There is a word in the dictionary called Mathophobia which is the feeling of fear, tension and anxiety about one’s ability to do Math. Stanford Professor Jo Boaler was aghast when she saw MRIs of young student brains reacting to numbers as if they were snakes or spiders.
However, after years of research, Boaler and many other scientists have now understood that there is no such thing as a math gene or a math brain. Almost anyone can learn math, even at high levels.
So let’s delve deeper into what lessons we can learn from their scientific research and how we can ace our math exam.
1. Flashlight Modes –
In her book ‘A Mind for Numbers’ Barbara Oakley says that – imagine there is a flashlight, it has two settings
a) Focus Mode –
when we concentrate on information. This is essential for math problem solving, especially when you are practicing.
b) Diffuse Mode –
A big picture understanding – this happens when you relax your mind and let it wander a bit. This helps gain new insights into problems that you are struggling with or to understand something new.
So basically, if anyone tells you that Math is all about practice, they are not optimally using the power of the diffuse mode. Let’s take an example – ‘Thiss sentence contains threee errors’
The first two are spelling errors which are obvious with a focused approach. But what is the third error? The statement itself is untrue, there is no third error – but this becomes clear only with a diffuse approach
Barbara Oakley says that the best way to learn math is to switch between focused mode, diffuse mode and sleep mode. As much as practice is essential for us to ace our math exam, sleep is as essential to power the brain.
Stanford Professor and Researcher Jo Boaler looked at MRI scans of students working on a math problem and found that 2 out of the 5 pathways engaged were visual. She believes that visual learning and counting on fingers is a very important support for our Math learning abilities. Let’s take an example from her book
A group of students were given these shapes and asked how they believed the shapes were growing – she got very different answers, extremely creative ways of seeing the growth. And if you move the squares around and re-arrange the shapes, you will find that it actually grows like a square. And that is why this is the solution. Seeing this formation visually solidifies your understanding.
So basically, while solving a math problem, draw a diagram or a graph or a table wherever possible (even if the examiner has not asked for it). It will make your problem solving easier.
3. Deep Practice
Most people have this belief that Math is about speed and accuracy and they will tell you to do 100 math problems in a day to get practice. But research has found that Math is problem solving and real problem solving is about patient and productive failure not fast computation. It is about struggling with one problem, trying different methods, failing, trying again. If you feel like you’re just not getting it, leave it and come back to it later. Repeat the process and you’ll get it easily.
Einstein once said that ‘It’s not that I am so smart, it’s just that I stay with the problems longer’
4. Exam Strategies
I will give you three exam strategies within this overall tip
a) Calmly read the toughest problem first, now complete the easy questions before getting to these tough problem. Many people will tell you to do the easiest problem first, but there is a reason why skimming over the toughest problems in the beginning is a good idea. Because, while you are solving the easy problems, your sub conscious mind is working on the tough problems. And when you approach it later, your brain would have already worked on it and it will appear easier
b) Read each question twice and first write down all the information given in the question, line by line. And even if you don’t know the answer or how to solve it, do as many steps as you possibly can with that information. Try to draw a diagram or graph on the side as well. You will get some points for all this work
c) While revising your paper, take a different sequence. This helps your brain spot careless mistakes.
Overall, don’t be in a rush and don’t worry if someone else finishes before you.
5. Apply Math to the real world
So many times when we are struggling with math we feel like – why do I have to study all this complicated stuff, I am never going to use it in my life. Understanding the real world applications of what we study is one of best ways of making it easy to understand. Let’s do this with examples
‘The regression effect states that if a variable produces an unlikely outcome – the next outcome will be closer to the mean’
This explains why a novelists second book is usually not as good as his first breakout success OR sometimes extremely short parents will produce a child who might be taller than them, or extremely tall parents might have an offspring who is closer to the mean.
a) Useful Websites – two websites that you can use to check your steps if you are badly stuck – one is https://www.wolframalpha.com but to see the step-by-step solution you need to get the paid version. The second website is https://www.symbolab.com where entering the formulae is a little harder but you can see the steps for free. There are several other apps too but be careful that you have first tried your best, struggled a bit, and stretched yourself fully before using these solvers
b) Review your mistakes in all previous tests, exams, mid terms etc. especially before an exam.
c) Circle / highlight questions in your book which you struggled with, so that you can go over these before an exam.
And before we conclude I want to share a quote by Stephen Hawking who said that no matter how difficult life may seem, there is always something you can do and succeed. So I hope that I am able to help you succeed in Math.