A Mind for Numbers

Simple explanations are possible for almost any concept, no matter how complex.

This is a companion book for Oakley's wildly successful online course, Learning How to Learn. Despite the name, the content is not tailored specifically for learning maths, but for learning in general.

I think it's quite worth it to internalize the ideas in this book. I took Oakley's online course during my first year in uni, and it helped me develop a systematic method of learning, and used the concepts to develop my SPM course — Atlas.

If you're interested in my 4-step system for learning anything quickly, check out my articles on studying

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🌈 3 Sentence Summary

1. Learning is a two-step process. Learn a complex topic by breaking it into little chunks of information, then finding the links between the chunks.
2. Relaxing is as important as focusing. Use focused mode to understand individual chunks, then use diffuse mode to find the links between chunks.
3. We learn by uploading information to our brain, but we memorize by downloading information out from our brains.

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💡 Thoughts

We spend our first few decades engaging in formal study. And our whole lives after that in informal learning. So, it's super important to maximize our efficiency and develop a systematic approach to learning.

This book made me realise that trying too hard can sometimes be part of the problem. Go easy on yourself. We are biological creatures with biological limits, and there are techniques to play around those limits.

I'm developing courses based on tips and tricks found in this book, and hopefully it will help others more than the traditional mode of teaching that they are currently receiving.

👤 Should You Read It?

You'll probably enjoy it if:

• If you want to maximize your results and minimize time spent studying.
• If you want to actually understand what you're learning.
• If you want to hack your brain to solve procrastination, overlearning, motivation.

Here's her talk if you want a preview of the book.

🚀 Actionable takeaways

• Alternate between periods of focused study, then relax (stop studying) to let the information sit in our subconcious mind.
• Use active recall and spaced repetition. Don't just re-read, scan through highlight, or summarize (Cornell system is way better)
• Incorporate tech tools like note-taking apps, pomodoro timers, flashcard apps into your study routine.

✍️ Summary + Notes

🧠 1. Chunking and memory

"The journey of a thousand miles begins with the first step”

This is the way to learn: Scope your subject. Break down complex topics into chunks. Learn each chunk individually. Then link these chunks together.

It's like playing a puzzle game. We have to know how the complete picture looks like. Scoping your subject helps you do that. We have to examine each piece of the puzzle individually, then find the links between each puzzle piece. We slowly complete the picture one piece at a time.

This information then goes into our short-term memory. We then need to reinforce it again after a while (following the principle of spaced repetition) to shift it into our long-term memory. At first, it's really hard to remember things. But after a bunch of active recalling and spaced repetition, it becomes as intuitive as remembering our name.

😠 2. Focused mode vs Diffuse mode

“Remember, the more effort you put into recalling material, the deeper it embeds itself into your memory.”

Learning is all about building neuronal connections. The harder it is to recall something, the more we remember it. This is why focused mode is so important.

But sometimes studying too hard is part of the problem. We need time for focused study, but also time to subconsiously digest the ideas when we're relaxed.

Focused mode is for learning about individual chunks of information, diffuse mode (relaxed) is for connecting the dots between different chunks.

🕹️ 3. Mind hacks against common problems

“It’s normal to sit down with a few negative feelings about beginning your work. It’s how you handle those feelings that matters.”

1. 🧐 Illusions of competence — We often recognise things when we re-read, scan through highlights, and summarise the text. But we go blank in exams or when someone asks what we've learned.
• Solution: Active recall. The way to memorize is not uploading information into our brains. It is to retrieve information from our brains from scratch. The Feynman Technique is a great exercise for this.
2. 🕐 Procrastination
• Solution: Develop habits (Cue, craving, response, reward). Focus on the process, not the product. Incorporate tech tools like note-taking apps, pomodoro timers, flashcard apps into your study routine.
3. 😕 Overlearning — You often start with chapter 1 in almost every study session. This means you learn chapter 1 over and over, but in the end there's no time left for the later chapters.
• Solution: Deliberate learning. Focus only on what you find difficult. Start study sessions from the hardest chapter.
4. 🪣 Bucket thinking — We can't solve a problem because we're stuck in one bucket of thinking. We forget that chunks have to be connected together. It's like there are 367 proofs for the Pythagorean Theorem (a²+b²=c²), but we only know how to use 1 method to prove it.
• Solution: Interleaving. Bounce back and forth between problems that require different chunks. Problems with different approaches, solutions, methods.

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