I have always been very interested in why i believe the things i believe. As a younger man, words like "bildung" existed in many of my paper titles. That spirit is still there, though today i am more likely to call it a 'ratioanal reconstruction'.
I do not know if there is a standard definition of 'rational reconstruction' or no. In philosophy of science we often use the term to distinguish what we are doing from the history of science. I do not know of a precise differentiation, both fields work with a lot of the same material, but i think history is more concerned with what can be confirmed to have happend and what can be deduced from that, and what people said about that ... where-as rational reconstruction is more concerned with approximating the period's body of knowledge and assumptions and its epistemological considerations.
'Bildung', for me, has always been something of a merger between the two ... necessarily, i think, due to the closeness of the subject material (i.e. me).
At its best, the rational reconstruction of my thoughts is an honest accessment of them, a real wanting to know how i moved from point A to point B ... more than just what i was moving toward, and thinking about, and acting against at any given point in time, but also a reflection of my metaphysical and epistemological committments (and changes there-in).
There is another word, rationalization, which is obviously etymologically related. One has to be careful with this word, however, as it is a loaded word ... as it is a negative psychological technical term ... one must be careful that one is using it properly. I think there is a good deal of rationalization in philosophy, that is, the search for (often bad) reasons to believe what we already believe. Given the negative connotations of the word i generally restrict the usage of it to cases of 'defense mechanism' speech. Those people who are not afraid to throw their opinion out there into the world, they often need to defend the opinion against attack. They rationalize it against the attack.
However, to the extent that one is a teacher, there comes a time when one needs to explain what one believes and why one believes it ... a descriptivist task. Often what the student wants to see is a rational reconstruction, not an actual history. They want to know why "someone" might want to believe this thing. When the teaching response is an open and detailed look into this why ... not an attempt to convert or to show the view is right ... but an true assesment of the assumptions and deductions and in some cases real world hostory of what goes into the idea or belief, there we have a rational reconstruction, and, i think, a very different thing from a rationalization.
Often, as in the case of a Bildung piece, one is trying to teach oneself. Some think such an attempt is really just fooling yourself, that you can only, effectively at least, rationalize. I happen to be amongst those that grant the self a lot more power of introspection. It takes time to learn how, and a lot of cases studies of others, and certainly will never be as thorough, or at least not the same kind of project, into which a well trained depth psychologist might endevour ... but it can certainly be very useful to oneself.
In this way: take an axiom or deduction one holds ... write 3 papers attacking it using at least two thought processes from other times and cultures. Really get into understanding the alternate thinking processes of those who oppose your axiom, understand why opposing it is important to them (honestly so) and what parallels you have in your life that could make it important to you. Then re-access the assumptions you hold that you think outweigh these other concerns.
That is 'Bildung' for me today. (No real papers, actually, moreso a set of bullet comments.) The proper use of Bildung, in this sense, arrives at an (more) honest rational reconstruction of belief, and less of a rationalization. This is not a movement from the latter to the former ... from one category to another, but more of a movement along a pole.
It might be being honest with oneself about oneself, and sometimes even about others.