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

by Barbara Oakley

Similarly, the most important part of your memorization practices is to understand what the formulas and solution steps really mean. Understanding also helps a lot with the memorization process.

Einstellung. The idea you already are holding in mind blocks you from fresh thoughts. A superb working memory can hold its thoughts so tightly that new thoughts can’t easily peek through. Such tightly controlled attention could use an occasional whiff of ADHD-like fresh air—the

IT’S NOT WHAT YOU KNOW; IT’S HOW YOU THINK

If you are one of those people who can’t hold a lot in mind at once—you lose focus and start daydreaming in lectures, and have to get to someplace quiet to focus so you can use your working memory to its maximum—well, welcome to the clan of the creative.

Having a somewhat smaller working memory means you can more easily generalize your learning into new, more creative combinations.

Here is a case for the generalized learning you have been doing.

You may have to work harder sometimes (or even much of the time) to understand what’s going on, but once you’ve got something chunked, you can take that chunk and turn it outside in and inside round—putting it through creative paces even you didn’t think you were capable of!

Chess, that bastion of intellectuals, has some elite players with roughly average IQs. These seemingly middling intellects are able to do better than some more intelligent players because they practice more.12

It is the practice—particularly deliberate practice on the toughest aspects of the material—that can help lift average brains into the realm of those with more “natural” gifts.

Smarter people also sometimes struggle because they can so easily imagine every complexity, good and bad.

Santiago Ramón y Cajal won the Nobel Prize for his many important contributions to our understanding of the structure and function of the nervous system.1

“Deficiencies of innate ability may be compensated for through persistent hard work and concentration. One might say that work substitutes for talent, or better yet that it creates talent.”6 —Santiago Ramón y Cajal

Cajal deeply regretted that he never had a “quickness, certainty, and clearness in the use of words.”10

What’s worse is that when Cajal got emotional, he lost his way with words almost entirely.

He couldn’t remember things by rote, which made school, where parroting back information ...

Cajal’s teachers, as Cajal later recollected, showed a sadly mistaken valuing of abilities. Quickness was taken as cleverness, memory for ability, and submissiveness for rightness.13

I remember this hell. Though some has changed much has stayed the same with this view.

Only after his drawing captured the synthesized essence, not of just a single slide, but of the entire collection of slides devoted to a particular type of cell, did Cajal rest.14

A synthesis—an abstraction, chunk, or gist idea—is a neural pattern. Good chunks form neural patterns that resonate, not only within the subject we’re working in, but with other subjects and areas of our lives. The abstraction helps you transfer ideas from one area to another.15

Once other people grasp that chunk, not only can they use it, but also they can more easily create similar chunks that apply to other areas in their lives—an important part of the creative process.

Mandelbrot’s in heaven He gave us order out of chaos, he gave us hope where there was none His geometry succeeds where others fail So if you ever lose your way, a butterfly will flap its wings From a million miles away, a little miracle will come to take you home

The equation is seen by the novice as just one more thing to memorize in a vast collection of unrelated equations. More advanced students and physicists, however, see with their mind’s eye the meaning beneath the equation, including how it fits into the big picture, and even a sense of how the parts of the equation feel.

“A mathematician who is not at the same time something of a poet will never be a full mathematician.” —German mathematician Karl Weierstrass

Simplify and Personalize Whatever You Are Studying

One of the most important things we can do when we are trying to learn math and science is to bring the abstract ideas to life in our minds.

It seemed their introversion made them more thoughtful and sensitive to others, and their humble awareness of their past failings gave them patience and kept them from becoming aloof know-it-alls.

Beware of Intellectual Snipers

there will always be those who criticize or attempt to undermine any effort or achievement you make.

Take pride in who you are, especially in the qualities that make you “different,” and use them as a secret talisman for success.

“The Man Who Knew Infinity: A Life of the Genius Ramanujan, by Robert Kanigel.

As leading neuroscientist V. S. Ramachandran has noted, the right hemisphere serves as a sort of “‘Devil’s Advocate,’ to question the status quo and look for global inconsistencies,” while “the left hemisphere always tries to cling tenaciously to the way things were.”6

Equations tell a story about how the physical world works. For me, the key to understanding an equation in physics is to see the underlying story. A qualitative understanding of an equation is more important than getting quantitatively correct numbers out of it.

Then when you start working problems, start first with what appears to be the hardest one. But steel yourself to pull away within the first minute or two if you get stuck or get a sense that you might not be on the right track.

“With my students, I talk about good worry and bad worry. Good worry helps provide motivation and focus while bad worry simply wastes energy.” —Bob Bradshaw, Professor of Math, Ohlone College

your desire to figure things out right now is what prevents you from being able to figure things out.

Great artists, scientists, engineers, and chess masters like Magnus Carlsen tap into the natural rhythm of their brains by first intently focusing their attention, working hard to get the problem well in mind. Then they switch their attention elsewhere.

Reshaping your brain is under your control. The key is patient persistence—working knowledgeably with your brain’s strengths and weaknesses.