A Mind for Numbers by Barbara Oakley

The Book in Two Sentences

Our educational goals are fundamentally at odds with the cultural values they seek to promote. Can we still study what we want and enjoy doing it in spite of this?

A Mind For Numbers Summary

Disclaimer: these are my notes from A Mind For Numbers by Barbara Oakley. This summary may contain my own ideas, references to other resources, as well as passages from the book.
We have unaligned goals. We want to learn, but we also need to get educated.
Educational institutions are not designed to give students the time they need for complete mastery of material. Instead, students are shuffled from topic to topic and many are left unequipped for dealing with the more difficult problems they encounter.
Directness. Practice what's graded. If your classes grading scheme consists of tests, then that should be your primary focus when studying.
Pianists don't merely practise a piece once and call it a day. Similarly, you should work through a problem several times to ensure that you can complete it correctly on an exam.
Try to explain what you're learning to someone else or yourself. You'll be surprised how clarifying it can be.
If you're feeling frustrated with a subject, don't focus on everything you need to learn. Nailing down a small subset of key ideas can really help.
"Learning organic chemistry is not any more challenging than getting to know some new characters. The elements each have their own unique personalities. The more you understand those personalities, the more you will be able to read their situations and predict the outcomes of reactions.” —Kathleen Nolta, Ph.D., Senior Lecturer in Chemistry"
You can make up for deficiencies in innate ability with sustained effort. Until you try, there is no use comparing different people.
The Law of Serendipity. Undoubtedly, some people are luckier than others, but luck tends to favour those who try.
There are two modes of processing, focused and diffuse. Learning requires alternation between the two.
The focused mode is active and narrow, which we experience as flow and concentration.
The diffused mode is loose and broad, and occurs during activities such as running, driving and showering.
Negative thoughts and emotions are part of the learning process, so the ability to patiently chip away at a problem without giving into negative self-talk is crucial.
Too much time in the focused mode can lead to irritability. When you feel that you are growing increasingly frustrated, that is a cue to switch to something more diffuse.
Learning something new is like exercising in the gym in two important ways.
Recall is the cognitive equivalent of a bicep curl. The greater the mental strain required to study something, the heavier its mental "weight" (recall > recognition).
Rest is as important as exercise. We tend to think that we need only be focused, but just as muscle growth happens during recovery, the mind also needs time in the diffused mode in order for new connections to be made.
Einstellung effect. Too much time spent focusing can prevent you from reaching the best solution or a working solution altogether.
You can't force insight and creativity. Moments of eureka tend to occur during periods of diffuse processing (such as shower thoughts), only when initial investments in focus have already been made.
"There is a deep connection between technical, scientific, and artistic creativity."
When we are learning something new, the ideas are stored in limited working memory. We can comfortably store about 7 ± 2 items.
Avoid multitasking, particularly for difficult subjects that require a lot of working memory, because doing so will fill those spots and prevent you from reaching deeper levels of focus.
Chunking is when you take a number of discrete facts, and wrap them in some sort of conceptual understanding. Doing so allows you to hold more ideas in your working memory, opening doors to more difficult topics.
Ideas are said to be encoded when they move from working memory to long term storage.
Chunks are abstractions. Good abstractions help us see new subjects from a different perspective, which is why inter-disciplinarians are so valuable.
Focused processing is used to form new chunks. Diffused processing is used to bring two or more chunks together in new and interesting ways.
Treat habits as energy savers.
To increase the chance that you'll stick with studying, limit the amount of frustration you feel when doing so. If you find it too difficult to study because of negative feelings and emotions, then find ways of making it more easy and satisfying.
Avoid your memory becoming context dependent. Studying too much in one place can lead to information being tied up to a particular environment. This is why it's a good idea to recall material outside of your usual place of study.

👋 Thanks for making it to the end!