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You need to use both big-picture, or focused mode and detail-oriented, or diffuse thinking to get good at math and science.
Focused thinking needs meaningful stretches of undisturbed time to focus and think.
Diffuse thinking occurs subconsciously by temporarily loosening attention.
Actively build time into each day to alternate between both modes.
One of the first steps towards gaining expertise in math and science is to create conceptual chunks.
Once you chunk an idea or concept, you don’t need to remember all the little underlying details; you’ve got the main idea - the chunk - and that’s enough.
Basic steps to forming a chunk:
Unfortunately, many of us find it too easy to procrastinate even starting our math homework because we see it as boring and difficult. This thinking comes from focusing on the idea that we only want to finish our work.
If we instead look at our goal as “For the next 15 minutes I’ll work on this math assignment,” it becomes a lot easier to just begin. When we center our mind on only the process of learning, it’s easier to just go with the flow and relax.
Interleaving means practicing by doing a mixture of different kinds of problems requiring different strategies.
Overlearning means continuing to study or practice a problem immediately after some criterion has been achieved. For example, correctly solving a certain type of math problem and then immediately solving several more problems of the same kind.
Overlearning provides diminishing returns.
Learning to use your memory in a more disciplined yet creative manner helps you learn to focus your attention.
There is a direct connection between your hand and your brain. The act of organizing and re-writing your notes is essential to breaking down large amounts of information into smaller digestible chunks.
Writing and saying what you are trying to learn seems to enhance retention.
The Einteilung Effect: An idea you already have in min, or your simple initial thought, prevents a better idea of solution from being found.”
Articulating your question is 80 percent of the battle. By the time you’ve figured out what’s confusing, you’re likely to have answered the question yourself!
Learning is often paradoxical. The very thing we need in order to learn impedes our ability to learn. We need to focus intently to be able to solve problems – yet that focus can also block us from accessing the fresh approach we may need. Success is important, but critically, so if failure. Persistence is key – but misplaced persistence causes needless frustration.
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