Explication and reflection on expert vs. novice considerations within the problem-solving process characterize a cognitive apprenticeship approach for the development of expert-like problem solving practices. In the context of grading, a cognitive apprenticeship approach requires that instructors place the burden of proof on students, namely, that they require explanations of reasoning and explication of problem-solving processes. However, prior research on instructors' considerations when grading revealed their reluctance to use such a grading approach, motivated by a perception of teaching that places the burden of proof on the instructor. This study focuses on physics graduate teaching assistants (TAs) who play a central role in grading. A short professional development activity was designed that involved eliciting TAs' perceptions regarding grading, presenting a cognitive apprenticeship-inspired grading rubric, followed by a discussion of the dilemma between placing the burden of proof on the instructor vs. the student. In this context, we examined TAs' grading considerations and approaches towards grading and the effect of the short professional development grading activity on them.