To reflect means to consider what was done or what you are doing, but typically the former. To be reflexive means to be vigilant in maintaining awareness about your privilege, which these two ignore.
Being a reflexive teacher, means that you may examine your assumptions and attitude toward your teaching methods! I think of Lisa Delpit and her writing on "child-deficit" assumptions.
Go back to the roots reflect and reflex. REFLECT is to be aware, to cognitively comb over, be aware, evaluate, compare, etc... REFLEX is automated, an impulsive response, without the ability to mull over options. So if I ask you "What is 2+2?" Reflex is in order. ... and if I ask you what is 383+474?, you need to be reflective, and reflex is possible only for the highly gifted. He is carving out a whole new semantic space regarding REFLEX, and it is not convincing. ... I suggest, create a word, or pick something that works better.
