A Mind For Numbers

Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. In her book, she offers you the tools needed to get a better grasp of that intimidating but inescapable field.

The companion book to COURSERA®'s wildly popular massive open online course "Learning How to Learn" Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a new skill set, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating material. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life. In A Mind for Numbers, Dr. Oakley lets us in on the secrets to learning effectively—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. The learning strategies in this book apply not only to math and science, but to any subject in which we struggle. We all have what it takes to excel in areas that don't seem to come naturally to us at first, and learning them does not have to be as painful as we might think.

A surprisingly simple way for students to master any subject--based on one of the world's most popular online courses and the bestselling book A Mind for Numbers A Mind for Numbers and its wildly popular online companion course "Learning How to Learn" have empowered more than two million learners of all ages from around the world to master subjects that they once struggled with. Fans often wish they'd discovered these learning strategies earlier and ask how they can help their kids master these skills as well. Now in this new book for kids and teens, the authors reveal how to make the most of time spent studying. We all have the tools to learn what might not seem to come naturally to us at first--the secret is to understand how the brain works so we can unlock its power. This book explains: • Why sometimes letting your mind wander is an important part of the learning process • How to avoid "rut think" in order to think outside the box • Why having a poor memory can be a good thing • The value of metaphors in developing understanding • A simple, yet powerful, way to stop procrastinating Filled with illustrations, application questions, and exercises, this book makes learning easy and fun.

A book for learners of all ages containing the best and most updated advice on learning from neuroscience and cognitive psychology. Do you spend too much time learning with disappointing results? Do you find it difficult to remember what you read? Do you put off studying because it’s boring and you’re easily distracted? This book is for you. Dr. Barbara Oakley and Olav Schewe have both struggled in the past with their learning. But they have found techniques to help them master any material. Building on insights from neuroscience and cognitive psychology, they give you a crash course to improve your ability to learn, no matter what the subject is. Through their decades of writing, teaching, and research on learning, the authors have developed deep connections with experts from a vast array of disciplines. And it’s all honed with feedback from thousands of students who have themselves gone through the trenches of learning. Successful learners gradually add tools and techniques to their mental toolbox, and they think critically about their learning to determine when and how to best use their mental tools. That allows these learners to make the best use of their brains, whether those brains seem “naturally” geared toward learning or not. This book will teach you how you can do the same.

How our intuitive understanding of numbers is deeply rooted in our biology, traceable through both evolution and development. Humans' understanding of numbers is intuitive. Infants are able to estimate and calculate even before they learn the words for numbers. How have we come to possess this talent for numbers? In A Brain for Numbers, Andreas Nieder explains how our brains process numbers. He reports that numerical competency is deeply rooted in our biological ancestry; it can be traced through both the evolution of our species and the development of our individual minds. It is not, as it has been traditionally explained, based on our ability to use language. We owe our symbolic mathematical skills to the nonsymbolic numerical abilities that we inherited from our ancestors. The principles of mathematics, Nieder tells us, are reflections of the innate dispositions wired into the brain. Nieder explores how the workings of the brain give rise to numerical competence, tracing flair for numbers to dedicated “number neurons” in the brain. Drawing on a range of methods including brain imaging techniques, behavioral experiments, and twin studies, he outlines a new, integrated understanding of the talent for numbers. Along the way, he compares the numerical capabilities of humans and animals, and discusses the benefits animals reap from such a capability. He shows how the neurobiological roots of the brain's nonverbal quantification capacity are the evolutionary foundation of more elaborate numerical skills. He discusses how number signs and symbols are represented in the brain; calculation capability and the “neuromythology” of mathematical genius; the “start-up tools” for counting and developmental of dyscalculia (a number disorder analogous to the reading disorder dyslexia); and how the brain processes the abstract concept of zero.

Mindshift reveals how we can overcome stereotypes and preconceived ideas about what is possible for us to learn and become. At a time when we are constantly being asked to retrain and reinvent ourselves to adapt to new technologies and changing industries, this book shows us how we can uncover and develop talents we didn’t realize we had—no matter what our age or background. We’re often told to “follow our passions.” But in Mindshift, Dr. Barbara Oakley shows us how we can broaden our passions. Drawing on the latest neuroscientific insights, Dr. Oakley shepherds us past simplistic ideas of “aptitude” and “ability,” which provide only a snapshot of who we are now—with little consideration about how we can change. Even seemingly “bad” traits, such as a poor memory, come with hidden advantages—like increased creativity. Profiling people from around the world who have overcome learning limitations of all kinds, Dr. Oakley shows us how we can turn perceived weaknesses, such as impostor syndrome and advancing age, into strengths. People may feel like they’re at a disadvantage if they pursue a new field later in life; yet those who change careers can be fertile cross-pollinators: They bring valuable insights from one discipline to another. Dr. Oakley teaches us strategies for learning that are backed by neuroscience so that we can realize the joy and benefits of a learning lifestyle. Mindshift takes us deep inside the world of how people change and grow. Our biggest stumbling blocks can be our own preconceptions, but with the right mental insights, we can tap into hidden potential and create new opportunities.

Why is math so hard? And why, despite this difficulty, are some people so good at it? If there's some inborn capacity for mathematical thinking—which there must be, otherwise no one could do it —why can't we all do it well? Keith Devlin has answers to all these difficult questions, and in giving them shows us how mathematical ability evolved, why it's a part of language ability, and how we can make better use of this innate talent.He also offers a breathtakingly new theory of language development—that language evolved in two stages, and its main purpose was not communication—to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the emergence of true language. Why, then, can't we do math as well as we can speak? The answer, says Devlin, is that we can and do—we just don't recognize when we're using mathematical reasoning.