a_mind_for_numbers.md

A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)

By Barbara Oakley

"The Law of Serendipity: Lady Luck favors the one who tries"

Chapter 1: Open the Door

Chapter 2: Easy Does It: Why Trying Too Hard Can Sometimes Be Part of the Problem

Prime Your Mental Pump

• It helps to take a "picture walk" through the chapter as you first begin looking at a chapter or section of a book that teaches concepts of math or science
• Glance not only at the graphics, diagrams, and photos, but also at section headings, summary, and even questions at the end of the chapter

Focused Mode - A Tight Pinball Machine

• Focused mode thinking 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
• 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
• In focused mode, sometimes you inadvertenly find yourself focusing intently and trying to slove a problem using erroneous thoughts that are in a different place in the brain from the "solution thoughts you need to actually slove the problem

Diffuse Mode - A Spread-Out Pinball Machine

• Diffuse mode allows us to suddenly gain a new insight on a problem we've been struggling with and is associated with "big-picture" prespectives
• 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
• Diffuse mode is less affiliated with any one area of the brain
• Diffuse mode is useful when you are learning something new, it doesn't allow you to focus tightly and intently to slove a specific problem; It can allow you to get closer to where that solution lies because you are able to trabel much farther before running into another bumper
• The connections are further apart

Focused Vs Diffuse Mode

• You can have a concentrated beam of light that only illuminates a small area very brightly or you can have a less concentrated beam that illuminates a much broader area with a dimmer light

Pinball Machine Analogy of Focused Mode and Diffuse Mode

Why Math and Science Can Be More Challenging?

• Abstractness and encryptedness adds levels of complexity; they can make the pinball bumpers a bit spongier
• Einstellung effect - An idea you already have in mind, or your simple initial thought prevents a better idea or solution from being found
• Think of Einstellung as installing a roadblock because of the way you are initially looking at something
• One significant mistake students make in learning math and science is jumping into the water before they learn to swim

Why Are There Two Modes of Thinking?

• Vertebrates have to stay alive and pass their genes on to their offspring
• e.g A bird needs to focus tiny pieces of grain as it pecks the ground for food and scan the horizon for predators at the same time
• In humans, we see a similar splitting of brain functions
• The left side of the brain is associated with careful, focused attention, more specialized for handling sequential information and logical thinking
• The right side is more tied to diffuse scanning of the environment and interacting with other people, more associated with emotions
• To learn about and be creative in math and science, we need to strengthen and use both the focused and diffuse modes
• One mode will process the information it receives and then send the result back to the other mode

Procrastination Prelude

• When you procrastinate, you are leaving yourself only enough time to do superfical focused-mode learning
• You are also increaseing your stress level because you know you have to complete what feels like an unpleasant task
• Pomodoro technique - Set a 25 minute timer and focus on a task, reward yourself with web surfing, checking your phone etc. when the time is up

Chapter 3: Learning is Creating: Lessons from Thomas Edison’s Frying Pan

Shifting Between the Focused and Diffuse Modes

• The key is to do something else until your brain is consciously free of any thouoght of the problem
• Once you are distracted from the problem at hand, the diffuse mode has access and can begin pinging about in its big-picture way to settle on a solution
• Thomas Edison took a nap when faced with a difficult problem instead on focusing intently on it

Creativity Is about Harnessing and Extending Your Abilities

• Enlisting the diffuse mode helps you learn at a deep and creative level
• Most people think they are not creative, but we all have the ability to make new neural connections and pull from memory something that was never put there in the first place

Working Back and Forth between Modes to Master Material

• We learn a great deal from out failures in math and science; Edison is said to have noted "I have not failed, I've just found 10,000 ways that won't work."
• Mistakes are inevitable. To work past them, start early on your assignments and keep your working sessions short
• Sleep is the most effective and import factor in allowing your diffuse mode to tackle a difficult problem
• Diffuse mode is as a base station when you are mountain climbing. Base stations are essential resting spots; you use them to pause, reflect, check your gear
• Constanly lifting weights won't make your muscles any bigger - your muscles need time to rest and grow before you use them again

Duffuse Mode Tools as Rewards After Firm Focused Mode Work

General diffuse mode activators:

• Go to the gym
• Play a sport - e.g., football, basketball
• Jog, walk or swim
• Dance
• Go for a drive
• Draw or paint
• Take a bath or shower
• Listen to music, especially without words
• Play songs you know well on a musical instrument
• Meditate or pray
• Sleep (the ultimate diffuse mode) Best used briefly as rewards
• Play video games
• Surf the web
• Talk to friends
• Volunteer to help someone with a simple task
• Read a relaxing book
• Text friends
• Go to a movie or play
• Television

Don't Worry about Keeping Up with the Intellectual Joneses

• Students who are beginning to struggle in math and science often look at others who are intellectual racehorses and tell themselves they have to keep up
• Learning slowly can mean you learn more deeply than your fast thinking classmates

Avoid Einstellung (Getting Stuck)

• Chess players who experience Einstellung truly believe they are scanning the board for a different solution
• But where their eyes are moving shows that they are keeping their focus on the original solution; Not only their eyes, but their minds
• Blinking is a vital activity that provides another means of reevaluating a situation
• Closing our eyes provide a micropause that momentarily deactivates our attention and allows us to refresh and renew our consciousness and perspective; disconnect us from our focused mode perspective
• Figuring out a difficult problem or learning a new concept always requires one or more periods when you aren't consciously working on the problem
• When you turn your focused attention back to the problem, you consolidate new ideas and patterns that the diffuse mode has delivered
• The diffuse mode allow you to synthesize and incorporate the new ideas in relation to hwat you already know
• Working in the focused mode is like providing the bricks, while working in the diffuse mode is like gradually joining the bricks together with mortar
• Rising frustration is a good time out signal to shift to diffuse mode

Introduction to 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
• The working memory holds only about four chunks of information (We automatically group memory items into chunks)
• Working memory is the mental equivalent of a juggler, the four items only stay in the air because you keep adding a little energy
• You need to maintain these memories actively; otherwise, your body will divert your energy elsewhere and you will forget the information you've taken in
• You keep things in working memory through rehearsal
• Long term memory can be thought of as a storage warehouse
• 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
• When your brain first put 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
• Short term memiry = RAM, Long term memory = Hard Drive

The Importance of Sleep in Learning

• Being awake creates toxin products in your brain
• During sleep, your cells shrink, causing a 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 toxin is believed to explain why you can't think very clearly
• Sleep is a vital part of memory and learning. This sleep time tidying erases trivial aspects of memories and simultaneously strengthen areas of importance
• Your brain also reheasres some of the tougher parts of whatever you are trying to learn during sleep, going over neural patterns to deepen and strengthen them
• If you go over the material right before taking a nap, you have an increased chance of dreaming about it