The reality of unconscious mental processing leading sometimes to the Aha! moment is increasingly recognized by the scientific community. Research attention is shifting to conducting experiments with an aim to understand more about this effect. A study just published in Thinking & Reasoning (2017) is called “Insightful solutions are correct more often than analytic solutions”. The authors (Salvi, Kounios, Beeman, Bowden, and Bricolo) conducted a variety of puzzles comparing insightful solutions to analytically determined answers. They were able to show that those answers coming into consciousness from unconscious processing were more likely to be correct than answers constructed through conscious reasoning. A timed deadline was imposed on each puzzle which created anxiety among test subjects. A majority of answers tossed out just before the imposed deadline appeared to be either a guess or analytically derived and often wrong. The authors conclude that encouraging insightful solutions to learning and problem solving requires a relaxed atmosphere where the factor of time is not present. The need for incubation time is mentioned in my book on page 56 where an argument is made that formal education is too often run by the clock thus imposing a deadline on thought. As this research report indicates, deadlines short circuit the use of intuitive processes hence sometimes leading to wrong solutions.
Tacit knowledge is all about generating the “AHa” effect which embeds understanding into a more intuitive form of cognition than analytically encoded symbolic notation. I am always happy to see someone working hard to accomplish that as Kalid Azad does in his mathematics teaching blog. He complains (correctly) that most explanations for difficult ideas are offered in a logic based format (seems the best way by experts) rather than through a holistic approach. I recall as a former professor of physics the standard approach to teaching a topic in physics was to begin with an equation and show how that equation is derived. Students typically find the derivation quite baffling and may desperately memorize the steps. An alternative is to offer some exposure to examples of how the physical system behaves. Throw in a few problems, and then later work through the derivation when the learner has some grasp of what the topic is all about. Watch how Azad explains topics in mathematics to see an example of how this is done. He points out how a particular explanation may not work for you when a different one does so you might need to cast around looking for just the right kind of explanation to suit your own prior understandings. Kalid has several excellent books on Amazon to help anyone learning math develop an intuitive sense of what it all really means. Check out the calculus book here. His books make an excellent present for grandkids taking STEM in high school and college. The students themselves are not likely to realize they need his books but a parent and grandparent could help them get ahead by making sure the kids have these books to get them ahead in their education.