If you think math and science are a piece of cake, this book might not be for you. “A Mind for Numbers” is for the rest of the population — those of you who want to be proficient at math and science so you can enhance your career options or use STEM skills in your daily life. This book review will give you a new determination to tackle subjects that held you back in the past, along with the confidence to keep learning.
Discover proven strategies to excel in math and science courses from a professor who once flunked her way through them.
READ THIS BOOK REVIEW IF YOU:
- A student struggling in a math or science class
- An adult making a career change that requires new STEM skills
- A lifelong learner interested in mastering subjects that have always given you trouble
Table of Contents
Introduction (Open the Door)
You could think of A Mind for Numbers as an instruction manual for your brain. It will improve your existing skills and provide new techniques for learning, especially when it comes to math and science.
Barbara Oakley’s approach is different. She offers many simple, practical tools for training your mind to become more adept when approaching problems. One of the most surprising things you’ll learn is that your mind can continue working on problems even when you’re not aware of it — like when you’re sleeping or involved in other activities. When the analytical side of your mind rests, it comes up with new, creative solutions to the problems you’ve given it. This goes for both social problems and math equations.
Sometimes when you’re faced with concepts that are difficult to understand, it’s tempting to keep reading through them over and over, hoping they will sink in and make sense. But Oakley believes this is inefficient and ineffective, and she’s developed proven methods for tackling the most elusive problems. Her simple techniques, used by professionals all over the world, can change the way you learn — and therefore change your life.
The truth is, your brain is actually designed to perform complex mental calculations. You’re doing it unconsciously all the time when you catch a ball, balance on a ladder, or dance to a song. To tap into this potential, just apply Oakley’s proven techniques. Are you ready to take on the challenge of retraining your brain?
Learning Is Creating
Have you ever said to yourself, “Today is the day! I’m going to sit down and learn this math concept, no matter how long it takes me”? Then you spend hours reading and rereading the same page, wishing it would somehow sink in. According to Oakley, trying too hard is part of the problem — it sets up mental blocks that distract you from real learning.
Instead, follow her easy-does-it approach: Glance through the material casually, walking yourself through the charts, graphics, and diagrams, and the questions at the end of a chapter. Then allow yourself to step away and do something else. This helps you organize your thoughts before you read through the material again in more depth. In doing this, you’re creating tiny neural pathways in your brain that get even stronger the next time you pass through the information.
This technique allows your brain to process material in two different types of networks: focused mode and diffuse mode.
- Focused-mode thinking is a function of the prefrontal cortex, and it uses rational and analytical approaches to solve problems directly.
- Diffuse-mode thinking is a function of multiple networks in your brain, and it employs a big-picture perspective to help you gain new insight on a problem.
When these two modes work together, the brain moves complex problems back and forth between the two hemispheres and comes up with creative solutions. To put this technique into practice, start in focused mode and allow your mind to send out signals along neural pathways — kind of like an octopus stretching out its tentacles. Next, practice thinking in diffuse mode by pulling back from your tight focus on the problem and allowing your mind to wander a bit. As it wanders, it builds new connections between the neural pathways that were created in focused mode, allowing you to see the solution to the problem. To be successful in math and science, you must use both modes of thinking.
Rumor has it that both Thomas Edison and Salvador Dali used a clever trick to help them switch between focused mode and diffuse mode. When faced with a difficult problem, each man would take a nap in a chair while holding something in his hands. The object would drop to the floor once he fell asleep. The clatter of the dropped object startled him awake, leaving him with fragments of diffuse-mode thinking still swirling in his mind. Those fragments could be applied to the problem when he switched back to focused mode.
Another important technique for approaching difficult problems is called chunking. Chunks are pieces of information that are collected together by their shared meaning. Linking important material in this way helps your brain run more efficiently. For example, when you decide to cook dinner, your mind is already organizing all the necessary tasks it associates with accomplishing that goal.
How do you form a chunk when working with math and science?
- Focus on the information you want to put into the chunk.
- Make sure you understand the basic idea that will go into the chunk.
- Get context so you can decide when and how to use the chunk.
Chunking enables you to get a better perspective on complex problems so that your mind can begin working through them, even when you’re not deliberately concentrating on them. And the more you add to your “library” of chunks, the easier it is for your mind to recognize different types and classes of problems and identify patterns between them. Practice and repetition help your mind access those chunks rapidly and build expertise.
Tools, Tips, and Tricks
As with anything in life, good habits are essential to succeeding at whatever you want to learn. Habits save your mind the energy of thinking through every step of a task, which opens up space for other activities. Think about the first time you backed your car out of the driveway. It probably seemed almost impossible at first, but with practice, your mind was able to chunk all the relevant information involved in the task, greatly simplifying your thought process and turning the task into a habit.
You can harness your habits — the things you do on autopilot — to achieve your goals. Make a habit of giving yourself a reward when you work on something important for a certain amount of time. This is called learned industriousness, and it helps you stay motivated to complete tasks you might find uninteresting or unappealing. It’s important to spend time developing these habits and processes so you can stay focused when there are unpleasant tasks that need to be done.
One helpful approach is the Pomodoro technique, which helps focus your attention over a short period of time. First, set a timer for 25 minutes. During this time, you agree not to give in to distraction — no texting, checking social media, or looking at articles online. It’s best to put all distractions as far out of reach as possible and inform people around you, so they’ll know not to interrupt you until the timer goes off. When distraction arises, train yourself to ignore it. The more you do that, the easier it becomes. Afterward, reward yourself with free time to nurture creative thinking. Researchers have found that putting yourself “on the clock” creates a mild amount of stress, and this makes it more likely that you’ll succeed in a highpressure scenario, like taking a test or giving a presentation.
Another way to reduce anxiety and sharpen your expertise is to give yourself mini-tests during the studying process. Research shows that testing is a type of learning process because it allows your mind to form powerful connections between diverse material. Mini-tests alter and enrich what you know simply because you’re finding ways to recall information under pressure. And testing can help you recognize a feeling of rightness when you’re on the path to a solution — a very important skill when working with complex problems. Lastly, mini-tests help your mind become accustomed to working under slight pressure so that it performs with confidence in any situation.
Enhancing Your Memory
Did you know that pausing and reflecting are key elements to learning? Oakley says that once you’ve dedicated time to chunking important material together in your “library” through repetition and self-testing, you should step away and reflect on what you’ve learned. You could go for a walk, talk with a friend, or have an imaginary conversation where you explain what you’ve learned to someone else. These types of activities allow your mind to reset and make important unconscious connections between information.
Another proven way to enhance your learning and memory skills is to practice creating memorable, visual images. Oakley uses the bizarre (but effective) image of a flying mule to remember Newton’s second law, F = ma. F stands for flying, m stands for mule, and she leaves it up to you to determine what a stands for. In any case, this strange image makes it easier to remember the formula, and a new chunk is born.
Songs and rhymes can also help you cement meaningful information into your memory. You’re aware of the alphabet song, and maybe you use other songs or poems to remember historical dates and figures. Adding music, rhythm, or motion to material you want to remember activates many parts of the brain, so whenever you want to access the information, it can be reached through the interconnected neural pathways you’ve created.
One word of caution: A memory trick is not the same as knowledge. A memoryenhancing tool can help you build knowledge out of the chunks you remember, but true knowledge requires the ability to synthesize and apply information in a coherent way.
Sculpting Your Brain
One of the best ways to learn is to simplify and personalize the subjects you’re studying. Take the abstract ideas in math and science and bring them to life in your mind. You can create imaginative narratives to remember complex mathematical formulas or populate your science texts with dreamlike creatures that remind you of important principles. For example, Einstein imagined himself as a photon! There’s no end to how creative you can be.
It may sound silly, but many celebrated scientists and Nobel Prize winners have similar methods for immersing themselves in their work. Barbara McClintock, a pioneering geneticist who won the Nobel Prize for her work on corn, imagined gigantic, person-size versions of the tiny molecules she studied, and she made friends and interacted with these imagined versions. Her imaginative approach brought the molecules she studied to life and enabled her to engage with them as fully as possible.
Finally, never underestimate the value of brainstorming with others — it can open your mind to how other people structure their thoughts and categorize information. Everyone has blind spots, and working with another person can be the catalyst you need for a breakthrough. Einstein and his brilliant friend Niels Bohr often bounced ideas off each other and challenged each other to pursue new avenues of thought. Brainstorming with others helps you catch your own areas of weakness, and explaining things you understand well helps strengthen your knowledge base.
Storytelling, personalization, imagination, and brainstorming are all very effective ways to sculpt your brain and make it easier to master math and science.
Summary
Create Mental Scaffolds
“One important key to learning swiftly in math and science is to realize that virtually every concept you learn has an analogy—a comparison—with something you already know. Sometimes the analogy or metaphor is rough—such as the idea that blood vessels are like highways, or that a nuclear reaction is like falling dominoes. But these simple analogies and metaphors can be powerful tools to help you use an existing neural structure as a scaffold to help you more rapidly build a new, more complex neural structure.” – Barbara Oakley
As you learn and develop analogies (strong imagery) related to the topic you’re trying to master, abstract concepts are made concrete and tangible. The more analogies you learn, the easier it is to learn complex material.
Focus and Diffuse
Switch between focus mode (conscious thinking), to expedite the learning process.
“One mode (focus mode) will process the information it receives and then send the result back to the other mode (diffuse mode). This volleying of information back and forth as the brain works its way toward a conscious solution appears essential for understanding and solving all but trivial problems and concept.” – Barbara Oakley
When learning something, engage in mental interval training: a short period of intense focus followed by a period of subconscious mental processing (force yourself to step away and stop thinking about the problem/concept). Extended periods of conscious learning and problem solving are counter-productive. Instead, think-don’t think-think-don’t think…- solve-daydream-solve-daydream…focus-diffuse-focus-diffuse…
Recall & Retell
“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… Attempting to recall the material you are trying to learn—retrieval practice—is far more effective than simply rereading the material.” – Barbara Oakley
When attempting to retrieve information, your brain automatically reshapes the information to under-stand it, thus making it unique and more likely to stick. A 2007 study by Dr. Karpicke at Purdue University found that “retrieving knowledge improves one’s ability to retrieve it again in the future. Practicing retrieval does not merely produce rote, transient learning; it produces meaningful, long-term learning.”
You can take recall one step further and explain what you’ve learned to other people: “Retelling whatever you are learning about not only helps fuel and share your own enthusiasm, but also clarifies and cements the ideas in your mind, so you’ll remember them better in the weeks and months to come. Even if what you are studying is very advanced, simplifying so you can explain to others who do not share your educational background can be surprisingly helpful in building your understanding.” – Barbara Oakley
To supercharge your learning, recall and retell what you’re learning by stepping away and asking yourself: “What was the most important thing?” –> Recite whatever that may be without looking at the material.
Conclusion
As you’ve learned in this summary, there are many useful techniques for increasing your math and science skills:
- Toggle your thinking. Get a glimpse of what you’re trying to learn. Then take some time away before returning to get a deeper understanding.
- Embrace befuddlement. Confusion is a stepping stone to curiosity, so don’t get discouraged if you don’t understand something right away.
- Alternate between focused mode and diffuse mode when studying.
- Learn techniques for chunking information into meaningful pieces that can be accessed quickly and easily when you need them
- Avoid distractions by training yourself in the Pomodoro technique, which allows you to relax and settle in to the flow of work.
- Make time to pause and reflect so that your mind can absorb and classify information.
Remember that the key to reshaping your brain is patience and persistence, and long-term learning requires periods of relaxation and creativity, as well as times of focused attention.
About Barbara Oakley
Barbara Oakley is an engineer, author, and speaker. Her work focuses on the relationship between neuroscience and social behavior. She’s been married to her husband, whom she met at the South Pole, for 33 years.
Review
The book is a guide for anyone who wants to improve their learning skills, especially in math and science. The author, Barbara Oakley, is an engineering professor who overcame her own difficulties with math and science by applying the principles of neuroscience and cognitive psychology to her studies. She shares her insights and strategies on how to overcome mental blocks, enhance memory, avoid procrastination, and optimize learning.
The book is divided into two parts. The first part explains the basics of how the brain works and how we can use different modes of thinking to learn better. The author introduces the concepts of focused and diffuse modes, which are two complementary ways of processing information. Focused mode is when we concentrate on a specific problem or task, using our logical and analytical skills. Diffuse mode is when we relax our attention and let our mind wander, using our creative and intuitive skills. The author suggests that we should alternate between these two modes to gain a deeper understanding of the material and avoid getting stuck.
The second part of the book provides practical tips and techniques on how to apply the principles of learning to various aspects of studying, such as reading, listening, note-taking, recalling, testing, reviewing, and problem-solving. The author also covers topics such as chunking, which is the process of breaking down complex information into smaller and more manageable units; memory techniques, such as using mnemonics, metaphors, stories, and memory palaces to encode and retrieve information; and habits and attitudes, such as setting goals, managing time, overcoming procrastination, dealing with stress, and cultivating curiosity.
I think this book is a useful and inspiring resource for anyone who wants to learn more effectively and efficiently. The book is well-written and easy to follow, with clear explanations, examples, illustrations, exercises, summaries, and references. The book is also engaging and fun, with anecdotes, jokes, quizzes, stories, and quotes from various sources. The book is not only informative but also motivational, as it shows that anyone can improve their learning abilities with the right mindset and methods.
I would recommend this book to students who are struggling with math or science or any other subject that they find challenging or intimidating. I would also recommend this book to teachers who want to help their students learn better or to lifelong learners who want to enhance their knowledge and skills in any field. I think this book is a valuable addition to the literature on learning how to learn.