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Multiplication tables are important, not so much as a body of knowledge In themselves, but for their role in solving all types of mathematical problems.  In the national curriculum, they are not described as tables but as number facts. This is misleading, as the facts are virtually impossible to remember without some form of organisation, and are useless as an amorphous body of knowledge.  We have to be able to pick out what we want for a particular purpose.

A table consists of three types of information.  First is the key number – eg 2s or 5s – which remains constant. This might seem easy, but keeping one number constant while the numbers around it are changing poses a problem similar to that met by a drummer, who must keep his bass drum going at a steady beat while playing different patterns on the other drums.  Next, the first column in the table moves up one at each step, while the third column in the table grows in multiples.  Saying a table accurately and confidently is, therefore, a task that requires co-ordination as well as memory work. In effect, the child has to do three things at once.

I have never seen this aspect of learning tables discussed. Attention is almost always focused on the mathematical role of tables, and then usually to criticise them for constricting thought.  For the pupils I have been teaching over the past year, aged 7 to 13, the issue of co-ordination has, however, been both the source of the problem and the key to its solution. 

Every single one of them has found themselves slipping from one column to another – for example, saying two twos are four, six twos are eight, an example in which the child goes straight to the next number in the sequence of twos, without the intermediate steps, and has completely lost his place. An eight year old last night said ten twos are twenty, eleven twos are forty – doubling twenty. It took careful work and explanation to rebuild the table from 20. I disagree, incidentally, with the idea of stopping tables at 10 – their scope and children’s satisfaction in using them are greatly extended by using 11 and 12, which also unlock interesting mathematical patterns.

I have found that the solution in all cases – and six out of the eight children I’ve been working with have statements of special educational needs – has been to work on the two times table very carefully.  I explain the problem of switching between columns and getting lost, and focus very closely on those parts of the table where the child breaks down. The normal tactic is to concentrate on the table up to five times first. Then, if a child makes a mistake later in the table, I usually go back one or two places before the mistake and build up from there. It has taken one seven year old several weeks to understand where he was going wrong, and to save the two times table correctly up to five times two.  Once he could do this, however, he was able, slowly but accurately, to say the rest of the table. Other children, including a verbally very bright 10 year old, have been extremely hesitant over tables they knew in part until I have been able to get the twos right with them. They have then been able to make progress, tackling the tables that are supposed to be hardest with relative ease.

Chanting tables helps reinforce them for most children, but it is no use to children who find them difficult, as they can lean on other children’s chanting to disguise the problem. If chanting is used, someone needs to observe carefully to see who is not joining in fully, and it should be backed up by individual checks and questioning. My work with the pupils I’m currently teaching suggests strongly that the solution is to explain to the child clearly, and above all in terms he or she can understand, exactly what we are asking them to do and why.  The rest is careful, often slow, practice, backed by humour and encouragement.