A fourteen year old unable to read any text used in his school - in practical terms a complete non-reader, as the old definition of someone unable to recognise any words at all is unrealistic and useless. Explanation of English spelling, including its history and why it does not always tell us all we need to know, enabled him to read the title page and first two paragraphs of The Goalkeeper's Revenge after three lessons. This pupil could use phonics, but had to piece words together very slowly in doing so. As soon as a letter did not indicate the sound it most often did, he was completely lost. A "perfect storm" then - slow processing, combined with no ability to read any irregular words.

The solution is to unpack each spelling that is not straightforward, explain it with examples of similar words, and then to practise, so that the words become inserted in long term memory, and the pupil does not have to start working them out from scratch each time. I've divided words into three broad categorise for this purpose:

1. Completely regular - cat, catamaran.

2. Secondary phonic patterns, where a letter influences the sound of a nother - eg "soft c and g" - face, city, cycle: gentle, gin, gyrate.

3. Irregular patterns, usually historical, where the letter simply does not indicate its usual sound or where pronunciation has changed over time. Egs. was, water (from German Wasser), table (French), the (th replacing phonically regular Anglo-Saxon alternative, at behest of Norman scribes).

Words in these categories included Naughton (caught, naughty) Dalt (alter, Walter, salt) Revenge (ge) satisfied, touched (fr touchÃ©). I can't see how anyone, from a standing start, could deduce "touched" from its letters without explanation. More to come on this pupil.

Straight line graphs. These involve a simple formula, in which one item - x - is defined in a constant way against another - y. Sometimes an additional variable, m, is added to the solution, and this causes great confusion. A typical question would ask a pupil to plot X = 2y +1. The pupil would calculate the solution for two or three values of y, plot the points on a graph, and they should end up in a straight line. Pupil, however, had a problem with the difference between 2x and x squared. Leaving out the multiplication sign in what would otherwise have been written 2 (x) x was a contraction he found it hard to keep in his head. One suggestion was to have a pencil as well as a pen, and put in the multiplication sign if he was likely to forget it. In fact, a lot of practice enabled him to use the contraction and he phoned me having achieved three straight-line graphs in a row in response to questions. This took a lot of hard work, though, and the real problem was with the compaction of information in the maths. Not everyone finds it easy to hold an absent multiplication sign in their head.

Geometry. 64 year old who had struggled painfully with Euclid in his youth, spending hours and getting migraines over work which took people who knew what they were doing five minutes, obtained from the internet and understood the first three propositions, which use the fact that the radius of a cirle is the same at any pont in the circle, so that we know that one straight line is of exactly the same length as another. There are three possible sources for this individual's initial confusion - 1. He missed a lesson. 2. He wasn't paying attention. 3. The postulates and axiioms of Euclid were thought to be too obvious to be worth mentioning. At this distance in time, I really can't remember which it was...