Can experiential education teach wisdom?

Real world experience teaches two things (at least)--how to do something and, over time, how to make sense of that thing in the world.  The "how to make sense" part, in morally complex settings, becomes wisdom.

So, for example, when a first child is born, her parents learn how to parent--how to feed and clothe and comfort and educate their daughter.  But they also learn harder things--how to discipline, how to choose between competing needs, how to suffer because of and with the child, how to find joy.

Or, as Confucius purportedly put it: By three methods we may learn wisdom: First, by reflection, which is noblest; Second, by imitation, which is easiest; and third by experience, which is the bitterest.

Experiential education (as separate from experience) focuses overwhelmingly on how to do things.  So, for example, if you want students to learn how to run a genetics experiment, then have them run an experiment.  They will make mistakes (because doing something is riskier than learning about something) and those mistakes, together with a smidgen of success and guidance from the teacher, will become understanding of how to do something.

But does learning in this way also make students wise?  I have been around variations of experiential education for most of my career, but I cannot think of a time when I, or anyone else, focused explicitly on wisdom as a result of our service-learning, or undergraduate research, or simulation, or group project (or whatever the experiential education happens to be.)

Occasionally wisdom shows through in student reflections, but it almost always has to sneak through whatever the assigned reflection is.  And increasingly, it seems, reflection focuses more on content acquisition than about the student becoming better acquainted with how she wants to be in the world.
Consider the typical reflection prompt: "What did doing X teach you about [the topic of the class]?  Or even the widely used ABC model of reflection; "How did doing X affect you? How did it influence your behavior?  how did it change your cognition?

I don't have good ideas about learning wisdom through education, let alone experiential education.  Outside of schools, wisdom comes from religious practice, or from failure, or from age.  Does it come from anywhere inside of schools?