Last updated April 10, 2022

Status:: #literature/books/finished Author:: Medium:: { Books MOC Tags:: Links: { A Mind for Numbers Application

{ A Mind for Numbers

2 - Modes of Thinking

Reading Ahead/Skimming

You’ll be surprised at how spending a minute or two glancing ahead before you read in depth will help you organize your thoughts. You’re creating little neural hooks to hang your thinking on, making it easier to grasp the concepts. — location: 304 ^ref-32220

Change between thinking modes

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. The diffuse mode does seem to be able to work quietly in the background on something you are not actively focusing on.3 Sometimes you may also flicker for a rapid moment to diffuse-mode thinking. Focused-mode — location: 311 ^ref-64766

Focused Thinking

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.4 Turn your attention to something and bam—the focused mode is on, like the tight, penetrating beam of a flashlight. — location: 314 ^ref-14103

When you focus on something, the consciously attentive prefrontal cortex automatically sends out signals along neural pathways. These signals link different areas of your brain related to what you’re thinking about. This process is a little like an octopus that sends its tentacles to different areas of its surroundings to fiddle with whatever it’s working on. — location: 346 ^ref-5446

the focused mode is used to concentrate on something that’s already tightly connected in your mind, often because you are familiar and comfortable with the underlying concepts. — location: 340 ^ref-26512

Diffuse Thinking

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 of the brain—you can think of it as being “diffused” throughout the brain. — location: 321 ^ref-6776

In our pinball analogy, it’s as if the abstractness and encryptedness of math can make the pinball bumpers a bit spongier—it takes extra practice for the bumpers to harden and the pinball to bounce properly. — location: 376 ^ref-20151

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: 408 ^ref-24813

The harder you push your brain to come up with something creative, the less creative your ideas will be. — location: 416 ^ref-57687

Einstellung Effect

Einstellung effect (pronounced EYE-nshtellung). In this phenomenon, an idea you already have in mind, or your simple initial thought, prevents a better idea or solution from being found. — location: 379 ^ref-21682

Excerpt

• Always seek new perspectives when you don’t understand
• Find an activity to take a break with like driving
  • Just has to be something that will completely distract you from what you were previously doing
    • Bed, bath, bus

3 - Learning is Creating

• do math and science in small doses
• review material within a day oops
  • always review material the night of or after learning new material?

Work sessions and breaks

• Keep focused work sessions short to allow to not get too tunneled
• allow for the creative break sessions
  • Learning continues the back and forth between the two modes
• Be careful of considering switching to learning something else new is a break, as it’s still using the same energy?
  • Recharge by talking or doing something familiar
• Examples
  • Fitness
  • Instrumental music
  • Meditate
  • Sleep
  • Potentially focusing activities
    • Games
    • Web surfing
    • Friends
    • Reading

One of the most important tricks that helped me retool my brain was learning to avoid the temptation to take too many math and science classes at once.

Fighting persistence

• If you usually like to last longer and are persistent, have an external clock to guide you

memory types

• working memory
  • acts as a mental blackboard to juggle ideas together

4 - Chunking and Competence Illusions

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

Forming chunks in math and science

• A chunk could be how to solve a specific problem
  • Memory trace
  • Goal is to have chunks stored in long-term memory

Steps to chunking

• Solely focus on what you want to chunk
  • No distractions, octopus should have all tentacles on the task at hand
• Understand the basic idea
• Gain context to know when its needed through practice
• active recall to fortify

Types of learning

• bottom up, practice and repttition

• top down big picture, see where things fit in

• both are necessary for mastery, connected through context

• Even if we miss a few pieces, we can see the main picture in a puzzle

• Only highlight one sentence max per paragraph, esp those that synethsize concepts

• recall

“Getting a concept in class versus being able to apply it to a genuine physical problem is the difference between a simple student and a full-blown scientist or engineer. The only way I know of to make that jump is to work with the concept until it becomes second nature, so you can begin to use it like a tool.” — Thomas Day, Professor of Audio Engineering, McNally Smith College of Music

If you work a problem by just looking at the solution, and then tell yourself, “Oh yeah, I see why they did that,” then the solution is not really yours—you’ve done almost nothing to knit the concepts into your underlying neurocircuitry. 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.

• Math takes a lot of set-up time, but once you master it, it becomes compressed and easily retrievable

  • Days spent learning a single topic can eventually be recalled instantaneously to be used in a different concept

• Concept maps are questionable because if you try to “build connections between chunks before the basic chunks are embedded in the brain, it doesn’t work as well.”

When you practice every day the information is just there—you do not have to search for it

• Intuitively unconscious

Recall

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

• Helps account for when testing environments are different
• Flashcards on the bus !

Interleaving

doing too many problems of the same kind in immediate succession provides diminishing returns.

• Several short sessions focused on different topics

Doing problems

• Make sure you’re not just copying what you did the previous problem, and that you’re still actively engaged
• After finishing a problem, ask yourself what’s special about this problem to make you do a specific procedure?

Students need to think of every homework problem in terms of test preparation and not as part of a task they are trying to complete

Excerpt

Paul’s advice for limited time

1. Read (but don’t yet solve) assigned homework and practice exams/quizzes
2. Review lecture notes, review notes next day, ask questions after
3. Only do things with solutions so you know if you’re right
4. Assignments and practice quiz

5 - Procrastination

• Don’t waste willpower on procrastination because of its demand

• Addictive qualities of distraction

  • Cope by saying you’ll forget if you start early
  • Cramming and hoping is like gambling on the material covered and the difficulty

• Procrastination prevents us from engaging our diffuse mode of thinking

  when you procrastinate, you are leaving yourself only enough time to do superficial focused-mode learning.

6 - Habit of Procrastination

• Generic cue, routine, reward, belief
  • Find what makes you procrastinate
    • About to start assignment? Seeing schedule? Distracted by discord?
    • Develop new cues instead
    • Come up with external reward if it’s important
    • Believe your new system works and is better
      • Contrast it with your previous self
• Focus less on product and more on process
  • Less intimidating, encourages small steps

Next time you feel the urge to check your messages, pause and examine the feeling. Acknowledge it. Then ignore it. Practice ignoring distractions. It is a far more powerful technique than trying to will yourself to not feel those distractions in the first place.

Excerpt

• Guy who had 0.4 GPA

We all have a failure rate. You will fail. So control your failures. That is why we do homework—to exhaust our failure rate.

• Fail during practice

7 - Chunking vs choking

Steps to Chunking

• Work through a problem all the way
  • Don’t skip steps or prematurely look
  • Make sure you understand each step
• Do another repetition and focus on key processes
• Break, Sleep
• Again
• Add a new problem
• Think about steps while doing other things like fitness
  • Flashcards

8 - Tools, tips, tricks

A last important trick is to reframe your focus. One student, for example, is able to get himself up at four thirty each weekday morning, not by thinking about how tired he is when he wakes but about how good breakfast will be.

• Reward myself with chocolate for getting up
  • Think about how tasty my breakfast smoothies are yum
• Self-experimentation on procrastination habits to see what works
  • haven’t been adressing it huh
• be more specific with task delegation in the morning

11 - More memory tips

• metaphors

17 - Test taking

Checklist

Answer “Yes” only if you usually did the things described (as opposed to occasionally or never). Homework

_Yes _No 1. Did you make a serious effort to understand the text? (Just hunting for relevant worked-out examples doesn’t count.)

_Yes _No 2. Did you work with classmates on homework problems, or at least check your solutions with others?

_Yes _No 3. Did you attempt to outline every homework problem solution before working with classmates?

Test Preparation

The more “Yes” responses you recorded, the better your preparation for the test. If you recorded two or more “No” responses, think seriously about making some changes in how you prepare for the next test.

_Yes _No 4. Did you participate actively in homework group discussions (contributing ideas, asking questions)?

_Yes _No 5. Did you consult with the instructor or teaching assistants when you were having trouble with something?

_Yes _No 6. Did you understand ALL of your homework problem solutions when they were handed in?

_Yes _No 7. Did you ask in class for explanations of homework problem solutions that weren’t clear to you?

_Yes _No 8. If you had a study guide, did you carefully go through it before the test and convince yourself that you could do everything on it?

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

_Yes _No 10. Did you go over the study guide and problems with classmates and quiz one another?

_Yes _No 11. If there was a review session before the test, did you attend it and ask questions about anything you weren’t sure about?

_Yes _No 12. Did you get a reasonable night’s sleep before the test? (If your answer is no, your answers to 1–11 may not matter.)

_Yes No TOTALz

Test Taking

• Find hardest question, work on it for 1-2 minutes until you get stuck
  • Loads problem into mind, and switches to allow for diffuse mode
  • Switch to an easier problem, and return later
• Keep repeating
  • Just be sure to have discipline to pull off problem

Coping

• Just say that if you don’t get good grades, you can switch careers
• Breathe vs mindfulness

You’ll need both your focused-mode and diffuse mode “muscles” the next day, so you don’t want to push your brain too hard.

• Really criticize your answers from a higher-order perspective

if you write about your thoughts and feelings about an upcoming test immediately before you take the test, it can lessen the negative impact of pressure on performance

• already attended, less likely to pop back up

• pause

18 - Unlock potential

A central theme of this book is the paradoxical nature of learning. Focused attention is indispensable for problem solving—yet it can also block our ability to solve problems. Persistence is key—but it can also leave us unnecessarily pounding our heads. Memorization is a critical aspect of acquiring expertise—but it can also keep us focused on the trees instead of the forest. Metaphor allows us to acquire new concepts—but it can also keep us wedded to faulty conceptions.

10 Quick Tips

Use as checklist to make sure

• Recall after consumption and during the night
• Test
• Chunk
• Spaced reps
• Interleave
• Breaks
• Simple analogies
• Focused environment
• Eat frogs
• Mental contrast

10 Quick Dangers

• Rereading
• Too many highlights
• Confident observation
• Cramming
• Blocked practice
• Leisure study time
• Application before theory
• Not asking for help
• Constant distraction
• No sleep

Afterword

After all, isn’t education supposed to be about getting good at challenging things?

Backlinks

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Created:: 2022-03-17 17:03