design.
Findings
Three of four factors significantly affect grammar construction difficulty
Perceived difficulty partly aligns with objective performance
Pushdown automata tasks show inconsistent effects
Abstract
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…
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