The pupil, whom we'll call Simon, is 9, and did not know the 2x table two months ago - he got lost after 2x2, and guessed wildly. Yesterday, he said the 2x table up to 8x2, then got lost - not a maths problem, but one of co-ordination. Once he was back on track, he had no further problems. As we'd worked through all of the other tables, we went straight to 7x, the most difficult, as 7 is a prime, and the final digit does not repeat itself until 11x7. He got to 5x7 without error, and then got lost, so we worked on the second part of the table. Once he can say a table, he is pretty good at picking out individual items, which is the key to using tables for multiplication and division, as well as to the manipulation of fractions.

Key steps:

1. Learn to say 2x very carefully, and don't go on until it's in place with only slight hesitations. This may involve spending much more time on 2x than is usual. We do not stop at 10x, but go to 12x. Not only does this prepare for the calculation of annual rates from monthly contracts in later life, but reinforces the pattern of the first two digits in the table.

2. Move through the tables to 5x. Do not jump straight to 5x. This allows a sense of number to build as the intervals between items steadily increase. Jumping straight to larger numbers does not allow this. The "top down" approach is as fallacious in maths as in reading.

3. From 5x, go to 11x, effectively the 1x table, or counting, in two columns, then 12x, counting plus 2x table. Touch on 10 breifly, then 9x, with final digit decreasing by 1, and 8x, with final digit decreasing by 2. This section can be covered in one lesson.

4. This leaves 7x and 6x. Explain why 7x is difficult, and say it together, slowly. Depending on how quickly the child learns, either introduce 6x as something easier, or leave it until 7x is in place. Expect 7x to be learned over a few weeks with daily practice. Pick out items and simply supply them without criticism of the child does not yet know them

Now we'd got this far, we moved to calculation. Simon could add single digits, though not always reliably, particularly 6 + 7, 8+7. So, we use the trick taught to me by a parent of taking two packs of cards, removing the 10s and aces, and throwing down cards in twos and threes for the pupil to add up instantaneiously. An excellent way of speeding up knowledge and recall of addition facts.

Writing things down, Simon can add single digits, and two columns. Moving to three, he gets mixed up in moving (carrying) a unit to the next colum of tens - he both carries the unit, and inserts it into the answer. We tackle this by writing the outcome of each sub-section diagonally, so that the unit is inserted into the next column, and Simon starts to get the sums right. I give him six to do at home for practice.

The school has told his mother, "We don't do it like that. We use a numberline." The boy is nine, not six, and cannot go through life drawing a long line to add things up. HMI have said that the traditional, formal method (aka algorithm) is more efficient than the alternative. But why should the school take any notice of HMI? Ofsted, which no longer inspects standards in subjects, rated them outstanding before Christmas, and that should be the end of the matter.

Simon has read 100 pages of his relatively easy book, Diary of a Wimpy Kid. He reads three more to me, hesitating only over "wallet" and "relative", which we explain. Wallet is a word in which the letters don't tell us everything, and we explain the shortening of the a between relate and relative. Simon remembers things he's learned very well.

More on his French shortly. The school doesn't do any languages, so I do.