**For many children, it’s important to visualise multiplication tables as they’re learning them.**

I work with pupils of all ages and often find that gaps in knowledge are down to the same factors – usually something really basic but fundamental to the understanding of mathematical concepts.

As a year six teacher (many moons ago) I had a group of pupils – all intelligent, well-behaved children – who were stuck at level 3. I was expected to teach them how to find equivalent fractions, yet these children couldn’t master basic times tables.

Within the first few minutes of an extra after-school maths session, it became clear that these children did not know what times tables were. They could recite some of the simpler ones, such as 3 x 4, but didn’t realise until shown an array of counters that this could be represented by three rows of four or four rows of three.

We often assume that, just because children tell us the answer to something, they must also understand the concept behind it. This really isn’t always the case. And without that understanding, these children were unable to make links between multiplication, division, fractions, and other essential mathematical concepts.

Now I’m working with GCSE pupils who are struggling with maths, and it’s always the same problem: a lack of basic number understanding, which means they take longer to work out calculations. A sixteen-year-old who has to count on fingers to work out 7 x 6 is going to take a lot longer to answer questions in an exam than someone who already knows the answer and who can then instantly apply that information to working out the value of *x* when 60*x* = 4200, or when 6*x* = 4.2. Even in the calculator exam, it helps if you don’t have to use the calculator for every single calculation involved in a complex problem: this saves time and minimises the probability of making an error as a result of pressing the wrong calculator buttons.

The older the pupil, the more difficult it is to get them to learn their basic number facts: really, you just have to persuade them of the value of this, and that’s no easy task.

Getting younger children to learn number facts can be fun, especially when using games, but practice must be regular so they don’t forget.

And keeping on top of this learning is essential when children leave primary school: I’ve lost count of the number of secondary pupils who say ‘I knew that in primary school but I’ve forgotten it now.’

I’m not a great fan of rote learning, but I do believe that learning off-by-heart facts such as doubling and halving, number bonds and multiplication tables are essential. Learning these basics saves time and opens doors to all kinds of more challenging number concepts.

It’s essential that we make sure children actually understand what it is they are learning, as well as why it’s useful, otherwise they will be unable to make necessary links and will struggle more as the level of maths progresses.

It’s a sad fact that schools do not have enough time to ensure every child really understands rather than just remembers facts; as parents, we need to make sure our children are equipped with the knowledge and understanding they need to retain their confidence with maths. I hope my videos will help you with that.

*Kathy*

**The Cambridge Tutor**