What does it look like to “solve” unsolvable problems?

One key component of change leadership is a deep dissatisfaction with the status quo. Knowing that your school must change is the first step. But how do you solve the problems of your current reality in order to push toward your vision? New problems are sure to arise as you change. How will you solve those?
Barry Johnson, author of Polarity Management: Identifying and Managing Unsolvable Problems offers this essential advice: The key to effective leadership is recognizing that some problems do not have “solutions,” per se. He suggests that some problems cannot be solved by selecting one best solution, but rather must be “managed” by negotiating a balance between two competing but equally valuable ideas. The chart below helps demonstrate the difference between solvable and unsolvable problems.

Problems with Solutions	Unsolvable Problems
Should we start the school day at 8:00 or 8:30? Should students with poor grades be eligible for extracurricular activities? How often should teachers update their grade books?	Should we focus on basic skills or big ideas? Should students read “just right” texts or complex texts? Should we enforce consistent routines across classrooms or allow teacher autonomy?

Problems with solutions require “either/or” thinking — there are two or more options and we can only choose one solution. We can’t both start the day at 8:00 and 8:30, we have to choose either 8:00 or 8:30. Unsolvable problems, though, present two competing but equally compelling and valuable ideas that actually require “both/and” thinking. Kids need to read books that are “just right” for their reading level, AND they need to work with complex texts. The “solution” is BOTH, not one or the other. And in fact, the seemingly opposite poles actually reinforce and need each other in order to be successful.
Johnson calls these unsolvable problems “polarities” and suggests that leaders learn to balance the two ends of the pole so that the organization or school experiences the benefits of both and the drawbacks of neither.

For instance, after weeks of PD on using complex texts, you may notice that teachers in your school have started to neglect students’ need to read books at their individual reading level and have stopped encouraging or making time for this important practice. A good leader would recognize that poles were out of balance and would manipulate structures to push the balance the other way. Perhaps focus PD or coaching on “just right” books, or set aside time for grade level teams to collaborate and plan for “just right” reading time. The key is not to choose to focus on one, but to figure out how to do both at once.
Robert Jacobs, a colleague of Barry Johnson at Polarity Partnerships, suggests that polarities like these actually energize an organization and lead to innovation and productivity. Rather than seeing these polarities as problems at all, leaders should approach them with gusto, asking him or herself how s/he can engage other leaders and staff members in maintaining the benefits of the “both/and” mindset. Check out an article with more detail here and a larger summary here.
Which problems in your school are not really problems? Which challenges have you been applying “either/or” thinking to when you should have been applying “both/and” thinking?