CityReads│Everyone Can Excel at Math & Science

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Everyone Can Excel at Math & Science, If You Learn How to Learn

If you’re simply convinced you don’t have a knack for numbers or science, A Mind for Numbers may change your mind.

 Barbara Oakley, 2014. A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra), Penguin.

Source: http://barbaraoakley.com/books/a-mind-for-numbers/

I came across this chart, “The gender gap in PhDs, 2015”the other day. It illustrates that the gender gaps in math and sciences are still the largest. In other areas, education, arts and humanities, social sciences, and health science and Biology, female PhDs outnumbered the male PhDs. 

This gender gap is largely socially constructed. It requires a lot of efforts to address it, both socially and individually. A change of mind and learning tricks can help too. It is tremendously useful to read Professor Barbara Oakley’s book, A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra).

The first half of Barbara’s life trajectory fits the stereotype. Growing up, she hated math and science. And she flunked her way through high school math and science courses. She had come to think of numbers and equations as akin to one of life’s deadly diseases—to be avoided at all costs. Barbara’s interests lay in other areas--history, social studies, culture, and especially language. She studied Russian and went to the University of Washington to get a bachelor’s degree in Slavic languages and literature, where she graduated with honors.

But Barbara changed her life course after she served in the U.S. Army Signal Corps. She was thrown into a new technological world where she was made to enroll in mathematically oriented electronics training. She was surrounded by competent engineers, who used a language of formulas and equations. She figured that if she stayed in the army, her poor technical know-how would always leave her a second-class citizen.

Barbara decided to retrain her brain and went back to university to study Math. She earned a bachelor’s degree in electrical engineering and then a master’s in electrical and computer engineering. Finally, She earned a doctorate in systems engineering. How did she do that? How did she retool her brain from mathphobe to math lover? From technophobe to technogeek? You will find out in this book. More importantly, you can apply the tricks to improve your study.

If you’re simply convinced you don’t have a knack for numbers or science, this book may change your mind. When you follow these concrete tips based on how we actually learn, you’ll be amazed to see the changes within yourself, changes that can allow new passions to bloom. What you discover will help you be more effective and creative, not only in math and science, but in almost everything you do.

Your brain at learning: the focused and diffuse modes

Our brain uses two very different processes for thinking—the focused and diffuse modes. These modes are highly important for learning.

Focused-mode thinking is essential for studying math and science. It involves a direct approach to solving problems using rational, sequential, analytical approaches. The focused mode is associated with the concentrating abilities of the brain’s prefrontal cortex, located right behind your forehead. Turn your attention to something and bam—the focused mode is on, like the tight, penetrating beam of a flashlight.

Diffuse-mode thinking is also essential for learning math and science. It allows us to suddenly gain a new insight on a problem we’ve been struggling with and is associated with “big-picture” perspectives. Diffuse-mode thinking is what happens when you relax your attention and just let your mind wander. This relaxation can allow different areas of the brain to hook up and return valuable insights. Unlike the focused mode, the diffuse mode seems less affiliated with any one area ofthe brain—you can think of it as being “diffused” throughout the brain. Diffuse-mode insights often flow from preliminary thinking that’s been done in the focused mode.

You frequently switch back and forth between these two modes in your day-to-day activities. You’re in either one mode or the other—not consciously in both at the same time.

Focused mode(left) vs diffused mode(right)

Learning involves a complex flickering of neural processing among different areas of the brain, as well as back and forth between hemispheres. So this means that thinking and learning is more complicated than simply switching between the focused and diffuse modes. Both hemispheres are involved in focused as well as diffuse modes of thinking. To learn about and be creative in math and science, we need to strengthen and use both the focused and diffuse modes.

Working and Long-Term Memory

Working memory is the part of memory that has to do with what you are immediately and consciously processing in your mind. It used to be thought that our working memory could hold around seven items, or “chunks,” but it’s now widely believed that the working memory holds only about four chunks of information.

When you master a technique or concept in math or science, it occupies less space in your working memory. This frees your mental thinking space so that it can more easily grapple with other ideas. Your working memory is important in learning math and science because it’s like your own private mental blackboard where you can jot down a few ideas that you are considering or trying to understand. How do you keep things in working memory? Often it’s through rehearsal.

In contrast, long-term memory might be thought of as a storage warehouse. Once items are in there, they generally stay put. The warehouse is large, with room for billions of items, and it can be easy for stored parcels to get buried so deeply that it’s difficult to retrieve them. Research has shown that when your brain first puts an item of information in long-term memory, you need to revisit it a few times to increase the chances you’ll later be able to find it when you need it.

Long-term memory is important for learning math and science because it is where you store the fundamental concepts and techniques that you need to use in problem solving. It takes time to move information from working memory to longterm memory. To help with this process, use a technique called spaced repetition.

If you try to glue things into your memory by repeating something twenty times in one evening, for example, it won’t stick nearly as well as it will if you practice it the same number of times over several days or weeks.

Why sleep is important to learning?

During sleep, your cells shrink, causing a striking increase in the space between your cells. This is equivalent to turning on a faucet—it allows fluid to wash past and push the toxins out. This nightly housecleaning is part of what keeps your brain healthy. When you get too little sleep, the buildup of these toxic products is believed to explain why you can’t think very clearly.

Brain awake: toxin accumulates 

Brain asleep: cell shrinks 

Brain asleep: fluids push the toxins out

Studies have shown that sleep is a vital part of memory and learning. Part of what this special sleep-time tidying does is erase trivial aspects of memories and simultaneously strengthen areas of importance. During sleep, your brain also rehearses some of the tougher parts of whatever you are trying to learn—going over and over neural patterns to deepen and strengthen them.

Finally, sleep has been shown to make a remarkable difference in people’s ability to figure out difficult problems and to find meaning and understanding in what they are learning.

Chunking and avoiding illusions of competence

Chunks are pieces of information that are bound together through meaning. You can take the letters p, o, and p and bind them into one conceptual, easy-to-remember chunk, the word pop. It’s like converting a cumbersome computer file into a .zip file. Underneath that simple pop chunk is a symphony of neurons that have learned to trill in tune with one another. The complex neural activity that ties together our simplifying, abstract chunks of thought—whether those thoughts pertain to acronyms, ideas, or concepts—are the basis of much of science, literature, and art.

One of the first steps toward gaining expertise in math and science is to create conceptual chunks—mental leaps that unite separate bits of information through meaning. Chunking the information you deal with helps your brain run more efficiently. Once you chunk an idea or concept, you don’t need to remember all the little underlying details.

When you first look at a brand-new concept in science or math, it sometimes doesn’t make much sense, as shown by the puzzle pieces above on the left. Just memorizing a fact (center) without understanding or context doesn’t help you understand what’s really going on, or how the concept fits together with the other concepts you are learning—notice there are no interlocking puzzle edges on the piece to help you fit into other pieces.Chunking (right) is the mental leap that helps you unite bits of information together through meaning. The new logical whole makes the chunk easier to remember, and also makes it easier to fit the chunk into the larger picture of what you are learning.

The first step in chunking, then, is to simply focus your attention on the information you want to chunk.

The second step in chunking is to understand the basic idea you are trying to chunk. Understanding is like a superglue that helps hold the underlying memory traces together. It creates broad, encompassing traces that link to many memory traces.

The third step to chunking is gaining context so you see not just how, but also when to use this chunk.

The ability to combine chunks in novel ways underlies much of historical innovation.

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. That’s why great art, poetry, music, and literature can be so compelling.

Metaphors and physical analogies also form chunks that can allow ideas even from very different areas to influence one another.17 This is why people who love math, science, and technology often also find surprising help from their activities or knowledge of sports, music, language, art, or literature. My own knowledge of how to learn a language helped me in learning how to learn math and science.

One trait that successful professionals in science, math, and technology gradually learn is how to chunk—to abstract key ideas. Regardless of your current or intended career path, keep your mind open and ensure that math and science are in your learning repertoire. This gives you a rich reserve of chunks to help you be smarter about your approach to all sorts of life and career challenges.

Reshape your brain, learn efficiently

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

Rote memorization, often at the last minute, has given many lower-level learners the illusory sense that they understand math and science. As they climb to higher levels, their weak understanding eventually crumbles. But our growing understanding of how the mind truly learns is helping us move past the simplistic idea that memorization is always bad. We now know that deep, practiced internalization of well-understood chunks is essential to mastering math and science. We also know that, just as athletes can’t properly develop their muscles if they train in last-minute cramming sessions, students in math and science can’t develop solid neural chunks if they procrastinate in their studies.

No matter what our age and degree of sophistication, parts of our brain remain childlike. This means that we sometimes can become frustrated, a signal to us to take a breather. But our ever-present inner child also gives us the potential to let go and use our creativity to help us visualize, remember, make friends with, and truly understand concepts in math and science that at first can seem terribly difficult.

Ten rules of good studying

1. Use recall. After you read a page, look away and recall the main ideas. Highlight very little, and never highlight anything you haven’t put in your mind first by recalling. An ability to recall—to generate the ideas from inside yourself—is one of the key indicators of good learning.

2. Test yourself. On everything. All the time. Flash cards are your friend.

3. Chunk your problems. Chunking is understanding and practicing with a problem solution so that it can all come to mind in a flash. After you solve a problem, rehearse it. Make sure you can solve it cold—every step.

4. Space your repetition. Spread out your learning in any subject a little every day, just like an athlete. Your brain is like a muscle—it can handle only a limited amount of exercise on one subject at a time.

5. Alternate different problem-solving techniques during your practice. Never practice too long at any one session using only one problem-solving technique. Mix it up and work on different types of problems. Quiz yourself randomly on different types of problems.

6. Take breaks. It is common to be unable to solve problems or figure out concepts in math or science the first time you encounter them. This is why a little study every day is much better than a lot of studying all at once.

7. Use explanatory questioning and simple analogies. Whenever you are struggling with a concept, think to yourself, How can I explain this so that a ten-year-old could understand it?

8. Focus. Turn off all interrupting beeps and alarms on your phone and computer, and then turn on a timer for twenty-five minutes. Focus intently for those twenty-five minutes and try to work as diligently as you can. After the timer goes off, give yourself a small, fun reward. A few of these sessions in a day can really move your studies forward.

9. Eat your frogs first. Do the hardest thing earliest in the day, when you are fresh.

10. Make a mental contrast. Imagine where you’ve come from and contrast that with the dream of where your studies will take you. Post a picture or words in your workspace to remind you of your dream. Look at that when you find your motivation lagging. 

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