May 15, 2020
How we can all be fantastic mathematicians.
Although increasing in popularity, maths has had bad press. Some adults feel that ‘they just aren’t good at maths’ and with the current situation, this is becoming more relevant. As a primary school teacher, and a lover of maths, I am passionate about finding ways of making maths accessible and enjoyable to all. This article aims to highlight key ways of becoming better mathematicians than we all are already.
I can’t do this question… yet.
I believe our perspective on life and its problems determines the outcome. This particularly applies to maths. I remember at the start of the year, I had many children state that they ‘just can’t do maths’ and I had a huge battle changing their mindsets. The concept of mindset was popularised by Carol Dweck who categorised mindset into fixed mindset and growth mindset. Fixed mindset relates to a fixed way of thinking and is usually associated with negative thinking ‘I’ll never be able to complete column subtraction,’ or, ‘I can’t do this question’. Growth, on the other hand, accepts that a problem may be difficult, however they will get better or they will learn something from the process. It is based on the belief that with effort, we will become a better person and that failure is a springboard for growth in ourselves. With this form of thinking, Carol believes it is possible to tackle problems more positively allowing for a better outlook on subjects such as maths. We can change our mindset. Through repetition, people can adopt a growth mindset approach to maths and can spread this to others. The children I teach now have a better outlook on maths and will attempt questions which are unfamiliar to them. Although we have a way to go with this, I am currently teaching them strategies to help them problem solve.
One of the wonders of maths is the phenomenal number of patterns that can be spotted and used to make our maths lives easier. Times tables is a prime example of this – even though many of us have learnt these by rote, there are many different patterns. Starting off, commutativity helps us to learn double the number of facts in half the time. For example, 7 x 6 = is the same as 6 x 7 =. This means for children who feel like they don’t know their 7s, they can use their 6s.
Have a look at your phone’s keypad. Think about (or write down on some paper) your 3 times tables. Look at the ones digit on each answer, then look at the phone’s keypad. The pattern in this is the order of the digits on the keypad; 3, 6, 9, 2, 5 8, 1, 4, 7, 0 and it carries on.
Whilst you’re at it, when you’ve written the 3x tables down, next to it, write down the 7x tables. Look at the ones digit for the 7x tables. You may notice the pattern 0, 7, 4, 1, 8, 5, 2, 9, 6, 3. If you look closer, you’ll find out that this order is the reverse order for the 3x tables. This works for pairs of times tables such as 4s and 6s, 2s and 8s, 9s and 1s, and this works as those times tables, when added together, equals a number in the 10x tables! To think I spotted this pattern by accident in the middle of tutoring one of the children. These sort of discussions with children really get them excited and engaged with maths.
Draw it out
Lastly, we shouldn’t underestimate the power of drawing problems out. With younger children, I encourage them to draw and act the problem out to understand the context and therefore the method. As they grow older, I still encourage drawing problems out. Drawing bars is a very effective model to allow the child to visualise the problem with increasingly larger numbers. I would suggest researching ‘Singapore Bar Modelling’ if you would like to find out more.