Do you find it hard to grasp Math and Science concepts? Or perhaps you’re already good at them and wish to get even better? In A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra), Barbara Oakley explains exactly how to do so. In this free version of A Mind for Numbers summary, you’ll learn the powerful concepts and techniques for improving math, science, and virtually any topic or area in life. The insights are relevant for students and learners of all ages who wish to learn better, faster and deeper.
Do you have a Mind for Numbers?
As a child, Barbara Oakley disliked math and science because she couldn’t grasp the technical details. After she started work, she realized that those inadequacies were limiting her career opportunities. So, she decided to rewire her brain and teach herself to get good at math and science. The more progress she made, the more she started to enjoy the subjects and the better/faster she learned.
Barbara Oakley is now a professor of engineering, and actively researches different areas ranging from engineering to humanities and social sciences. In this book, she shares learning insights from scientists, educators, students, famous inventors (such as Thomas Edison and Richard Feynman), as well as her personal experiences.
In our book summary of A Mind for Numbers, we’ve organized the key ideas into 2 parts:
• Understanding how the brain works; and
• Strategies, concepts and ingredients for learning.
Learn how to learn: Know your brain
Your brain is capable of handling complex mental calculations and problems. Each day, you’re already making countless unconscious decisions involving distances, speed, and quantities. To get better at math and science, you must learn how your brain works so you can use it to learn faster and deeper.
Focused vs Diffused Thinking
Neuroscientists found that our brain switches frequently between 2 sets of thought processes: focused thinking and diffused thinking.
The focused mode concentrates your prefrontal cortex (which handles logical, analytical thinking) to consciously target a specific issue. It’s like shining a strong beam of flashlight in the dark, and is great for intense study or execution.
The diffuse mode occurs in a more relaxed state. Your mind starts to wander, picking up scattered thoughts and ideas from different parts of the brain, and combining them creatively to arrive at fresh insights. This often happens in the background without your conscious awareness. It’s better for big-picture thinking when you’re exploring new/unfamiliar concepts.
In short, the diffuse mode allows you to quickly scan for new inputs, while the focused mode allows you to get things done. We need both modes of thinking to learn and survive.
However, you can’t apply both modes concurrently. You can only toggle repeatedly between the 2 modes: scan for data => process/integrate it => scan for more data/ideas.
To learn math and science, you need the focused mode to analyze a problem rationally and sequentially, and the diffuse mode to grasp abstract concepts like integrals or electric currents.
The 2 Key Memory Systems
Learning involves 2 key memory systems: your short-term and long-term memory. These are like your computer’s random-access memory (RAM) and hard-drive.
Your short-term memory or working memory holds whatever information you’re processing consciously. It has a limited capacity, and can hold about 4 main clusters of information at any point in time, like a juggler who can keep only 4 balls in the air.
Your long-term memory is like a warehouse that can store huge amounts of material. However, it can be hard to find a parcel of information in a room filled with parcels. To keep the memories accessible, you need to revisit them occasionally.
To learn effectively, improve your memory and how you transfer information from the short-term to long-term memory.
Learning Strategies, Concepts and Ingredients
Now that you know the basics of how your brain works, you can learn how to learn more effectively. Barbara Oakley explains several interconnected concepts about learning, and how they can be applied to math and science. In our complete A Mind for Numbers summary (get the full 16-page summary here), we’ll break down each of these concepts in detail.
In the meantime, here’s a quick synopsis:
Math and science are best learned in small daily doses so your brain has the time to absorb and internalize what you’ve learned. So, make sure you alternate between focused and diffused thinking. This is also known as “distributed practice”, i.e. taking breaks between learning sessions instead of doing mass-learning.
In our full summary for A Mind for Numbers, we’ll break down the whys and hows of distributed practice, and how it helps to prevent the “Einstellung effect” (where you get stuck because you’re fixated on a wrong approach or a flawed concept, thus blocking out better approaches or solutions).
Chunking and Practice
To get good at math and science, you must grasp the concepts, equations/formulas and recall and apply them to different types of problems. This requires both memory and understanding.
Chunks are bits of information that are connected by meaning. For example, the word “sum” comes from the letters “s”, “u” and “m”. To do a “golf swing” you must string together a series of steps from positioning yourself to moving your arms, torso, and hips.
When you first learn something new, you’re processing each step or component separately, which makes it hard and effortful. With enough practice, your brain forms neural patterns or conceptual chunks so you no longer need to remember every detail.
Chunking frees up your working memory. The more you chunk, the more easily and intuitively you can solve problems because (i) you have a larger library of mental chunks, (ii) each chunk contains more data, and (iii) it’s easier to connect between chunks.
In the complete A Mind for Numbers summary, we explain more on:
• How build chunks in 3 steps;
• How to use retrieval practice (i.e. recall or mental retrieval) to accelerate chunking;
• How to adjust your chunking practices (e.g. incorporate “interleaving”) as you become more familiar with a task or subject; and
• Why and how you should simplify and personalize abstract math/science ideas to understand and internalize them.
Improving your Memory
When you first learn or notice something, it’s stored in your working memory. To move it to your long-term memory, you must repeat the idea and make it memorable.
Instead of rote memorization, use all 5 senses to create neural hooks to “hang” your ideas. For example, you’ll remember a cow more clearly if you see, feel, hear and smell one (instead of merely seeing the word “cow”). Here, you’ll learn various memory tricks and techniques to tap into your brain’s huge visual and spatial memory. These include the “memory palace technique”, using music/rhymes, metaphors/analogies, and creating meaningful groups (e.g. acronums and stories) to string concept together.
To learn more about memory techniques, do also check out the Unlimited Memory summary.
Learning math/science is like laying a brick wall. You need brief periods of focused study to lay the neural bricks, with some time in between for the mortar to dry. Procrastination hinders learning since: (i) it leaves you with no time to explore or synthesize the concepts, and (ii) it’s harder to absorb new material when you’re stressed.
Barbara Oakley spends several chapters addressing the issue of procrastination. She explains why we procrastinate, how habits are formed, how to motivate yourself, overcome procrastination and form new habits, and even how you can create “positive procrastination” by leveraging diffuse mode thinking.
Getting the Most from “A Mind for Numbers”
Ultimately, your brain and mental capacity are not fixed. You can change your brain by changing how you think. The more you practice something, the more chunks and neural highways you build, and the easier it is to learn and solve problems. By applying the strategies and techniques in this book, you can learn more deeply and enjoy guilt-free rest and play!
If you’d like to dive into the tips and concepts above (and get additional tips on exam preparation and performance), check out the our full book summary bundle that includes an infographic, 16-page text summary, and a 25-minute audio summary!
Remember: learn at your own pace, but take full responsibilty for your own learning. The book includes numerous illustrations, examples, exercises and Q&As to help you understand and apply the insights. Barbara Oakley also includes quotes, anecdotes and ideas from students and professors who’ve applied the methods above. You can purchase the book here or visit barbaraoakley.com for more details.
About the author of A Mind for Numbers
A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra) was written by Barbara Oakley–an American professor of engineering at Oakland University and McMaster University. Oakley is involved in various areas of research from STEM education to learning practices. She was previously enlisted in the U.S. Army. She holds a B.A. inSlavic Languages and Literature, a B.S. in Electrical Engineering, an M.S. in Electrical and Computer Engineering, and a Ph.D. in Systems Engineering.
A Mind for Numbers Quotes
“We all have a natural feel and flair for math and science. Basically, we just need to master the lingo and culture.”
“It’s best to work at math and science in small doses—a little every day…That’s how solid neural structures are built.”
“Focused attention…can often help solve problems, but it can also create problems by blocking our ability to see new solutions.”
“There are hidden meanings in equations, just as there are in poetry.”
“Simple explanations are possible for almost any concept, no matter how complex.”
“Procrastination can be like taking tiny amounts of poison. It may not seem harmful at the time. But the long-term effects can be very damaging.”
“Accomplishing a lot of difficult tasks is like eating a salami. You go slice by slice—bit by bit.”
Master the learning techniques to improve math, science or any area in life!