id: mfn title: A Mind for Numbers previous: sdl next: afh date: 2021-02-05 ---

## A Mind for Numbers

For my first look at a specific book I have decided on A Mind for Numbers by Barbara Oakley. Partially because it is a very good explanation of ideas found elsewhere and mostly because it is the first book on the subject I read and my most used by far.

Before I dove deeply into the subject of productivity (in this case specifically learning optimization) I was given this book. I was still in my undergrad studying chemistry and this book helped immensely. It was a few years before I started down the rabbit hole I find myself in today.

A Mind for Numbers specifically talks about learning math and science, however, the learning techniques help with any subject. There is a public perception of math and science being difficult so that people think that they are just not good at it and give up.

How to study is unfortunately not taught at any point in regular schooling and students are left to just figure it out. This is a huge oversight and it scares me to think how many hours have been spent in futile frustration because one was never taught how to properly study.

The way that most students study is moderately effective at best and, at worst, completely ineffective over the long term. Repeated reading and rote memorization does little to promote understanding. Cramming may help with the test the next day but the material won’t be retained for longer than that if it even makes it to the test. The reason that re reading material over and over is not helpful is that it continually reinforces the idea in short term memory and makes you feel like you know it. Stop thinking about it, and most of it will fly away. Learning retention takes time, dedication and perseverance.

Working memory is limited to somewhere between 4 and 7 items depending on the topic and the individual. Understanding an idea or concept deeply reduces the strain on this relatively limited resource. Unfortunately the times when we most feel like giving up entirely are often on the edge of the greatest shift in understanding. Learning is not a linear process, it can be characterized more like steps with rapid leaps in understanding and periods of seeming stagnation. Sometimes new information we are taking in requires our brain to restructure our understanding of the world creating the feeling of hitting a wall when trying to learn new information. Once this reorganization is complete we make that jump in understanding. ‘Chunking’ occurs when ideas coalesce together into a single concept. You have to understand the relationship between ideas to chunk them together. This is why just memorizing information won’t lead to chunks and makes recall difficult. With a chunk you no longer have to remember each idea individually, experts can’t hold more in their working memory at a time but appear to due to the library of large and complex chunks they have built up over time. They work with the concepts as a whole rather than individual ideas.

The brain has two modes of thinking, often referred to as focussed and diffuse. Focussed thinking is when we direct our attention at an idea. It gets the idea into our working memory in order to solve problems, however it limits our ability to connect various ideas. This is where diffuse mode comes in. When we are not directly focussing on anything our brain will keep working on the problem outside of our awareness. Without the laser-like focus our brain draws on knowledge from all sorts of areas and tests out the fit with other ideas, forming relationships and eventually chunks. This helps link our knowledge together, solving the problem many of us face when we think harder and harder, staying stuck on the same solution that is not working. Alternating between these two modes of thinking is the key to understanding.

When you are studying or working on a problem and you get stuck; take a break. What you do during your break is important. Stick to activities that don’t grab your attention and pull you into focussed thinking on another subject. Go for a walk, hit the gym, play with a dog or anything else that does not suck in your attention. Things like video games or the internet will pull your attention away from the problem but focusses your thinking and will not let you reach the diffuse state you need. The break should be long enough that you are no longer actively thinking about the problem, usually a couple hours. When you come back to it you will often find that you leap ahead in your progress and understand the concept more deeply.

Long term memory is reinforced by repeatedly recalling information. This learning tool is ‘spaced repetition’. You have to wait long enough for it to move from your working memory, then come back to it the next day and try to remember it without looking at your text. Only use the text to confirm if you are right and correct if you are wrong. When first learning a new subject you want to revisit it daily, then space out the repetition more and more. In order to keep the new information in your long term memory you need to revisit it periodically to reinforce the memory. As the connections get stronger you need to revisit it less and less.

‘Interleaving’ is a tool of learning that involves alternating between two different but somewhat related topics in your studying. This is opposed to doing one thing over and over until you feel that you get it. Interleaving helps with memory because each time you move back to a topic you have to pull all the relevant information from your long term memory back into your working memory. It works like spaced repetition explained above but within a single study session. The new topic helps get the old one out of your working memory in less time. This helps understanding by increasing your exposure to different types of problems. Understanding learning techniques allows you to know when to pull a particular tool out of your toolbox, and how they can fit together.

A good test to see if you understand a subject (and a great tool for studying) to explain it to someone with little to no background in the field. If you can explain it in a way that they can understand you have a very good grasp of it yourself.

Studying for memory and understanding requires spreading out the same amount of studying time across a much longer period so that the information can be assimilated. This makes procrastination the largest enemy of learning. Even if it is just for a short time each day you will retain more than trying to cram the night before a test. Periods of intense focus (without distraction) are needed to properly learn and understand anything. This works along with the breaks to form the connections and incorporate the new information into your understanding of the world.

A Mind for Numbers also covers test taking, overcoming procrastination, why we procrastinate, the importance of sleep in learning and various memory tricks such as: visualization and the famous “memory palace” technique. It goes into depth on all these subjects and has very helpful diagrams and illustrations that help understanding. Of all the books on learning that I have read I think it is the most beginner friendly with helpful suggestions and exercises as opposed to just giving the reader the information.

Books like this do their part to fix the problem of studying faced by students everywhere. The more that we know of and use them the better off we will all be. So if this sounds interesting to you take a look at the book A Mind for Numbers and save on time and frustration when learning something new.