A MIND FOR NUNBERS

·       If you ever wanted to become better at anything, this book will help serve as a guide.

·       I´d followed my inner passions without also being open to developing new ones

o   I want to develop all of what I always wanted

§  German

§  Other languages

§  Piano

§  Really good at the guitar

§  Singing

§  Composing

§  Lyric writing – I should start writing a song everyday.

·       I have to retrain my brain to learn better, deeper and in a bigger amount.

o   And also on the subjects that I am not really good yet

·       Learn not to take too much at once, allowing plenty of time to practice.

·       The brain is designed to do extraordinary mental calculations

·       Master the lingo and culture of those difficult subjects.

o   Accounting.

o   Financing Math

o   Economy

·       Trying too hard can sometimes be part of the problem.

·       Being able to toggle your thinking – getting a glimpse of what you are learning before returning later to more fully understand what´s going on, is itself one of the main ideas in the book.

·       Diffuse mode thinking         

o   Is also essential for learning math and science.

o   It allows us to suddenly gain a new insight on a problem we´ve been struggling with and is associated with “big picture” perspectives.

o   It is what happens when you relax your attention and just let your mind wander.

·       Diffuse mode insights often flow from preliminary thinking that´s been done in the focused mode.

·       Metaphors are powerful tools for learning in math and science.

·       Einstellung effect –

o   Is this phenomenon, an idea you already have in mind, or your simple initial thought, prevents a better idea or solution from being found.

·       You have to unlearn your erroneous older ideas even while you´re learning new ones.

·       Give yourself the time to learn and understand the concepts before jumping into solving the problems.

·       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.

·        The harder you push your brain to be creative, the less creative your ideas will be.

·       This means that relaxation is an important part of hard work – and good work, for that matter.

·       As long as we are consciously focusing on a problem, we are blocking the diffuse mode.

·       Being confused is normal and necessary.

·       When you procrastinate you are leaving yourself only enough time to do superficial focused mode learning.

·       Don´t worry about finishing the task, just worry about working on it.

·       Know that you are making progress with each mistake you catch when trying to solve a problem – finding errors should give you a sense of satisfaction.

·       Unless you are really enjoying what you are doing, keep your working sessions short.

·       It´s the distributed practice – the back and forth between focused-mode attention and difuse-mode relaxation – that does the trick.

·       Consistency over time is key.

·       Diffuse mode activators

o   Play a sport

o   Listen to music

o   Go for a walk

o   Go for a drive

o   Play songs you know well on a musical instrument.

·       Take a step back and look dispassionately at your strengths and weaknesses. If you need more time to learn math and science, that´s simply the reality.

·       Learning slowly can mean you learn more deeply

·       Figuring out a difficult problem or learning a new concept almost always requires one or more periods when you aren´t consciously working on the problem.

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

·       Ask someone else for a different perspective on how to solve the problem or a different analogy to understand the concept; however, it´s best that you first wrestle with the problem yourself before you talk to anyone else.

·       Putting a day between bouts of repetition – extending your practice over a number of days – does make a difference.

·       Take short power naps.

·       Reading for one hour with a well-rested mind brain is better than reading for three hours with a tired brain.

·       It´s best to work at math and science in small doses  - a little every day.

·       Spaced repetition helps move items from working memory to long-term memory.

·       Figure out tough problems and find meaning in what you are learning.

·       Find ways to switch from focused to diffuse mode:

o   Working out

o   Riding a bike

o   Laying down

o   Playing the guitar

o   Playing beach tennis

o   Watching comedy.

·       The first step in chunking is to simply focus your attention in what you want to chunk.

o   Your octopus tentacles can´t make connections very well if some of then are off on other thoughts.

·       Understanding is like a superglue that helps hold the underlying memory traces together.

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

·       Chucking may involve your learning how to use a certain problem-solving technique.

o   Context means learning when to use that technique instead of some other technique.

·       Attempting to recall the material you are trying to learn – retrieval practice – is far more effective than simply rereading the material.

·       Train yourself to look for main ideas before making any marks, and keep your text marking to a minimum.

·       Give emphasis on:

o   Showing your work and giving your reasoning on tests.

·       Rewrite your notes during the evening after a lecture.

·       Work with the concept until it becomes second nature.

·       It is key that you are the one doing the problem solving, not whoever wrote the solution manual.

·       Merely glancing at the solution to a problem and thinking you truly know it yourself is one of the most common illusions of competence in learning.

·       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.

·       Once you put the first problem or concept in your library, whatever it is, then the second concept will go in  a bit more easily.

·       Solving problems in math and science is like playing a piece on the piano. The more you practice, the firmer, darker, and stronger your mental patterns become.

·       Doing something physically active is especially helpful when you have trouble grasping a key idea.

·       Recalling material when you are outside your usual place of study helps you strengthen your grasp of the material by viewing it from a different perspective.

·       Do what you can to mix up your learning.

·       Emphasize interleaving instead of overlearning.

·       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.

·       Long sessions are fine as long as students don´t devote too much time to any one skill or concept.

·       It´s best to write the initial solution, or diagram, or concept, out by hand. There´s evidence that writing by hand helps get the ideas into mind more easily than if you type the answer.

·       A common illusion of competence is to continue practicing a technique you know, simply because it´s easy and if feels good to successfully solve problems.

·       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 learn more deeply.

·       Avoid mimicking solutions

o   Practice changing mental gears.

·       Chunks are built with:         

o   Focused attention

o   Understanding of the basic idea

o   Practice to help you gain big picture context.

o   Simple recall.

·       Mathobes (fobia de matemática)

o   Appear to avoid math because even just thinking about it seems to hurt. The pain centers of their brains light up when the contemplate working on math.

o   But, it was anticipation that was painful.

§  When mathphobes actually did math, the pain disappeared.

·       The dread of doing a task uses up more time and energy than doing the task itself.

·       You put off studying math and it becomes even more painful to think about studying.

o   Same thing with money here.

·       Procrastination is a single, monumentally important “keystone” bad habit

o   A habit, in other words, that influences many important areas of your life.

o   Change it, and a myriad of other positive changes will gradually begin to unfold.

·       The better you get at something, the more you´ll enjoy it.

·       The real reason you are doing so badly in organic chemistry is that you have been continually procrastinating.

·       The higher you go in math and science, however, the more important it is to take control of procrastination.

·       A little goes a long way.

·       Try to recall ideas in a different room, or better yet, outside.

·       Chucking, that automatically connected neural pattern that arises from frequent practice, is intimately related to habit.

·       It helps to add a new reward if you want to overcome your previous cravings.

·       Simply getting into the flow of your work can become its own reward, giving you a sense of productiveness you might not have imagined was possible when you first sat down to begin working.

·       The better you get at something, the more enjoyable it can become.

·       The most important part of changing your procrastination habit is the belief that you can do it.

·       A powerful approach is mental contrasting.

o   In this technique, you think about where you are now and contrast it with what you want to achieve.

·       Set a time for 10 minutes of work before doing things of pleasure or that you usually procrastinate with.

·       You need to focus on the process, the small chunks of time you need over days or weeks, to solve the homework problems or prepare for tests.

·       Put your best effort for a short period.

·       Deliberately put yourself under difficult tasks

·       When you multi task while doing school work you get tired more quickly.

·       Practice ignoring distractions

o   Know that it is there but continue doing the work anyway.

·       A little bit of work on something that feels painful can ultimately be very beneficial.

·       Be sure to schedule free time to nurture your diffuse mode

·       What kind of subtle change could you make in one of your current habits that could help you avoid procrastination?

o   The 10 minute studying routine.

§  Do 10 minute studying pomodoro before doing anything on the internet  or anything that is not studying.

·       Focusing on taking small, manageable steps forward and time management are key.

·       Preparation is key to success.

·       The best learners are the ones who cope best with failure and use it as a learning tool.

·       Do another repetition of the problem, paying attention to the key processes.

o   Like learning a song, do it over and over again until is perfect.

·       Sleep

o   Before you go to sleep, work on the problem again.

·       As soon as you can the next day, work the problem again.

·       Add a new problem

o   Pick another key problem and begin working on it in the same way that you did the first problem.

·       Do active repetitions

o   Mentally review key problem steps in your mind while doing something active, such as walking to the library or exercising.

·       Recalling

o   Helps you learn more effectively than simply rereading it.

o   The more effort you put into recalling material, the deeper it embeds itself into your memory.

·       Don´t feel overwhelmed with everything you need to learn about a subject.

o   Focus on nailing down a few key ideas

o   You´ll be surprised how much that simple frame can help.

·       Focus and become quicker at the hardest parts of the solution procedures you are trying to learn.

·       Write by hand

o   What is written will be retained in memory.

·       Testing

o   Is a powerful learning experience.

o   It changes and adds to what you know, also making dramatic improvements in your ability to retain the material.

·       Interaction with peers as well as instructors helps with the learning process.

·       When you are building a chunked library, it´s important to keep deliberate focus on some of the toughest concepts and aspects of problem solving.

·       If you prepare well by practicing a and building a good mental library, you will find that luck will be increasingly on your side.

·       You guarantee failure if you don´t try, but those who consistently give a good effort will experience many more successes.

·       Immense power

o   Systematically understanding and writing  each step of what I really wanted to learn.

·       Try to get the main ideas of each page you are reading cemented in you mind before you turn the page.

·       A special place devoted just to working id particularly helpful.

·       Keep notes on when you don´t complete what you had intended to complete, what the cues are, and your zombie mode habitual reaction to procrastination cues.

·       Keeping a written history over several weeks appears to be critical in helping you make changes.

·       To combat procrastination make a schedule of everything you have to do.

·       It´s important to transform distant deadlines into daily ones.

·       Pick a small portion of a task you have been avoiding.

o   Plan where and when you will tackle that portion of task.

·       Remind myself that it will pay off in the long run.

·       To be effective you must master your habits.

·       Practice ignoring distracting thoughts by simply letting them drift past.

·       Write your daily task list the day before.

·       Pausing gives you time to access your library of chunks and allows your brain to make connections between a particular problem and the bigger picture.

·       It is important not to let frustration take control and dismiss those concepts as too difficult or abstract.

·       We develop a passion for what we are good at.

·       Write your planned tasks out the night before, so your brain has time to dwell on your goals to help ensure success.

·       Deliberately delay rewards until you have finished a task.

·       We must continue jiggling and playing mentally with things we have memorized in order to form chunks.

·       Try making a very memorable visual image representing one key item you want to remember.

·       Images connect directly to your right brain´s visuospatial centers.

·       The more neural hooks you can build by evoking the senses, the easier it will be for you to recall the concept and what it means.

·       The funnier and more evocative the images, the better.

·       The Memory Palace

o   You´d imagine yourself walking through a place you know well, coupled with shockingle memorable images of what you might want to remember.

·       Using meaningful motions

o   Movement produces sensation that become part of the memory.

·       Memorization techniques remind you to make what you learn in your life meaningful, memorable, and fun.

·       It is important to make use of multiple areas of the brain when learning.

o   By using more areas of the brain while learning, we build stronger memory patterns weaving a web that is less likely to be forgotten during the stress of an exam.

·       Learning to use your memory in a more disciplined, yet creative manner helps you learn to focus your attention, even as you create wild, diffuse connections that build stronger memories.

·       By memorizing material you understand, you can internalize the material in a profound way. And you are reinforcing the mental library you need to become a genuine master of the material.

·       The better you are at spatial thinking, the more creative and innovative you will be.

·       Create a Lively Visual Metaphor or Analogy

·       Spaced Repetition to Help Lodge Ideas in Memory.

o   Repetition is important; even when you make something memorable, repetition helps get that memorable item firmly lodged in long-term memory.

·       Writing appears to help you to more deeply encode (that is, convert into neural memory structures) what you are trying to learn.

·       The more you can turn what you are trying to remember into something memorable, the easier it will be to recall.

o   You will want to say the word and its meaning aloud, to star setting auditory hooks to the material.

·       When memorizing strange names and terms, it´s always  best to practice over several days.

o   Repeat the terms out loud over a period of several days.

·       It´s much easier to remember numbers by associating them with memorable events.

·       Don´t think of lectures as lectures but as stories where there is a plot, characters, and overall purpose to the discussion.

o   The best lectures in math and science are often framed like thrillers.

·       There s a direct connection between your hand and your brain, and the act of rewriting and organizing your notes is essential.

o   Quit typing and start writing.

§  Including the annotations for books like this one.

·       Many educators have observed that there seems to be a muscle memory related to writing by hand.

·       Reading formulas or problems aloud helps them understand better.

o   Reading in a foreign language also help memorizing and internalizing the words and the sounds, as well as the meaning and intonation. (me)

·       Talk to yourself instead of just reading or highlighting the text.

·       Exercise.        

o   Several experiments in both animals and humans have found that regular exercise can make substantive improvement in your memory and learning abilities.

·       By using mental pictures instead of words to remember things, you can leap more easily into expert status.

o   The more you memorize using these innovative technique, the more creative you become.

o   Building wild, unexpected possibilities for future connections early on, even as you are first internalizing the ideas.

·       Understanding also helps a lot with the memorization process.

·       Make up a song to remember.

·       Writing and saying what you are trying to learn seems to enhance retention.

·       Exercise is powerfully important in helping your neurons to grow and make new connections.

·       Take a piece o paper and doodle to create a visual or verbal metaphor for a concept.

·       Look at a chapter in a book you reading in math or science. Create a questions about that material that would make you want to learn more about.

·       Just before you go sleep review something mentally that you are trying to learn. To boost this process, review it yet again when you first wake up.

·       Smooth repetition creates muscle memory, so that your body knows what to do from a single thought.

·       People learn by trying to make sense out of information they perceive. They rarely learn anything complex simply by having someone else tell it them.

·       Eistellung –

o   The idea you already are holding in mind blocks you from fresh thoughts.

·       Your ability to solve complex problems may make you overthink simple problems.

·       If you are one of those people who can´t hold a lot in mind at once – you lose focus and star daydreaming in lectures, and have to get to someplace quiet to focus so you can use you working memory to its maximum – well, welcome to the clan of the creative.

·       It is practice – particularly deliberate practice on the toughest aspects of the material – that can help lift average brains into the realm of those with more “natural” gifts.

·       Extremely smart people are more likely than people of normal intelligence to procrastinate because it always worked when they were growing up, which means they are less likely to learn certain critical life skills early on.

·       Think of an area where persistence has paid off for you in your life

o   English

o   Love

o   Guitar

o   Tennis bt

o   ?

·       “Deficiencies of innate ability may be compensated for through persistent hard work and concentration. One might say that work substitutes for talent, or better yet that it creates talent”

·       Practice appears to strengthen and reinforce connections between different brain regions.

·       We can make significant changes in our brain by changing how we think.

·       Chunks

·       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.

·       Once we have created a chunk as a neural patter, we can more easily pass that chuncked pattern to others.

·       Once you grasp a chunk in one subject, it is much easier for you to grasp or create a similar chunk in another subject.

·       “My own knowledge of how to learn a language helped me in learning how to learn math and science.”

·       Virtually every concept you learn has an analogy – a comparison – with something you already know.

·       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.

·       Metaphors and physical analogies from chunks that can allow ideas from very different areas to influence one another.

·       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 o help you be smarter about your approach to all sorts of life and career challenges.

·       Can you find ways to turn your disadvantages into advantages?

·       Simplify and Personalize Whatever You Are Studying

·       One of the most important things we can do when we are trying to learn math and science is to bring the abstract ideas to life in our minds.

·       Imagine the elements and mechanics you are studying as living creatures, with their own feeling and thoughts.

·       When you cultivate simple explanations by breaking down complicated material to its key elements, the result is that you have a deeper understanding of the material.

·       Understanding arises and a consequence of attempts to explain to others.

·       The challenge is that it´s often easier to pick up on a mathematical idea if it is applied directly to a concrete problem – even though that can make it more difficult to transfer the mathematical idea to new areas later.

·       Students who interrupt their work constantly not only don´t learn as deeply, but also aren´t able to transfer what little thy do learn as easily to other topics.

·       Equations are just ways of abstracting and simplifying concepts. This means that equations contain deeper meaning, similar to the depth of meaning found in poetry.

·       Transfer is the ability to take what you learn in one context and apply it to something else.

·       It´s important to grasp the chunked essence of a mathematical  concept, because then it´s easier to transfer and apply that idea in new and different ways.

·       Multitasking during the learning process means you don´t learn as deeply – this can inhibit your ability to transfer what you are learning.

·       Write a paragraph that describes how some concepts you studying could be visualized in a play.

·       Take a mathematical concept you have learned and look at a concrete example of how that concept is applied. Then step back and see if you can sense the abstract chunck of an idea underlying the application.

·       Persistence is often more important than intelligence. Approaching material with a goal of learning it on your own gives you a unique path to mastery.

·       Research has shown that students learn best when they themselves are actively engaged in the subject instead of simply listening to someone else speak.

·       Personal goals help you learn more deeply.

o   How can I reflect that in the concurso studies?

·       Taking responsibility for your own learning is one of the most important things you can do.

·       Truly great teachers make the material seem both simple and profound.

·       Failures are better teachers than success because they cause you to rethink your approach.

·       Pick a seemingly bad trait and describe how it could be beneficial in helping you learn or think creatively or independently. Could you think of a way to diminish the negative aspects of that trait even as you enhance the positive ones?

·       Learning on your own is one of the deepest, most effective ways to approach learning.

·       In learning, persistence is often far more important than intelligence.

·       Train your yourself to occasionally reach out to people you admire. You can gain wise new mentors who, with a simple sentence, can change the course of your future.

·       Explaining to friends help build your own understanding.

·       Nonjudgmental, agreeable interactions are less productive than sessions where criticism is accepted and even solicited as part of the game.

·       Working with others who aren´t afraid to disagree.

·       How can you make your study sessions with your classmates more effective?

·       Think before you calculate

·       Testing is itself an extraordinary powerful learning experience.

·       The day before a test have a quick look over the materials to brush up on them.

o   You don´t want to push your brain too hard.

·       If you prepare well by practicing and by building a strong mental library of problem-solving techniques, and approach test taking wisely, you will find that luck will increasingly be on your side.

·       Deep, practiced internalization of well understood chunks is essential to mastering math and science.

·       Students in math and science can´t develop solid neural chunks if they procrastinate in their studies.

·       Relentless focus on a problem blocks our ability to solve that problem.

·       Big-picture, long term persistence is key to success in virtually any domain

o   10 Rules of Good Studying

§  1. Use recall;

§  2. Test Yourself;

·       On everything. All the time.

§  3. Chunk your problems.

·       After you solve a problem, rehearse it.

·       Pretend it´s a song and learn to play it over and over again in your mind.

§  4. Space your repetition.

·       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.

·       After every assignment and test, go over your errors, make sure you understand why you made them, and then rework your solutions.

·       (Handwriting builds stronger neural structures in memory than typing.)

§  6. Take breaks

·       A little study every day is much better than a lot of studying all at once.

§  7. Use explanatory questioning and simple analogies.

·       The additional effort of speaking and writing allows you to more deeply encode (that is, convert into neural memory structures) what you are learning.

§  8. Focus

·       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.

§  9. Eat your frogs first

·       Do the hardest things earliest in the day, when you are fresh.

§  10. Make a mental contrast.

·       Contrast that with the dream of where your studies will take you.

·       This work will pay off both for you and those you love.

·       Read the textbook before starting working problems.

·       Clear up points of confusion.

·       You will only learn deeply if you are not constantly distracted.

·       Get enough sleep.

·       “Get good at it and then see if you still want to quit”