# Arithmetic

There are the traditional ways of doing arithmetic in the UK. Then there are the ways that have been introduced in the UK as part of the National Curriculum. These have revitalized the teaching and learning of mental arithmetic, in particular. Whilst the methods taught in school suit many children very well, unfortunately others can really struggle, and their parents may not really grasp they method they are trying to use. If this happens to you:

• Try asking the teacher to explain it to you! It may be very simple, and just need a couple of minutes, to clear up the confusion.
• Video links for some of the main alternatives are referenced below.

Beyond the curriculum, there are a rich variety of alternative methods. There is good reason for not covering them in school – a huge choice would be bewildering and there really isn’t time. However, in my work as a Maths Tutor, I find it can be well worth the effort to find out how the student is struggling and explore different ways of solving the same problem, until we hit one one the student really likes.

If you are struggling to recall tables facts, then print out this sheet and use it freely until you are confident you can do without it.

I can think of about 10 ways to do long multiplication for example, and they all suit different students at different stages. Some students want one, powerful, method to multiply together any two, multi-digit numbers. I would try out the “Chinese method” with them. Others refer the very simple grid method that reinforces their grasp of Place Value. Some schools insist that students use the traditional column method – with them, I carefully look at what they are doing and see where the confusion is arising and help them to become fluent. Sometimes what a student most needs is a confidence boost – in which case, a method for mentally squaring any number under 20 is fun, plus a great introduction to multiplying in algebra! Beyond those, on occasion I might use a Vedic approach,  Russian-style peasant multiplication, Trachtenburg’s wonderful method for multiplying by 11…

Division causes endless confusion for many people sometimes even when they have access to a calculator – with very good reason. The “bus stop” method which is universally taught in schools in the UK is a complex process which is often only partially remembered, and any sense of how it relates to actual mathematical problems is sometimes completely missing! I check out the absolute basic level of understanding (what does the divide symbol actually MEAN???) and, if the student has a poor recall of times tables, then I encourage them to use a printout, I can offer a powerful way of jotting any table right up to the 29 times table if they need it!

Adding is the easiest of the 4 operations for everyone – it can make a lot of sense to build on this strength, and play games to encourage lots of practice. If a student repeatedly makes mistakes when adding it could be evidence of a deeper issue with maths which needs tackling in the tutorials.

Subtraction (or taking away) can present problems to many children (and adults!) Wonderful though it would be to sweep away the traditional method and teach Scottish Subtraction in school from the start, in the real world kids may just need a much more powerful method of borrowing that the one normally taught… click here to read about it. Sometimes a problem with subtraction is actually a symptom of a genuine weakness in a child’s understanding of Place Value.

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