Tuesday, October 28, 2014

The Fundamental Nature of Problem Solving

Wisdom Seeker from halfsatori.com
One morning, exactly at sunrise, a Buddhist monk began to climb a tall mountain. The narrow path, no more than a foot or two wide, spiraled around the mountain to a glittering temple at the summit. - The monk ascended the path at varying rates of speed, stopping many times along the way to rest and to eat the dried fruit he carried with him. He reached the temple shortly before sunset. After several days of fasting and meditation, he began his journey back along the same path, starting at sunrise and again walking at variable speeds with many pauses along the way. His average speed descending was, of course, greater than his average climbing speed.  (Source; Scientific American Magazine - June 1961)

One of the exercises we do in the Design Thinking workshops is a story problem which involves a monk who takes a journey up and down a mountain. The problem is to prove that there is one point on the mountain which the monk passes at the same time of day during the ascending and descending trips. For most people, solving the problem is very difficult because they don't choose to reframe the problem visually. They apply the tools of logic which they have been taught in school and attempt to deduce an answer numerically, based on time and distance traveled.

There is a "mathematical" method to solve the problem, using a graph, which Nathaniel Highstein illustrated on his Reflections on Teaching blog. He states:

"I love this problem because the answer becomes totally clear when you make a time vs. elevation graph – and the answer violates nearly everyone’s expectations and leads to a surprise!"
Time-Position Graph

I love this problem because solving it requires reframing; Making a word problem into a picture problem. This illustrates how different thinking styles are applicable to different types of problems. Another way to solve it is to break a conceptual block and imagine the monk doing the journeys up and down simultaneously. They will meet themselves somewhere on the mountain.

Murai Hodaka meets herself.
In many cases a "problem" exists precisely because there are ambiguities and unknowns. Much of what we are taught about problem solving relates to "finding the unknown" or "solving for x". The real challenges start when the equations are non-linear, the answers are imaginary numbers or there a many inter-related variables. In other words; when the behavior of the system is un-predictable.

There is another aspect to this problem solving thing. It is a skill, which can be learned and therefore taught. Much of teaching these days is concerned with finding effective ways to teach problem solving skills - so that students can discover the answers for themselves.  The body of material on this is huge and growing daily. What is even more interesting are the parallels between the methods of Design Thinking and Problem Based Learning. This discovery is partially what led me to begin to think of Design Thinking as a method of learning rather than a method of problem solving. If you already knew everything you needed to know to solve the problem, it wouldn't be a problem, would it?

It's also why Design Thinking involves brilliant detective work and a lot of background knowledge.

The game's afoot!
(From Dee Garretson's Historical Mysteries and Romantic Suspense blog)

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