To take the last pupil first, the parent who wrote me the kind email two postings below brought her daughter, aged nine, one of the quickest learning pupils I've known. Explaining English spelling took about twenty minutes, and she was able to apply the principles immediately. The pupil had been taught little or no phonics, and was using her high intelligence to guess at things. She had worked out some patterns - eg ea in sea, tea etc, but not in head, bread etc, and did now know ou (ground, found) or ow. own. The explanation that voice letters - vowels -are overworked, and that we need to know what they are telling us in particular words, did the trick, and we worked on each pattern that she did not know as they arose in the text - this is a perfectly reliable way of covering phonics, as the patterns are so imbued in the language that they will all turn up in a few pages of text. In this case, we used the first book of the Narnia series.
The approach also avoids a huge snag that arises in using simplified texts that focus on just one pattern at a time - when we read, we need to recognise and use each pattern quickly, with immediate support of a whole series of the same words. Too many phonics schemes do not enable the learner to do this.
Mother and daughter set off on their two-hour drive home with a happy wave, and left us with a request to see her nephew, and a cake.
Pupil 2 was having trouble with arithmetic, his teacher no doubt having seen that moving him from simple division to three places of decimals last week was too big a jump. We went back over smple division, and worked out the steps he needed to take, as follows (in shorthand):
To divide, say 162 by 8:
Set out the bus stop
Try - find the first number 8 will go into - in practice, move along the line till you reach a number that is 8 or over. It helps to add a zero each time you can't divide a number - doing this in the hundreds column is redundant, but helps you remember to do it later on, when it is important.
Add to the answer (in the correct column, on the bus stop roof)
Multiply what you've added to the answer by 8
Subtract from the number we are dividing
Bring down the next digit
Repeat
So, dividing even by a single digit number takes five steps that have to be repeated accurately and in order. Understanding the importance of columns in denoting tens, hundreds etc is important, but you also need to make sure you don't miss a step, put a figure in the wrong place, or take away the wrong number. These are matters of co-ordination rather than maths - we have to know in our mind exactly which stage of the process we are at, and not lose our place.
We made some progress - the pupil can use his tables, if hesitantly, and understands correcting to to places of decimals. We will see if he manages the half dozen I left him for homework, using the steps as set out on a card. One thing is certain - if you don't know your tables, and can't subtract accurately, you can't do division at all, which may be why it has been abandoned in so much of primary mathematics.
Pupil one is preparing for entry to a local private school, and is not being taught to write properly at his primary school - in effect, he is doing very little writing at all. I'm using the Galore Park English books with him, selectively - even they are capable of occasional improvement - and he is beginning to control punctuation, though he slips from past to present time without knowing what he's doing. He is ten, and the Galore Park book is designed for seven year olds, but we have to start with what he already understands. My thoughts on presenting grammar in ways that are easier for children to understand are here.