The key ideas

A Mind for Numbers: How to Excel at Math and Science

Barbara Oakley, 2014

Barbara Oakley failed mathematics at school and was sure it was not for her. Today she is an engineering professor. In this book she explains learning: why we get stuck on problems, how rereading can mislead us, and how to stop putting difficult things off.

Who it is for

For anyone who thinks the exact sciences are “not for them,” university and school students, parents, and anyone learning something new as an adult.

The law of serendipity: fortune favors those who try.

What the book is about

As a child, Barbara Oakley could not understand how to read a clock: why did the small hand show the hour when an hour mattered more than a minute? She failed mathematics and science at school, deliberately, she says: she refused to understand what was forced on her. She only began studying trigonometry, in a remedial course at that, at twenty-six.

Today she is an engineering professor. How did someone who considered herself “not a technical person” retrain her own brain?

A Mind for Numbers is Oakley’s answer. It is a practical guide rather than a scientific monograph, drawing on brain and memory research, hundreds of teachers’ experience, and her own journey. Its models are simplified images for understanding, as Oakley herself emphasizes.

Idea 1. Two pinball machines in your head

After school, Oakley joined the Army because it paid people to learn a language. Russian came so easily that she was sometimes mistaken for a native speaker. Then the Army made her a Signal Corps officer and suddenly expected knowledge of radio and telephone systems. She finished last in her electronics class.

Later, she found an explanation. In her model, the brain switches between two modes. Focused mode resembles a pinball machine with tightly packed bumpers: thought bounces along familiar, well-worn paths. This suits a problem resembling something you already know. Diffuse mode is a machine with widely spaced bumpers: thought travels farther and may encounter an unexpected connection, but precise thinking is difficult this way.

Oakley qualifies this: the brain’s real operation is more complex than two modes. Pinball is an explanatory image, not anatomy.

You spend half an hour on an Excel spreadsheet, unable to make the formula work. That evening in the shower, you suddenly realize the problem lies in the approach rather than the brackets.

In Oakley’s model, getting stuck on a new problem may mean the brain is working in one mode, rather than necessarily lacking ability. Switching modes can sometimes help more than pushing harder.

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About the author

Barbara Oakley is an American engineering professor. After school, she served in the US Army, studied Russian, was a communications officer in Germany, and worked as an interpreter on Soviet trawlers in the Bering Sea. She later earned degrees in electrical and systems engineering. With neuroscientist Terrence Sejnowski, she created the popular online course Learning How to Learn.

All books by this author: Barbara Oakley

A Mind for Numbers: How to Excel at Math and Science Quiz

Terms from the book

  • Spaced repetition
  • Focused mode: In Oakley’s model, concentrated thinking along familiar paths. Useful when a problem resembles one you already know. An image from the book rather than a precise description of brain function.
  • Diffuse mode: In Oakley’s model, relaxed thinking that can connect distant ideas. She associates it with sudden insights after a break.
  • Einstellung effect: A phenomenon in which an idea already in your mind can obstruct a better solution.
  • Chunk: A meaningfully connected block of information that can occupy one place in working memory instead of several.
  • Illusion of competence: The feeling that material has been learned, which can arise from rereading or looking at a finished answer even when you cannot yet reproduce it yourself.

All terms

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