Page 110 - A Mind For Numbers: How to Excel at Math and Science

5. Do another repetition. As soon as you can the next day, work the problem again. You
should see that you are able to solve the problem more quickly now. Your
understanding should be deeper. You may even wonder why you ever had any trouble
with it. At this point, you can start lightening up on computing each step. Keep your
focus on the parts of the problem that are the most difficult for you. This continued
focus on the hard stuff is called “deliberate practice.” Although it can sometimes be
tiring, it is one of the most important aspects of productive studying. An alternative or
supplement at this point is to see whether you can do a similar problem with ease.)
6. Add a new problem. Pick another key problem and begin working on it in the same
way that you did the first problem. The solution to this problem will become the second
chunk in your chunked library. Repeat steps one through five on this new problem.
And after you become comfortable with that problem, move on to another. You will be
surprised how even just a few solid chunks in your library can greatly enhance your
mastery of the material and your ability to solve new problems efficiently.
7. Do “active” repetitions. Mentally review key problem steps in your mind while doing
something active, such as walking to the library or exercising. You can also use spare
minutes to review as you are waiting for a bus, sitting in the passenger seat of a car,
or twiddling your thumbs until a professor arrives in the classroom. This type of active
rehearsal helps strengthen your ability to recall key ideas when you are solving
homework problems or taking a test.

That’s it. Those are the key steps to building a chunked library. What you are
doing is building and strengthening an increasingly interconnected web of
4
neurons—enriching and strengthening your chunks. This makes use of what is
known as the generation effect. Generating (that is, recalling) the material
helps you learn it much more effectively than simply rereading it.
This is useful information, but I can already hear what you’re thinking: “I’m

spending hours every week just solving all my assigned problems once. How am
I supposed to do it four times for one problem?”
In response, I would ask you: What is your real goal? To turn in homework?
Or to perform well on the tests that demonstrate mastery of the material and
form the basis for most of your course grade? Remember, just solving a problem
with the book open in front of you doesn’t guarantee you could solve something
like it again on a test, and, more important, it doesn’t mean that you truly

understand the material.
If you are pressed for time, use this technique on a few key problems as a
form of deliberate practice to speed and strengthen your learning and to help
you speed your problem-solving skills.