A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)

by Barbara Oakley

top-down “big picture” process that allows you to see where what you are learning fits in.

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.”

Words or notes in a margin that synthesize key concepts are a good idea.

Using recall—mental retrieval of the key ideas—rather than passive rereading will make your study time more focused and effective.

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.

Just focus on whatever section you are studying. You’ll find that once you put the first problem or concept in your library, whatever it is, then the second concept will go in a bit more easily. And the third more easily still.

Most difficult problems are solved through intuition, because they make a leap away from what you are familiar with.

If you don’t understand a method presented in a course you are taking, stop and work backward. Go to the Internet and discover who first figured out the method or some of the earliest people to use it. Try to understand how the creative inventor arrived at the idea and why the idea is used—you can often find a simple explanation that gives a basic sense of why a method is being taught and why you would want to use it.

The more you practice, the firmer, darker, and stronger your mental patterns become.

strengthening an initial learning pattern within a day after you first begin forming it is important.

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.

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.

If you don’t practice with your growing chunks, it is harder to put together the big picture—the pieces are simply too faint.

Interleaving means practice by doing a mixture of different kinds of problems requiring different strategies.

The reality is, 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.

Consider creating index cards with the problem question on one side, and the question and solution steps on the other.

When you first review the cards, you can sit at a desk or table and see how much of the solution you can write on a blank sheet of paper without peeking at the back of the card. Later, when mastery is more certain, you can review your cards anywhere, even while out for a walk.

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.

Long sessions are fine as long as students don’t devote too much time to any one skill or concept.

Once they understand ‘X,’ they should move on to something else and return ...

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.

Students need to think of every homework problem in terms of test preparation and not as part of a task they are trying to complete.”

Practice helps build strong neural patterns—that

gives you the mental fluidity and agility

Chunks are best built with: Focused attention. Understanding of the basic idea. Practice to help ...

trying to remember the key points without looking at the page—is one of the best ways to...

We procrastinate about things that make us feel uncomfortable.

Procrastination is a single, monumentally important “keystone” bad habit.

the better you get at something, the more you’ll find you enjoy it.

Procrastination can be like taking tiny amounts of poison. It may not seem harmful at the time. But the long-term effects can be very damaging.

Habit is an energy saver for us. It allows us to free our mind for other types of activities.

The only place you need to apply willpower is to change your reaction to the cue.

The key to rewiring is to have a plan. Developing a new ritual can be helpful.

The Pomodoro technique—the twenty-five-minute timer—can be especially helpful in shifting your reaction to cues.

it helps to have something in your stomach when starting particularly difficult tasks.

Belief that your new system works is what can get you through.

Part of what can underpin your belief is to develop a new community.

mental contrasting.

you think about where you are now and contrast it with what you want to achieve.

You can change your reality.

Get into the Flow by Focusing on Process, Not Product

Learn to focus on process, not product.

The product is what triggers the pain that causes you to procrastinate.

Focus on doing a Pomodoro—a twenty-five-minute timed work session—not on completing a task.

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.

A little bit of work on something that feels painful can ultimately be very beneficial.