Mindfulness of Process is one of the key tenets of design thinking at the d.school. In essence, it is a call to find ways to be thoughtful not only of the work that you do, but of how you do that work, and of how you will improve on your methods in the future.
Being "Mindful of Process" makes you keenly aware of what stage of the design process you are engaged in and what behaviors and goals you may have at any given moment (i.e. when you need to be highly generative vs. when you need to converge on a single path). This conciseness can help you guide yourself and your team into interesting areas and can alleviate some of the anxiety that comes with an open and freewheeling process such as ours. In addition, articulating a process allows you to iterate not just on "what you are working on" but on "how you are working on" it.
At it's core, process is one of the main constructs the d.school uses to impart design thinking, everything we do touches on it. Here are some specific exercises that might help students become more "Mindful of Process"
Articulating Your Own Process, Mapping Methods to Process, Reflection Methods