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\section{Method}
-This section explains the three main components of our approach: extracting patterns from student submissions, learning classification rules for correct and incorrect programs, and using those rules to generate hints.
+This section explains the three main components of our approach: automatically extracting patterns from student submissions, learning classification rules for correct and incorrect programs, and using those rules to generate hints.
\subsection{Extracting patterns}
\label{sec:extracting-patterns}
@@ -18,7 +18,7 @@ we select the following pairs of nodes: \{\code{A},\,\code{A\textsf{'}}\}, \{\co
For each selected pair of leaf nodes $(a,b)$ we build a pattern by walking the AST in depth-first order, and recording nodes that lie on the paths to $a$ and $b$. We omit \textsf{and} nodes, as explained in the previous section. We also include certain nodes that do not lie on a path to any selected leaf. Specifically, we include the functor or operator of all \textsf{compound}, \textsf{binop} or \textsf{unop} nodes containing $a$ or $b$.
-Patterns constructed in this way form the set of features for rule learning. To keep this set at a reasonable size, we only use patterns that have appeared in programs submitted by at least five students.
+Patterns constructed in this way form the set of features for rule learning. To keep this set at a reasonable size, we only use patterns that have appeared in programs submitted at least five times.
\subsection{Learning rules}