The first intelligent tutoring systems for computer programming have been proposed more than 30 years ago, mostly focusing on well defined programming tasks e.g. in the context of logic programming. Recent systems also teach complex programs, where explicit modelling of every possible program and mistake is no longer possible. Such systems are based on data-driven approaches, which focus on the syntax of a program or consider the output for example cases. However, the system's understanding of student programs could be enriched by a deeper focus on the actual execution of a program. This requires a suitable data representation which encodes information of programming style as well as its functionality in a suitable way, thus offering entry points for automated feedback generation. In this contribution we propose a representation of computer programs via execution traces for example input and demonstrate the power of this representation in three key challenges for intelligent tutoring systems: identifying the underlying solution strategy, identifying erroneous solutions and locating the errors in erroneous programs for feedback display. [For the full proceedings, see ED592609.]