  In education applications, knowledge tracing refers to the problem of
estimating students' time-varying concept/skill mastery level from their past
responses to questions and predicting their future performance. One key
limitation of most existing knowledge tracing methods is that they treat
student responses to questions as binary-valued, i.e., whether they are correct
or incorrect. Response correctness analysis/prediction ignores important
information on student knowledge contained in the exact content of the
responses, especially for open-ended questions. In this paper, we conduct the
first exploration into open-ended knowledge tracing (OKT) by studying the new
task of predicting students' exact open-ended responses to questions. Our work
is grounded in the domain of computer science education with programming
questions. We develop an initial solution to the OKT problem, a student
knowledge-guided code generation approach, that combines program synthesis
methods using language models with student knowledge tracing methods. We also
conduct a series of quantitative and qualitative experiments on a real-world
student code dataset to validate OKT and demonstrate its promise in educational
applications.
