Teaching like. . .a colony of ants?

I've been reading Melanie Mitchell's book about systems theory, Complexity, in which she describes how complexity arises in various systems out of the interactions of many individually simple elements.  For example, individually not-very-intelligent ants are able as a colony to very effectively find food and bring it back to the nest.  Mitchell describes the process, evolved over eons, that makes this group intelligence possible:

[W]e saw. . .the way ant colonies forage for food: the shortest trails leading to the best food sources attain the strongest pheromone scent, and increasing numbers of ants follow these trails.  However, at any given time, some ants are still following weaker, less plausible trails, and some ants are still foraging randomly, allowing for the possibility of new food sources to be found.

This is an example of needing to keep a balance between exploration and exploitation [of information gleaned].  When promising possibilities are identified, they should be exploited at a rate and intensity related to their estimated promise, which is being continually updated.  But at all times exploration for new possibilities should continue. . . .

My teaching is guided by a similar process of exploration balanced with exploitation.
Through experience I have come to know what stimuli will generally invoke a particular type of vocal response in a student.  But often, people don't respond the way one expects them to.  In these cases, I have to be flexible enough to try something different; one of the "less plausible trails" may lead to what I am trying to achieve.  Occasionally, even, when nothing logical seems to be working, a random change can shift things towards success.  I'll change some aspect of how we've been working—the vowel, the volume, the pitch range, for example—as see what effect that has on the singer's output.  (This may happen accidentally when a student misunderstands my instructions and sings something different than I had intended.  Sometimes, the "mistake" produces better results than what I had anticipated!)  If this change produces an improvement, I add it to my tool-box of promising possibilities.  If it doesn't produce an improvement, I simply try something else.

Earlier this week, I was working with a tenor on his high range, where he is learning to coordinate his falsetto with a very free chest participation, resulting in easy, stable high notes.  During this particular lesson, however, I noticed a breathy quality to the high notes, indicating a less-than-optimal chest register participation.  Since chest register produces clarity in the sound, I suggested to the student that he aim for a clearer tone quality.  Surprisingly, this suggestion brought an even more unfocused quality to his sound.  I moved on to a slightly "less plausible trail," and requested a louder volume, which generally brings in more chest register.  Still breathy.  Hmmm.  Momentarily stymied, I foraged in a random direction:  "Sing the next exercise in the opposite of a clear quality."  Bizarrely, that seemingly nonsensical instruction, the exact meaning of which neither of us was sure, resulted in an ideal register balance—and a free, clear tone.

I'll have to drag that morsel back to the nest and share it with the colony.