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

by Barbara Oakley

In other words, you may have a tool in your strategy or problem-solving toolbox, but if you don’t know when to use that tool, it’s not going to do you a lot of good.

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

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smoothly making new connections. Now you understand why it is key that you are the one doing the problem solving, not whoever wrote the solution manual.

If you work a problem by just looking at the solution, and then tell yourself, “Oh yeah, I see why they did that,” then the solution is not really yours—you’ve done almost nothing to knit the concepts into your underlying neurocircuitry. Merely glancing at the solution to a problem and thinking you truly know it yourself is one of the most common illusions of competence in learning.

SUMMING IT UP Practice helps build strong neural patterns—that is, conceptual chunks of understanding. Practice gives you the mental fluidity and agility you need for tests. Chunks are best built with: Focused attention. Understanding of the basic idea. Practice to help you gain big-picture context. Simple recall—trying to remember the key points without looking at the page—is one of the best ways to help the chunking process along.

Paul’s Techniques for Limited Study Time 1. Read (but don’t yet solve) assigned homework and practice exams/quizzes. With this initial step I prime my mental pump for learning new concepts—new chunks. 2. Review lecture notes (attend every lecture as much as possible). One hour of lecture is worth two hours reading the book. I learn far more efficiently if I am faithful in attending lectures and taking detailed notes—not just staring at my watch and waiting for it to be over. I review my notes the following day while the subjects are still fresh in my mind. I’ve also found that thirty minutes with a professor asking questions is easily worth three hours reading the book. 3. Rework example problems presented in lecture notes. It never helped me to practice problems given by either the instructor or the textbook that didn’t have solutions to provide feedback. With the example problems I already had a step-by-step solution available if necessary. Reworking helps solidify chunks. I use different-colored pens when I study: blue, green, red—not just black. I found that it helps me focus on reading my notes better; things pop out more, instead of blending together into a confusing collage of inexplicable mathematical chaos on the page. 4. Work assigned homework and practice exam/quiz questions. This builds “muscle memory” chunks for the mind in solving certain types of problems.

“The dread of doing a task uses up more time and energy than doing the task itself.”6

You tell others you couldn’t hack the math, when the reality was that you had simply let procrastination get the best of you.

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.

The higher you go in math and science, however, the more important it is to take control of procrastination.

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

“I often find that when I cannot bring myself to start something, if I go for a quick run or do something active first, when I come back to it, it is much easier to start.”

As you will find, simply getting into the flow of your work can become its own reward, giving you a sense of productiveness you might not have imagined was possible when you first sat down to begin working. Many people find that setting a reward at a specific time—for example, breaking for lunch with a friend at the deli at noon, or stopping the main tasks at five P.M., gives a solid mini-deadline that can help spur work.

Also remember that the better you get at something, the more enjoyable it can become.

Ignorance Is Bliss