**Maths**

Following on from this post, the 1 2 3 5 4 thing sorted itself out pretty quickly (without intervention, incidentally). The synaesthesia receded in importance, and the Numberjacks mania played itself out. So, thankfully, did the bit with me writing out pages full of numbers for the Oyster to colour in. He occasionally does that himself these days. Sometimes he just does the multiples of 11, because he likes them. He went through a brief phase of writing out the times table (or as he put it, a row of "counting in ones", a row of "counting in twos", a row of "counting in threes", and so on), but that petered out fairly quickly. He knows most of the products up to around 100, I think.

He spent a week or two as an infinity denier. At first he decided that the highest number was called Niall (love that!), and that Niall plus 1 was 0. I think he now gets that you can never stop counting. He's interested in very large numbers. He likes billions and trillions and quadrillions and bazillions. I like the way that even though a bazillion doesn't exist, we can still make statements about it (e.g. it's even, it's a multiple of 10, it's a positive integer greater than a trillion, it's 1 followed by a multiple of 3 zeroes, and so on).

He knows that there are numbers between the integers, but we haven't really got into how that works yet.

He's reasonably solid on place value, as far as I can tell. Sometimes he writes out columns of numbers where column 1 is the numbers from 1 to 9, column 2 is 10 20 30 ... 90, column 3 is 100 200 300 ... 900, and so on. Sometimes we multiply numbers by 2 until we exhaust first his capacity, then mine (to do it without stopping to concentrate or write it down, I mean), then my calculator's (to display the result without resorting to scientific notation). He really likes asking me sums, or having a repeated joke such as "What's 55 plus 55 - is it tenty-ten? *giggle*"

Did you know that if

*x*squared is

*y*, then

*(x + 1)*squared is

*y + 2x + 1*? (For example, 6 squared is 36, and 7 squared is 36 + 12 + 1.) I didn't, until the Oyster got me doing squares in my head (while driving - not recommended!) up to 30 or so.

He has the hang of the number line, and can add and subtract small positive and negative numbers fairly easily, particularly if he has a number line in front of him. His mental arithmetic above 0 is pretty good. "What's 54 plus 35 ... is it 89?" he'll say, or "Is 88 plus 88 176?" Béar Eile (his special bear) turned 107 at the weekend, and he accurately added up the ages of all the humans in the house, then had a reasonable stab at calculating the difference between that number (75, for those following along at home) and 107.

Today's little nugget was when he was counting a page full of pictures, and he counted across the first row of twelve, began to count the second row, then checked himself and counted the number of rows instead. "Four twelves, what's that? Is it 48?"

He has some grasp of bases other than 10. When he was talking to Niall about them, he observed that for base 5, you only need the numbers 0 to 4 to write any number. When the Erisian was visiting, he taught the Oyster about binary - and showed him how to count to 31 on the fingers of one hand. I'm not sure how much of that stayed in, but he appeared to grasp it - and at least when he encounters it again it'll be familiar.

It was also while the Erisian was here that the Oyster asked, "Do all the twelve numbers do that thing where ... like, 1 plus 1 is 2, and 1 2 is 12; 2 plus 2 is 4, and 2 4 is 24?" Turns out they do, as long as you put the original number in the tens column and add it to whatever's there (e.g. 5 plus 5 is 10, and (5+1) 0 is 60; 6 plus 6 is 12, and (6 + 1) 2 is 72). Not sure how far up that goes. But we were very tickled that he'd noticed.

My parents got him a 1st class maths book as a present. He takes it out a couple of times a week and does a few pages of exercises. He's done them easily, so far, once I've read the instructions to him. Mostly, what confuses him is the part about being required to demonstrate how he's getting his answers. The first module dealt exclusively with addition of two numbers with an answer of 10 or less. A few pages later, there were sums with an answer of 11 or 12. Later still, the sums had answers of 13 or 14. He's now even done some where you add more than two numbers. He flipped to the middle of the book and found sums demonstrating place value with columns of dots, and sums to calculate how much change you'd have from 10 cents if you bought an item with a given price.

If he were in school, this would be the book for his third year. To me, this seems generally supportive of our hypothesis that being home-educated is unlikely to lead to academic disadvantage for our children. Actually, what I love about the Oyster's engagement with maths is that from my perspective, it seems that he's Doing Numbers in exactly the same way that he Did Trains a while ago, or Did Robin Hood earlier this year. He's following what fascinates him, in other words, which is the key idea. It's kind of thrilling to see it in action.

**Books**

There is rather less to say about books, other than that the Oyster is an enviably prolific author. He has written books about Robin Hood, books about dragons, books about trains, monsters, aliens, dinosaurs, knights, numbers. He has written books in A4 and A5 size (stapled by patient relatives, often with several stapled booklets taped together); he has written tiny little books in A7 size (painstakingly assembled by me - so far, a 100-pager and a 256-pager, with cardboard covers).

By "written", I mean that generally he draws the pictures first, then asks for the spellings to write the words (which often go in speech bubbles). Recently, he has been asking only for the words he doesn't know - he can do "the", "and", "of", "book", among others, without assistance. Also, I've adopted the strategy of writing out the phrase he wants on a scrap piece of paper for him to copy, which is less hair-tearingly tedious than calling out the letters in batches of three or four.

Before beginning to write, however, the srs bsns of putting the book together must be completed. Page numbers are very important. So are front and back covers, end-papers, and the contents page. Recently he started adding barcodes (complete with little numbers written along the top), prices, blurbs, and endorsement quotes. Some of his books have had an index.

Today's titles, as a snapshot:

*Elementary Trains*(a present for K),

*Spaceman George*(not sure that one went very far before being abandoned), a recipe book called

*Oisín's Food*, and a two-part series:

*The Story of the Skull*and

*Further Adventures of the Skull*. These latter two were for the Boy Down the Road, who is ... ah ... very

*traditionally*socialised, and likes weapons and fighting and horror-type stuff (but is nonetheless more or less a sweetheart). The Oyster fits his material to his readership, in other words, which I find very interesting.

## 1 comment:

Rob says, in re (x+1)^2=x^2+2x+1, that he knew that, but "Cooooool." I faintly remember using the formula, too, but not when or why.

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