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September 15 - October 4, 2020
As it turns out, one of the first steps toward gaining expertise in math and science is to create conceptual chunks—mental leaps that unite separate bits of information through meaning.
The first step in chunking, then, is to simply focus your attention on the information you want to chunk.
The second step in chunking is to understand the basic idea you are trying to chunk,
just understanding how a problem was solved does not necessarily create a chunk that you can easily call to mind later.
The third step to chunking is gaining context so you see not just how, but also when to use this chunk.
Solving a lot of math problems provides an opportunity to learn why the procedure works the way it does or why it works at all.
There is a bottom-up chunking process where practice and repetition can help you both build and strengthen each chunk, so you can easily gain access to it when needed. And there is a top-down “big picture” process that allows you to see where what you are learning fits in.9 Both processes are vital in gaining mastery over the material. Context is where bottom-up and top-down learning meet. To clarify here—chunking may involve your learning how to use a certain problem-solving technique. Context means learning when to use that technique instead of some other technique.
Attempting to recall the material you are trying to learn—retrieval practice—is far more effective than simply rereading the material.
“Intention to learn is helpful only if it leads to the use of good learning strategies.”
Using recall—mental retrieval of the key ideas—rather than passive rereading will make your study time more focused and effective.
Along these same lines, always work through homework problems in math and science on your own.
This will help ensure that the material is more deeply rooted in your mind and make it much more accessible when you really need it.
you rewrite your notes during the evening after a lecture.
solidify newly forming chunks and reveals the holes in your understanding that professors just love to target on tests.
students often erroneously believe that they are learning by simply rereading material that is on the page in front of them.
You must have information persisting in your memory if you are to master the material well enough to do well on tests and think creatively with it.
Bill Gates and other industry leaders, Johnson notes, set aside extended, weeklong reading periods so that they can hold many and varied ideas in mind during one time.
The bigger your chunked mental library, the more easily you will be able to solve problems.
This is where the Law of Serendipity comes to play: Lady Luck favors the one who tries.23
Solving problems in math and science is like playing a piece on the piano. The more you practice, the firmer, darker, and stronger your mental patterns become.
But you can’t learn mathematics or science without also including a healthy dose of practice and repetition to help you build the chunks that will underpin your expertise.
But if you try to build connections between chunks before the basic chunks are embedded in the brain, it doesn’t work as well. It’s like trying to learn advanced strategy in chess before you even understand the basic concepts of how the pieces move.
recalling material when you are outside your usual place of study helps you strengthen your grasp of the material by viewing it from a different perspective.
But, here’s the real beauty of internalizing problem solutions in math and science. The more you do it, the easier it becomes, and the more useful it is.
Interleaving means practice by doing a mixture of different kinds of problems requiring different strategies.
mastering a new subject means learning to select and use the proper technique for a problem.
You want your brain to become used to the idea that just knowing how to use a particular problem-solving technique isn’t enough—you also need to know when to use it.
Rather than devote a long session to the study or practice of the same skill or concept so that overlearning occurs, students should divide their effort across several shorter sessions.
It’s best to write the initial solution, or diagram, or concept, out by hand. There’s evidence that writing by hand helps get the ideas into mind more easily than if you type the answer.
Interleaving your studies—making a point to review for a test, for example, by skipping around through problems in the different chapters and materials—can sometimes seem to make your learning more difficult. But in reality, it helps you learn more deeply.
Read (but don’t yet solve) assigned homework and practice exams/quizzes.
Review lecture notes
Rework example problems presented in lecture notes.
Work assigned homework and practice exam/quiz questions.
you can’t compete in math and science if you just cram at the last minute.
We procrastinate about things that make us feel uncomfortable.
Procrastination is a single, monumentally important “keystone” bad habit.
It’s easy to feel distaste for something you’re not good at. But the better you get at something, the more you’ll find you enjoy it.
Habit, after all, is simply when our brain launches into a preprogrammed “zombie” mode.
Habit is an energy saver for us. It allows us to free our mind for other types of activities.
Finding ways to reward good study habits in math and science is vital to escaping procrastination.
As procrastination expert Piers Steel, author of The Procrastination Equation, points out, “If you protect your routine, eventually it will protect you.”3
Remember, habits are powerful because they create neurological cravings.
Also remember that the better you get at something, the more enjoyable it can become.
believe that sometimes all it takes is one bad day to spark an important realization. After that, keeping your focus to find the way out of your current situation is much easier.”
Learn to focus on process, not product. Process means the flow of time and the habits and actions associated with that flow of time—as in, “I’m going to spend twenty minutes working.” Product is an outcome—for example, a homework assignment that you need to finish.
To prevent procrastination, you want to avoid concentrating on product. Instead, your attention should be on building processes—habits—that coincidentally allow you to do the unpleasant tasks that need to be done.
If you learn under mild stress, you can handle greater stress much more easily.
By focusing on process rather than product, you allow yourself to back away from judging yourself (Am I getting closer to finishing?) and allow yourself to relax into the flow of the work.
Multitasking is like constantly pulling up a plant. This kind of constant shifting of your attention means that new ideas and concepts have no chance to take root and flourish.
