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.

Interleaving versus overlearning

<ul><li>Focused mode is used to concentrate on something that’s already tightly connected in your mind because you are familiar and comfortable with the underlying concepts.</li><li>The diffuse approach involves a big-picture perspective. Useful when you are learning and understanding something new. As long as we are consciously focusing on a problem, we are blocking the diffuse mode. Do something else until your brain is consciously free of any thought of the problem.</li></ul>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 and diffused thinking

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:<ol><li>Focus your attention on the information you want to chunk. No television on in the background, don’t look at your phone, etc.</li><li>Understand the basic idea you are trying to chunk.</li><li>Gaining context so you see not just how, but also when to use this chunk.</li></ol>

Conceptual chunks

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.

Writing to improve your memory

Learning to use your memory in a more disciplined yet creative manner helps you learn to focus your attention.<ul><li>One of the best things you can do to remember and understand concepts in math and science is to create a metaphor or analogy for them.</li><li>Use spaced repetition to help lodge ideas in memory.</li><li>Create meaningful groups that simplify the material you are trying to remember.</li><li>If you are memorizing something commonly used, search online to see if someone has already come up with a particularly memorable memory trick.</li><li>Beware of mistaking a memory trick for actual knowledge.</li></ul>

Enhancing your memory

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.

Focus on process instead of product

Focused thinking needs meaningful stretches of undisturbed time to focus and think.<ul><li>Prioritize making distraction-free time and space to think deeply</li><li>(SQ3R: Survey, Question, Read, Recall, Review)</li><li>Practice purposefully (Work the hardest bits, generalize through variation)</li><li>Think on paper, there’s magic between the hand and the brain</li></ul>Diffuse thinking occurs subconsciously by temporarily loosening attention.<ul><li>Relax/disengage attention: Sleep, walk, drive, blink, exercise</li><li>Recall and test frequently (e.g., spaced repetition techniques).</li></ul>Actively build time into each day to alternate between both modes.

Create the best conditions for focused and diffuse thinking

The Einteilung Effect: An idea you already have in min, or your simple initial thought, prevents a better idea of solution from being found.”

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.

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!

How to become a quick learner and  use it to your advantage

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An engineering professor who started out doing poorly in mathematical and technical subjects in school offers tools, tips and techniques to learning the creative and analytical thought processes that will lead to achievement in math and science. Original.

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The companion book to COURSERA®'s wildly popular massive open online course "Learning How to Learn" Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a new skill set, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating material. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.   In A Mind for Numbers, Dr. Oakley lets us in on the secrets to learning effectively—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. The learning strategies in this book apply not only to math and science, but to any subject in which we struggle. We all have what it takes to excel in areas that don't seem to come naturally to us at first, and learning them does not have to be as painful as we might think.

Barbara A. Oakley is an accomplished writer whose work has resonated with readers around the world. Barbara A. Oakley has published several books that explore a range of topics, from fiction to nonfiction, and has received critical acclaim for the ability to weave compelling narratives. Barbara A. Oakley's writing style is known for its depth and authenticity, and has earned quite a loyal following of readers.

Focused thinking and diffused thinking

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Focused & Diffuse Modes - two modes of thinking