Arithmetical adventures

Last week the girls' school ran a workshop for parents to explain how they teach arithmetic to children Star's age. I went. It was ... interesting. For context, I should explain that over the last ten years or so British schools have been encouraging children to find their own methods of calculation. I gather it hasn't worked (how surprising) and they are now teaching selected methods again. Most bear little resemblance to the traditional methods we were taught.

So, for those of you who may be curious, these are the methods that are supposed to produce the most right answers (no marks for efficiency or elegance!) ...

Addition
Straightforward addition in columns with carrying of tens, hundreds and so on.

Subtraction
"Borrowing" tens and hundreds is considered too confusing for this age group because of those horrid problems with zeros in the top line. Instead of subtracting, they are supposed to count on using a number line. So for example, 384 minus 129 could be calculated this way ... start with 129, add 1 (=130), add 70 (=200), add 100 (=300), add 84 (=384). Add together 1+70+100+84 to get 255. It doesn't look quite as bad shown graphically with a number line. Not quite.

Multiplication
For multiplication they use a grid system, which I can't show very well using blogger formatting. Once you see this written neatly, it does make sense as the same method can be used for simple multiplication, long multiplication, problems with decimals, algebraic problems - anything involving multiplication. To find 256 x 34, you would draw a grid with three columns and two rows. Across the top write 200, 50 and 6; down the side write 30 and 4. Then multiply each combination something like this (the asterisks are because blogger won't let me leave a space) ...

**** | 200 | 50 | 6
____________________
30 |6000 |1500|180
4 | 800 | 200 | 24

Then add the six numbers (6000+1500+180+800+200+24) to get the answer (8704)

Angel was taught last week to use this method to expand algebraic expressions such as (3a+2b)(2a-b). It works. You can see clearly what you are doing, and it helps to avoid getting into positive/negative tangles.

Division
Trial and error. Let's try 125 divided by 4 ... you could start with 10 fours. OK, 10x4=40. Not enough. How about 20x4? 80. Not enough. 30x4? 120. Ah! Getting close. Five more to go. How many fours in five? One with a remainder of one. So we have 30 fours add 1 four ... answer is 31 r1. Are you converted? Would you tackle division that way? No, me neither.

Eat your heart out Singapore. Why teach arithmetic the good old fashioned way when you can make it so much more ... um ... interesting.