Yes, you’ve heard it before… ‘Students can’t do sums anymore’.

You had heard it before, hadn’t you ? Well, just in case you hadn’t, that’s exactly what someone was telling me last night at the pub: ’Oh, you’re a Maths teacher, eh ? Well, I’ll tell you one thing, mate: kids can’t do sums anymore !’

That was just in case you hadn’t heard it before.

True or not true ? Important or not ?

The purpose of this post is not to say whether this often heard back-to-basics and anti-modern-Maths verdict is right or wrong. Although I think that the objective result of any chemical reaction deserves respect. So, if after draining 150 pounds of human meat with a few pints of beer, the only remaining Maths notion is that at least kids should be able to do sums properly, I think this solid chemical residue and manifestation of *vox populi* has a valid point.

What I want to explain in this post is WHY it is important for kids to ‘do sums properly’ – or, to put it much more accurately and appropriately, WHY it is important for kids to do sums **smartly**, and therefore WHY it is important for them to have a sound number foundation.

This is no debate between advocates of old-fashioned versus progressive education thinkers. There is actually a simple WHY that has nothing to do with ideas on education.

The following explanation refers to the Maths ability pyramid I presented in my first post, so if you haven’t read it yet, please do so by clicking here.

**The key fact on this question is that the number foundation (counting, ordering, place value system, number bonds, mental operations) is the one area of Maths that enables kids to work their way up and down the Maths ability pyramid from a very young age.**

At primary school level, children start playing with numbers (counting, ordering) and, by doing so, they are building their own mental number space (fundamentals). Then, they gradually build up on this by practising more systematic skills (basic sums, number bonds, then more elaborate sums, 4 operations).

Students enter the third level of the pyramid when they start learning to do these 4 operations in a smart way. If all operations were done using vertical addition/subtraction and long multiplication/division, there would not be any third level and it would just be skills. But when you are learning such tricks as:

- Addition by partitioning: 18 + 56
- Addition by bridging: 146 + 25
- Addition by compensating: 15 + 49
- Subtraction by partitioning: 142 – 68
- Subtraction by bridging: 165 – 86
- Subtraction by compensating: 53 – 29
- Multiplication by partitioning: 12 x 23
- Multiplication by compensating: 24 x 39
- Division by partitioning: 147 ÷ 7
- Division by compensating: 297 ÷ 3

… you are actually solving an important problem: **how can I do these operations faster, smarter and safer ?**

Basically, you are using previously learned number skills, but bringing them to another level of thinking because doing smarter sums requires such typical problem-solving skills as: choosing a strategy, finding shortcuts, consider several possible ways, etc.

In turn, this smart-sums mental activity prepares the ground for the learning of new skills, such as fractions and Bidmas. It also deepens key concepts, such as place value and number line. And by doing so, more mental images of these concepts in action are generated and this increases both confidence and capacity to focus. So students are actually working on the 3 levels of the pyramid in a dynamic way.

One last question: are number activities important for all age groups ? I mean, surely, you’re not suggesting we should go back to number bonds with GCSE students ? I guess not – although sometimes, I wonder… But Mental Maths, yes, certainly. I have recently seen a young Head of Maths starting 6^{th} form lessons with 3-4 digits random countdown. And they use calculators as well to test and check some of their ideas; so here you are, the old ‘brain versus calculator’ debate is solved on the way.

But there’s one more reason to do it this way: the number foundation of a student may be sound at primary school level, but it does not remain sound forever. It is, like all things, easily forgotten as the brain develops in different directions, and therefore has to be refreshed and practised in many different ways.

**Seeing how Mental Maths performance really plummets from Year 7 to Year 8+ in many secondary schools is really scary.** Hence the importance of constantly working on fundamentals.

Which can be a lot of fun, actually. More about this later…