  Knowledge Tracing (KT), which aims to model student knowledge level and
predict their performance, is one of the most important applications of user
modeling. Modern KT approaches model and maintain an up-to-date state of
student knowledge over a set of course concepts according to students'
historical performance in attempting the problems. However, KT approaches were
designed to model knowledge by observing relatively small problem-solving steps
in Intelligent Tutoring Systems. While these approaches were applied
successfully to model student knowledge by observing student solutions for
simple problems, they do not perform well for modeling complex problem solving
in students.M ost importantly, current models assume that all problem attempts
are equally valuable in quantifying current student knowledge.However, for
complex problems that involve many concepts at the same time, this assumption
is deficient. In this paper, we argue that not all attempts are equivalently
important in discovering students' knowledge state, and some attempts can be
summarized together to better represent student performance. We propose a novel
student knowledge tracing approach, Granular RAnk based TEnsor factorization
(GRATE), that dynamically selects student attempts that can be aggregated while
predicting students' performance in problems and discovering the concepts
presented in them. Our experiments on three real-world datasets demonstrate the
improved performance of GRATE, compared to the state-of-the-art baselines, in
the task of student performance prediction. Our further analysis shows that
attempt aggregation eliminates the unnecessary fluctuations from students'
discovered knowledge states and helps in discovering complex latent concepts in
the problems.
