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\section{Introduction}
% why automatic feedback
Programming education is becoming increasingly accessible with massive online courses. Since thousands of students can attend such courses, it is impossible for teachers to individually evaluate each participant’s work. On the other hand, in-time feedback directly addressing student’s errors can aid the learning process. Providing feedback automatically could thus greatly enhance these courses.
% ITS background
Traditional intelligent tutoring systems use manually constructed domain models to generate feedback. Cognitive tutors model the problem-solving \emph{process}: how students write programs. This is challenging because there are no well-defined steps when writing a program (as there are in chess, for example). Many tutors instead only analyze individual versions of the student’s program, and disregard its evolution. These models are often coded in terms of constraints or bug libraries~\cite{keuning2016towards}.
% data-driven domain modeling
Developing the domain model requires significant knowledge-engineering effort~\cite{folsom-kovarik2010plan}. This is particularly true for programming tutors, where most problems have several alternative solutions and many possible implementations~\cite{le2013operationalizing}. Data-driven tutors reduce the necessary effort by mining educational data -- often from online courses -- to learn how to fix common errors and generate feedback.
% problem statement
This paper addresses the problem of finding useful features to support data mining in programming tutors. Features should be robust against superficial or irrelevant variations in program code, and relatable to the knowledge components of the target skill (programming), so as to support hint generation.
% our approach: patterns + rules
We describe features with \emph{patterns} that encode relations between variables in a program’s abstract syntax tree (AST). Patterns describe paths between certain “interesting” leaf nodes. By omitting some nodes on these paths, patterns match different programs containing the same relation. We then induce rules to predict program correctness based on AST patterns, allowing us to generate hints based on missing or incorrect patterns.
% contributions
The main contributions presented in this paper are: AST patterns as features for machine-learning, a rule-based model for predicting program correctness, and hints generated from incorrect or missing patterns in student programs.
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