Math is definitely not everyone’s cup of tea. Unfortunately, whether you are in school, college or even at work, you can’t escape it. Therefore, no matter how much you despise it, you have to have some sort of understanding of the basics. Most kids go through high school thinking they will never have to deal with maths again – only to head to college and realise that most degrees might actually need them to have basic math skills.
Barbara Oakley found herself in that exact predicament. She worked hard to overcome her poor relationship with math to become the engineering professor she is today. Along the way, she picked up some helpful tips to help others just like her, excel in math and science too.
In this book summary readers will discover:
- The way our brain processes learning and how sleeping helps
- What is chunking
- How to defeat procrastination
- Mental Tricks and Memorization Techniques
- Why practice and testing are important
Key lesson one: The way our brain processes learning and how sleeping helps
There are two modes of thinking that allow the human brain to learn. They are called the focused mode and the diffuse mode of thinking.
The focused mode occurs when we concentrate on something that is already a fixture in our minds. These are things which we are already comfortable with. Focused mode thinking is important for learning concepts in math and science. It is how we solve problems using rational and analytical thought. If we are already familiar with the concepts, we can call upon them when we focus on a particular problem.
Diffuse mode thinking is what we use to get a broader understanding or bigger picture view of something. It enables our minds to drift in thought as we consider something. This is also essential in learning as it allows you to obtain new perspectives regarding problems that you battling to solve. It is how we are capable of finding different methods to solving problems. Diffuse mode thinking comes in handy when you are faced with new problems that you are not familiar with. In these situations, you cannot focus on one thing and it is best to consider multiple angles.
Thus, they both have their unique functions in helping us learn. We switch between both modes constantly as we encounter different scenarios in our daily lives. However, it is important to remember that we only use one at a time – never both. This continuous switching between the two is important as it allows us to learn better by implementing both understanding and problem-solving. What information the one mode processes, it is passed to the other. This happens all day, every day.
In order for these two processes to work effectively, you need to get enough sleep. Yes, you heard right, sleep. Like any other muscle in the body, your brain also needs to rest before using it again. Sleeping also helps to clear toxins that collect in our brains when we are awake for too long. In addition, it is also known to help you retain the information you are studying, especially if you review it just before you sleep.
Thus, to understand and solve problems in math and science, you have to use these approaches. Try using both modes of thinking and if you are really battling, you might just need a little nap to refresh your brain. The most important thing is not to give up!
Key lesson two: What is chunking
Another extraordinary capability of the human mind is called chunking. It is the innate ability to process pieces of information that are connected in some way. These pieces of information are referred to as chunks. Examples of chunking are how our mind sees a forest and not individual trees, or words and not individual letters.
By storing information in chunks, the brain works more efficiently by not having to remember every single detail about a concept as long as we have the main meaning. Our brains, therefore, contain a library of chunks that we can search. Thus, when we try to solve a problem or puzzles, our brain does not just recognize specific problems but different types and classes of problems. In this manner, we are able to solve problems faster.
You can use the chunking process to your advantage when you are learning by trying to recall what you are learning. If you recall the main concepts of what you are trying to learn, it will help to build chunks that are added to your mental library. The most efficient way to build chunks is to focus on the main or basic ideas and linking them to other information you already know. This ensures that you thoroughly understand the concept.
Key lesson three: How to defeat procrastination
If you are a procrastinator, anything and everything is a temptation if you are trying to study math or science. It’s an easy pit to fall into to avoid the struggle and journey outside our comfort zones. Therefore the best defence when it comes to procrastination is a good offence.
You have to be able to prevent procrastination if you are serious about learning math and science. The best way to do this is to study in brief sessions. Think of it as building a house. You have to do everything in steps. You have to wait until one process is done before you move on to the next. You can’t build walls without the framework. Like so, your learning process needs to be spread out to allow maximum retention and minimum procrastination. If you attempt to learn everything last minute, procrastination will defeat you.
Focusing on the process of your studying rather than the product will help you defeat procrastination. If you know you have to study for one hour every day, you must put your focus on that process and not, for example, on how much content you have to study for your exam. Your approach to the one hour of study will change and you will be less likely to procrastinate.
Key lesson four: Mental Tricks and Memorization Techniques
When it comes to learning, there are simple mental tricks and memorization techniques that can be of great use. The easiest is to first figure out which learning environment suits you best. Not everyone can study in an isolated, silent place – they find the silence more distracting than helpful. Thus, identifying the environment you are most productive in is important.
Then, keep to-do lists. It’s basic but it works. Keep the lists brief and achievable and try and use them to build the other good habits you wish to have with regards to studying. Once you get used to your to-do lists, you can start setting your priorities accordingly to be more effective.
You can also practice mindfulness. Undoubtedly, you have heard of the concept of mindfulness before, but practising these techniques is extremely useful when studying. By focusing on the present moment and being completely mindful of your surroundings helps avoid distracting thoughts whilst you are studying. A good method to try is to try counting to focus your mind.
Reframing your focus by shifting your attitude from negative to positive also helps. Think of every cloud having a silver lining and try to focus on the lining. In this way, you will have a positive outlook on the situation.
Memorization techniques come in very handy in math and science. Equations can get pretty complicated and finding creative ways to remember them can actually be a fun process. You can use simple mnemonics – acronyms, metaphors or memorable sentences in order to recall what needs to be remembered. As much as the memorization techniques seem like something only kids use, they are very helpful in stimulating your thinking processes.
Key lesson five: Why practice and testing are important
Did you know people who are considered gifted or able to pick up new concepts easier are actually hindered by their talents? They have a longer working memory which is what is responsible for the stuff we are immediately and consciously processing. But this strong working memory means that they are so focused on what they are working on, new thoughts do not come through. This is why they often overthink problems, have complex thoughts and miss simple solutions.
Thus, people of average intelligence can benefit from practice and persistence. These actions work on long term memory instead. Therefore, whatever we practice is stored in our long term memory and can be easily accessed when needed. It does not get bogged down by an overly active working memory. So, don’t be disheartened if you feel like you’re not the smartest one in the class, you can achieve great results as well if you practice and exhibit persistence in your learning.
Another important aspect of learning is testing. It is not only effective in measuring how much we know but we can also learn from the process itself. Testing allows us to better retain what we have learned. This was proven in a study done by psychologists in 2009. They showed participants in the study slides of information. One group was tested at regular periods during the slideshow and the other was not. At the end of the slideshow, they were both given an exam. Those that were in the group that was tested during the slideshow performed better demonstrating what is now called the testing effect.
Testing has the added benefit of helping people deal with anxiety or stress. Sometimes math and science can be intimidating. If you don’t feel comfortable in your ability of the subject, it can lead to anxiety when faced with questions in an exam. Therefore, by becoming familiar with your body’s reaction, you can be better equipped to deal with it later on.
The key takeaway from A Mind for Numbers is:
Math and science are not easy for everyone. However, there is no need to give up on it for good. There are techniques that exist that can help you not only get better at these subjects but excel in them. The author is proof that it is very much possible. All you need is a little patience and an open mind.
How can I implement the lesson learned in A Mind for Numbers:
To eliminate procrastination, schedule your learning to occur over a longer period. You can therefore study for shorter times per day ensuring that you stay focused. Try giving yourself incentives as well. For example, if you finish a section in the time period allocated, reward yourself with a trip to the coffee shop.
