Someone moves into a flat with a small kitchen. They do not write a specification. They put the kettle where it seems sensible, cook for a week, and notice they keep walking round the table to reach the bin. The bin moves. A month later the kitchen works, and nobody could have designed it on paper on the first day.
That is design thinking at domestic scale. Schön described designers holding a conversation with the materials of a situation. You make a move, the situation talks back, and the back-talk tells you what the problem was. Lawson’s studies found that designers learn about a problem mainly by proposing solutions to it, where scientists tend to analyse first.
Rittel and Webber called the problems of planning wicked. They have no definitive formulation, no stopping rule, and every attempt to solve one changes it. Most of the problems a school faces are wicked in exactly that sense. That is the case for a way of thinking built for them.