Dr. Mario's 2nd 🧠

A Mind for Numbers

15 min read

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Highlights

dealing with procrastination, while important in studying any discipline, is particularly important in math and science. (Location 357)

one significant mistake students sometimes make in learning math and science is jumping into the water before they learn to swim.11 (Location 370)

If you are trying to understand or figure out something new, your best bet is to turn off your precision-focused thinking and turn on your “big picture” diffuse mode, (Location 388)

relaxation is an important part of hard work—and (Location 397)

When students approach a problem and don’t know how to do it, they’ll often decide they’re no good at the subject. Brighter students, in particular, can have difficulty in this way—their (Location 428)

Articulating your question is 80 percent of the battle. By the time you’ve figured out what’s confusing, you’re likely to have answered the question yourself!” (Location 431)

write a few key things that you would like to work on the next day. This early preparation will help your diffuse mode begin to think about how you will get those tasks done the next day. (Location 466)

The key is to do something else until your brain is consciously free of any thought of the problem. (Location 516)

You do, however, if you simply switch your focus to other things you need to do, and mix in a little relaxing break time. (Location 518)

keep your working sessions short. (Location 563)

When your energy flags, sometimes you can take a break by jumping to other focused-type tasks, such as switching from studying math to studying French vocabulary. But the longer you spend in focused mode, the more mental resources you use. It’s like a concentrated, extended set of mental weight lifting. That’s why brief interludes that involve movement or talking with friends, where you don’t have to concentrate intently, can be so refreshing. (Location 576)

Don’t Worry about Keeping Up (Location 599)

A good rule of thumb, when you are first learning new concepts, is not to let things go untouched for longer than a day. (Location 643)

Anger and frustration can occasionally have their place in motivating us to succeed, but they can also shut down key areas of the brain that we need in order to learn. Rising frustration is usually a good time-out signal (Location 654)

It seems that if you go over the material right before taking a nap or going to sleep for the evening, you have an increased chance of dreaming about it. If you go even further and set it in mind that you want to dream about the material, it seems to improve your chances of dreaming about it still further.27 Dreaming about what you are studying can substantially enhance your ability to understand—it somehow consolidates your memories into easier-to-grasp chunks.28 (Location 737)

Creativity is a numbers game: The best predictor of how many creative works we produce in our lifetime is … the number of works we produce. (Location 784)

“What would you do if you weren’t afraid?” I try to look at this daily, and I aim to do something fearless every day. (Location 787)

helps to start out with a fully worked-through example. (Location 862)

The first step in chunking, then, is to simply focus your attention (Location 878)

The second step in chunking is to understand the basic idea (Location 885)

Closing the book and testing yourself on how to solve the problems will also speed up (Location 896)

Context means going beyond the initial problem and seeing more broadly, repeating and practicing with both related and unrelated problems (Location 898)

Skimming through a chapter or listening to a very well-organized lecture can allow you to gain a sense of the big picture. (Location 922)

Using recall—mental retrieval of the key ideas—rather than passive rereading will make your study time more focused and effective. (Location 943)

Try to touch again on something you’re learning within a day, (Location 951)

Once you’ve got something down, you can expand the time between “upkeep” repetitions to weeks or months—and (Location 954)

You must have information persisting in your memory if you are to master the material well enough to do well on tests and think creatively with it. (Location 993)

a key difference between creative scientists and technically competent but nonimaginative ones is their breadth of interest.22 (Location 1002)

you can’t learn mathematics or science without also including a healthy dose of practice and repetition to help you build the chunks that will underpin your expertise.27 (Location 1053)

by simply practicing and recalling the material, students learned far more and at a much deeper level than they did using any other approach, including simply rereading the text a number of times or drawing concept maps that supposedly enriched the relationships in the materials under study. (Location 1059)

You have to prioritize how much you’re able to do, also keeping in mind that you must schedule some time off to keep your diffuse mode in play. (Location 1094)

mastering a new subject means learning to select and use the proper technique for a problem. The only way to learn that is by practicing with problems that require different techniques. (Location 1117)

You want your brain to become used to the idea that just knowing how to use a particular problem-solving technique isn’t enough—you also need to know when to use it. (Location 1124)

Rather than devote a long session to the study or practice of the same skill or concept so that overlearning occurs, students should divide their effort across several shorter sessions. This doesn’t mean that long study sessions are necessarily a bad idea. Long sessions are fine as long as students don’t devote too much time to any one skill or concept. Once they understand ‘X,’ they should move on to something else and return to ‘X’ on another day.”40 (Location 1142)

Beware—a common illusion of competence is to continue practicing a technique you know, simply because it’s easy and it feels good to successfully solve problems. Interleaving your studies—making a point to review for a test, for example, by skipping around through problems in the different chapters and materials—can sometimes seem to make your learning more difficult. But in reality, it helps you (Location 1151)

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. (Location 1183)

We procrastinate about things that make us feel uncomfortable. (Location 1255)

But there’s something important to note. It was the anticipation that was painful. When the mathphobes actually did math, the pain disappeared. Procrastination expert Rita Emmett explains: “The dread of doing a task uses up more time and energy than doing the task itself.” (Location 1258)

It’s easy to feel distaste for something you’re not good at. But the better you get at something, the more you’ll find you enjoy it. (Location 1268)

the trigger that launches you into “zombie mode.” (Location 1366)

A cue by itself is neither helpful nor harmful. It’s the routine—what we do in reaction to that cue—that matters. (Location 1368)

change a habit, you’ll need to change your underlying belief. (Location 1375)

avoid procrastination while minimizing your use of willpower. (Location 1381)

Placing pictures around your work and living spaces that remind you of where you want to be can help prime your diffuse-mode pump. Just remember to contrast those great images with the real, more mundane life that currently surrounds you, or that you are emerging from. (Location 1437)

Who cares whether you finished the homework or grasped key concepts in any one session? The whole point instead is that you calmly put forth your best effort for a short period—the process. (Location 1465)

researchers have found something fascinating and counterintuitive. If you learn under mild stress, you can handle greater stress much more easily. (Location 1481)

If you feel muzzy or featherbrained as you’re trying to look away and recall a key idea, or you find yourself rereading the same paragraphs over and over again, try doing a few situps, pushups, or jumping jacks. A little physical exertion can have a surprisingly positive effect on your ability to understand and recall. (Location 1545)

Mentally review key problem steps in your mind while doing something active, such as walking to the library or exercising. You can also use spare minutes (Location 1630)

takes time to assimilate new knowledge. You will go through some periods when you seem to take an exasperating step backward in your understanding. This a natural phenomenon that means your mind is wrestling deeply with the material. (Location 1678)

Research has confirmed that a special place devoted just to working is particularly helpful.2 (Location 1773)

Time after time, those who are committed to maintaining healthy leisure time along with their hard work outperform those who doggedly pursue an endless treadmill. (Location 1886)

when it comes to learning math and science, the bingeing excuse, “I do my best work under deadlines,” is simply not true.4 (Location 2036)

Emotions that goad you by saying, “Just do it, it feels right,” can be misleading in other ways. In choosing your career, for example, “Follow your passion” may be like deciding to marry your favorite movie star. It sounds great until reality rears its head. The proof is in the outcome: Over the past decades, students who have blindly followed their passion, without rational analysis of whether their choice of career truly was wise, have been more unhappy with their job choices than those who coupled passion with rationality. (Location 2065)

We develop a passion for what we are good at. The mistake is thinking that if we aren’t good at something, we do not have and can never develop a passion for it. (Location 2074)

Why should I memorize an equation that I can look up?’) But memorization of key facts is essential since it is these facts that form the seeds for the creative process of chunking! (Location 2181)

Supersized Visuospatial Memory (Location 2185)

Walk through your memory palace and deposit your memorable images. (Location 2224)

Teachers and professors can inadvertently get too caught up in following rules. In an intriguing study that illustrates this, six people were filmed doing CPR, only one of whom was a professional paramedic.3 Professional paramedics were then asked to guess who was the real paramedic. Ninety percent of these “real deal” expert paramedics chose correctly, remarking along the lines of “he seemed to know what he was doing.”4 CPR instructors, on the other hand, could pick the real paramedic out of the lineup only 30 percent of the time. (Location 2522)

A superb working memory can hold its thoughts so tightly that new thoughts can’t easily peek through. (Location 2550)

Research has shown that smart people can have more of a tendency to lose themselves in the weeds of complexity. People with less apparent intellectual horsepower, on the other hand, can cut more easily to simpler solutions.9 (Location 2553)

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 (Location 2697)

These students unfortunately sometimes think of themselves as not very bright, but the reality is that their slower way of thinking can allow them to see confusing subtleties that others aren’t aware of. (Location 2973)

One of the most-cited papers in sociology, “The Strength of Weak Ties,” by sociologist Mark Granovetter, describes how the number of acquaintances you have—not the number of good friends—predicts your access to the latest ideas as well as your success on the job market.11 (Location 3116)

_Yes _No 9. Did you attempt to outline lots of problem solutions quickly, without spending time on the algebra and calculations? (Location 3230)

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. This does something exceptionally helpful. “Starting hard” loads the first, most difficult problem in mind, and then switches attention away from it. Both these activities can help allow the diffuse mode to begin its work. (Location 3245)

The only challenge with this approach is that you must have the self-discipline to pull yourself off a problem once you find yourself stuck for a minute or two. For most students, it’s easy. For others, it takes discipline and willpower. In any case, by now you are very aware that misplaced persistence can create unnecessary challenges with math and science. (Location 3262)

research finds that it’s how you interpret those symptoms—the story you tell yourself about why you are stressed—that makes all the difference. If you shift your thinking from “this test has made me afraid” to “this test has got me excited to do my best!” it can make a significant improvement in your performance.4 (Location 3283)

When you are checking your work, if you start more toward the back and work toward the front, it sometimes seems to give your brain a fresher perspective that can allow you to more easily catch errors. (Location 3325)

Don’t just think your explanation—say it out loud or put it in writing. (Location 3460)

Highlighting your text can fool your mind into thinking you are putting something in your brain, when all you’re really doing is moving your hand. A little highlighting here and there is okay—sometimes it can be helpful in flagging important points. But if you are using highlighting as a memory tool, make sure that what you mark is also going into your brain. (Location 3476)

“Get good at it, and then see if you still want to quit.” (Location 3525)

According to the National Survey of Student Engagement (2012), engineering students spend the most time studying—senior engineering students spend eighteen hours on average per week preparing for class, while senior education students spend fifteen hours and senior social science and business students spend about fourteen hours. In a New York Times article titled “Why Science Majors Change Their Minds (It’s Just So Darn Hard),” emeritus engineering professor David E. Goldberg has noted that the heavy demands of calculus, physics, and chemistry can initiate the “math-science death march” as students wash out (Drew 2011). (Location 3951)

New highlights added 2023-03-14

one significant mistake students sometimes make in learning math and science is jumping into the water before they learn to swim (Location 370)

It seems that if you go over the material right before taking a nap or going to sleep for the evening, you have an increased chance of dreaming about it. If you go even further and set it in mind that you want to dream about the material, it seems to improve your chances of dreaming about it still further.27 Dreaming about what you are studying can substantially enhance your ability to understand—it somehow consolidates your memories into easier-to-grasp chunks. (Location 737)

You must have information persisting in your memory if you are to master the material well enough to do well on tests and think creatively with (Location 993)

a key difference between creative scientists and technically competent but nonimaginative ones is their breadth of interest. (Location 1002)

you can’t learn mathematics or science without also including a healthy dose of practice and repetition to help you build the chunks that will underpin your expertise. (Location 1053)

Rather than devote a long session to the study or practice of the same skill or concept so that overlearning occurs, students should divide their effort across several shorter sessions. This doesn’t mean that long study sessions are necessarily a bad idea. Long sessions are fine as long as students don’t devote too much time to any one skill or concept. Once they understand ‘X,’ they should move on to something else and return to ‘X’ on another day.” (Location 1142)

We procrastinate about things that make us feel (Location 1254)

But there’s something important to note. It was the anticipation that was painful. When the mathphobes actually did math, the pain disappeared. Procrastination expert Rita Emmett explains: “The dread of doing a task uses up more time and energy than doing the task (Location 1258)

Research has confirmed that a special place devoted just to working is particularly helpful. (Location 1772)

Time after time, those who are committed to maintaining healthy leisure time along with their hard work outperform those who doggedly pursue an endless (Location 1886)

when it comes to learning math and science, the bingeing excuse, “I do my best work under deadlines,” is simply not true. (Location 2036)

Emotions that goad you by saying, “Just do it, it feels right,” can be misleading in other ways. In choosing your career, for example, “Follow your passion” may be like deciding to marry your favorite movie star. It sounds great until reality rears its head. The proof is in the outcome: Over the past decades, students who have blindly followed their passion, without rational analysis of whether their choice of career truly was wise, have been more unhappy with their job choices than those who coupled passion with (Location 2065)

Blue

(‘Why should I memorize an equation that I can look up?’) But memorization of key facts is essential since it is these facts that form the seeds for the creative process of chunking! (Location 2181)

Research has shown that smart people can have more of a tendency to lose themselves in the weeds of complexity. People with less apparent intellectual horsepower, on the other hand, can cut more easily to simpler solutions. (Location 2552)

One of the most-cited papers in sociology, “The Strength of Weak Ties,” by sociologist Mark Granovetter, describes how the number of acquaintances you have—not the number of good friends—predicts your access to the latest ideas as well as your success on the job market. (Location 3116)

research finds that it’s how you interpret those symptoms—the story you tell yourself about why you are stressed—that makes all the difference. If you shift your thinking from “this test has made me afraid” to “this test has got me excited to do my best!” it can make a significant improvement in your performance. (Location 3282)

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