Following previous postings on this issue, I now have direct observation of four pupils, aged eight to twelve, who have been having problems with multiplication tables. As they have all been making the same type of mistake, and have all made progress following similar teaching, I think there is the basis for a a clear statement of the problem, and of a solution.
First, the problem. As we say a table, we count in single numbers and multiples alternately. One two is two, two twos are four, three twos are six, etc. When the tables are written out, we can see two columns clearly. When we say the table, we have constantly to switch from one to the other. Children have learned to count first, and the error all four children were making was to count on by one from the last number they said, rather than going back go the singles column and counting from there. Hence J, a ten year old girl:
One two is two
Three twos are
and this morning, after she'd made some progress
Three nines are twenty-seven
Eight....
Getting the two columns mixed up is, I suggest, a co-ordination problem; all four pupils have been assessed as having varying degrees of learning difficulty, including one statement for Asberger's, one for dyslexia and one for the type of language delay that would be considered dyslexia under Sir James Rose's working definition.
The solution? Explaining to the children exactly what they are doing, and then concentrating on getting twos right, slowly, followed by calling out individual facts from the table. Once the twos are right, and facts are recalled with little or no hesitation, repeat with other tables, and not just the easiest ones. The two older pupils are now quite good on 7 and 8. J is nearly there with 2s and just slight hesitation, and the younger pupil is at a similar level. All are making progress. I'm recommending using learnyourtables.co.uk for practice, and think we're on the right road. Correspondence welcomed.