A Mind For Numbers

Easy Does It

• Prime mental pump by skimming chapter ahead
• Brain switches between focused mode and diffuse mode
  • Focused mode: studying math and science. For well-trodden problem
  • Diffuse mode: gains new insight for problem. Turn away focus
• Einstellung effect: idea already in mind prevents new idea. Solution modes
  • Often seen when people work on homework without instruction
• Procrastination: superficial focus
  • Use Pomodoro/focus techniques

Learning is Creating

• Switch to diffuse by doing something else to occupy brain
  • Ex: naps with Edison and Dali
• Start assignments early and work on short periods with breaks
• Do not try to keep up with intellectual racehorses
  • Having own pace → understand problem better
• Avoid Eistellung by doing something else
• Learning new concepts: don’t leave it for a day, but do take breaks
• If super stumped
  • Listen to others if they sense your frustation
  • Wrestle with problem by asking people
• Memory types
  • Working memory: immediately holds 4 chunks of information
  • Long-term memory: storage warehouse
• Move things from working memory to long term memory by spaced repetition
• Naps: make dark room, breathe slowly, only for 20 minutes
• Sleep tidies memories and strengthens new connections
  • If you review problem before you sleep, you will solve parts of it in your sleep

Chunking and Avoiding Illusions of Competence

• Chunking helps you understand big picture
• Steps:

1. Focus and eliminate background distractions
2. Understand: test yourself
3. Gain context and understand when to use chunk
   1. Top down approach. Combine with bottom up approach of practice

• Recall >> rerearding
  • Only highlight main ideas, dont highlight useless details
  • Always do problem yourself. Do not copy answers
  • Do recall practice ASAP. Eg. Rewrite notes when you return home
  • Use Anki. Take any concept —> read —> close book —> recall
  • Recall practice helps transition chunks to long-term
• Need to master recall and chunking to do well
• Cannot grasp chunk: work from inventor/scientists —> modern and understand why that progression occured
• Practice: spaced reptition, different problems, skim before, recall in different contexts
  • Different problems: important in understanding when to use chunk.
  • Use index cards for problem strategies. Flip to sample problems

Preventing Procrastination

• Procrastination only for things that we percieve as painful
  • Habit with cue, routine, reward and belief that it will never change
• Apply willpower to change reaction to cue
  • Cue: identify and remove old cues with better ones
  • Routine: rewire by having a plan. Remove parts of old habit gradually
  • Reward identify why you procrastinate and use a new rewards
  • Belief: start believing in new habits. Contrast current state with goal
• Focus on process, not product, to beat procrastination
  • Pomodoro: little bit of stress —> learning bette
  • Ignore distractions (noise cancelling headphones) and do not multitask
• If you find yourself reereading paragraphs or featherbrained, do some physical exercise

Chunking vs. Choking

• Steps to build a powerful chunk:

1. Work through key problems all the way: understand each step and do not look at solutions
2. Do another repetition and break
3. Sleep: before sleep, do another rep
4. After wakeup, do another rep: lighten up on computation and focus on hardest aspect of problem
5. Add another problem
6. Do active reps: go over steps when active/waiting

• Takes time so do for key problems and difficult parts
• Sometimes will hit wall and wont make sense. Be patient
• Organize materials and handrwritten notes
• Choking: chunks too much and working memomry full
  • Solution: do mini tests to focus on which chunks are most important

Tools, Tips and Tricks

• Put yourself in new surrounding, like library, to get effective studying done
• Meditation is useful in drowning out distraction
• Reframe focus: think of actions in new way (4:30 isnt a wakeup, its to prepare for breakfast)
• Keep close tabs on procrastination and journal why you did or didnt procrastination
• Do weekly and daily to-do list night before
  • Have a quitting time —> much more effective
• Translate big deadlines into little small deadlines

Procrastination Zombie Wrap-Up

• Staying in zone will lead to productivity drop
  • Do not solely rely on deadlines to keep you accountable
• Pause and reflect is impprtant technique to fight procrastination
  • Helps clarify problem before you start

Enhancing Your Memory

• Use memorable visuals to memoraize touch concets
• Use Memory Palace with practice mental walks
  • Use mnemonics and put visuals with similar mnemonics in conspicous place
• Use multiple senses and exercise
• Use metapors and analogies
• To move memories into long term memories, the memory has to be memorable and be repeated
  • Flashcard and writing helps immensely
  • Repeat flashcards over few days and start spacing
• Group concepts into memorable line , image or mnemonic
• Create stories out of concepts

Learning to Appreciate Your Talent

• Work towards intuitive understanding to stop memorizing
• Deliberate practice pushes average mind into elite

Sculpting Your Brain

• Chunk abstract ideas in metaphors and analogies

Developing the Mind’s Eye Through Equation poems

• Think of equation in real life
  • Don’t just memorize; understand
• Personalize and visualize equations
• Learn abstractness of math to apply in dif. contexts

Renaissance Learning

• Persistence > intelligence
• Key to great path in math ad science if you can learn by yourself and seek out new connections
• Find out teachers and mentors
  • Ask to-the-point questions and always thank
  • Never say that they are wrong
• Note that many teachers look at books outside of suggested readings to create tests
• Be careful around intellectual snipers who demean others
  • Use other people: classmates, visiting instructors
  • Master dispassion: do not pay attention to under cutters
  • Use natural contrariness as secret weapon

Avoiding Overconfidence

• Always vet work and truly understand how it works in broad area
  • Dont just follow equaton sheet, recheck
• Use friends to check over work
  • Number of aquaintances makes huge difference in life
  • Should allow criticism —> more productive
• Tip: for intuitively hard problems, consider behaviour of problem at 0 or infinity

Test Taking:

• Testing is very powerful learning experience
• Checklist
  • Homework
    • Understood text
    • Check solutions with others
    • Outline homework problems before working with others
  • Preparation
    • Participate actively in homework group discussions
    • Consult with instructor when you have problem
    • Understand all hmwk problem solutins
    • Ask for explanations of homework in class
    • If there is a study guide, understand every part of it
    • Outline solutions not algebra
    • Go over study guide/problems with someone else and quiz
    • Attend test review sessions
    • Get good sleep
• Look through test —> try difficult questions —> move to easier question to activate diffuse. Alternate
  • Only do this is if difficult problems are valuable
• Always have a plan B on mind for career —> stress down
• If test = panic —> focus on breath
• Use mindfulness to disassociate from events with bad thought
• In multiple choice: make answer before you choose
• Relax day of big exam
• Key to checking: change perspectives (work back to front)

Unlock Your Potential

• Key is patient persistence and simplicity (explain concepts simply)
• Ten rules of good studying

1. Use recall whenever you can
2. Test yourself
3. Chunk problems so you know how to solve them cold
4. Spaced repetition
5. Mix up problem solving techniques via flash cards
6. Take breaks for diffuse mode activation
7. Use explantory questions and simple analogies
8. Focus
9. Do hardest in the beginning of the day
10. Mental contrast

• Read textbook before going into problem