When I told my wife that I was contemplating writing a maths blog, her response was genuinely warm: ‘I think that’s a good idea; you’ve got lots to offer,’ she said. This encouraged me so I went away and thought about all the possible subjects I could use for my very first post. A few days passed and then I announced my decision to her. ‘I’m going to write about the equals symbol!’ I said.
‘Sounds fascinating,’ she replied. I detected just a tad of sarcasm and my positivity diminished somewhat. I’m hoping that I just had the wrong audience so, undeterred, I have written it anyway.
The Humble Equals Symbol
A few months ago, I began a maths lesson by writing 5+3 = on the whiteboard and then asked my children to copy and complete the number sentence on their whiteboards. You could almost hear their thoughts of ‘This is easy!’ as they quickly recorded their answers and enthusiastically held them up. Unsurprisingly (and to a very small extent thankfully), pretty much every child showed me 5 + 3 = 8. I had just given them the most open-ended of tasks and yet they had all given me the same answer. They could have written 5 + 3 = 2 x 4; 5 + 3 = 20 – 12; 5 + 3 = 40 ÷ 5 or 5 + 3 = ¼ of 32 to name just a small selection of possibilities but they all answered in exactly the same way. This clearly wasn’t a coincidence.
Many children up and down the country grow up believing that when they see the equals symbol, it means that it’s time to write ‘the answer’, with whatever was on the left-hand side being seen as ‘the question’. There is a lack of understanding of what the equals symbol stands for and yet it is probably the one mathematical symbol that children write more than any other during their time at primary school.
Why does this happen?
Quite simply this happens because children get so used to always seeing = being used in the same way e.g.
6 + 5 =
12 – 8 =
7 x 3 =
49 ÷ 7 =
As a result, a missing number problem such as 5 + 3 = ? x 2 is often initially quite baffling to many children with some wanting to replace the question mark with an 8 because 5 + 3 = 8. In order to understand such a problem, children need to appreciate that the expressions on either side of the equals symbol have the same value i.e. they are equivalent. If this isn’t explicitly taught to children, they are far more likely to struggle when they first come up against algebraic expressions.
So what can we do about this widespread problem?
The good news is that it shouldn’t be a huge problem to overcome:
- Children need to be exposed to seeing the equals symbol in a variety of positions from an early age e.g. 8 = 5 + 3 not just 5 + 3 = 8. Having examples like this in a calculation policy is a really useful start.
- Explicitly teach children about what the equals symbol actually means. Maths displays often contain vocabulary for the 4 number operations but do you have the same for the equals symbol? Using pictorial representations such as a see-saw or balancing scales can also help.
- Give children missing number problems such as ? = 4 + 5 before moving on to examples such as 23 – ? = 10 + 5
- The NCETM give some great advice in their calculation guidance for primary schools document: Teach equality alongside inequality e.g. ask children to decide whether to fill the empty line with < = or > to complete examples such as
3 + 4 __ 12 – 4
On reflection my wife was probably right (and it’s not often that I say that!)
It’s not exactly fascinating stuff, but I believe that it’s certainly worthy of some thought and discussion in primary schools.