Focused mode of thinking is when you concentrate intently on something, like solving a math problem. While, diffused mode of thinking is a more relaxed kind of thinking. It is when you zoom out of the problem and see new connections, new patterns, and the bigger perspective. At any given point in time, you are either in focused mode of thinking or the diffused mode. It seems you can't be in both thinking modes at the same time.
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Learning How to Learn: Powerful mental tools to help you master tough subjects is an interesting course offered on Coursera. The instructors, Barb Oakley and Terry Sejnowski have put together a series of videos and reading material that are concise yet full of information. There are interview videos with experts with multiple backgrounds that are insightful. Here are some of my take aways from the course.
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