tell me how i should explain this to ds's year 2 teacher

[witchwithallthetrimmings]

DS got really really angry and frustrated with his maths homework last week, to the extent that he put his head inside the sofa and refused to talk to me. All it was, was using a number line to add and substract 2 digit numbers. Now ds has worked out himself how do to this in his head so it is not the maths that is the problem but he cant get the number line to look neat and clear (think he is also confused as i would by the idea that you go in the same direction when taking away as you do by addding). I asked his teacher whether he could show his work like this instead
35-23
23= 20+3
35+20=55
55+3=58
she said no as he needs to work on his presentation, but it is the same steps ffs. If i make ds do the number line now (i understand he might need to do it later) we will turn something that is a lovely game for him into something that is at best a chore and at worst a source of stress for everybody.

Thanks everybody esp snowball and DWRT ,now i understand, i thought they were simply another way to get them to understand things that my ds worked out himself. He is (i think) very good at maths but more importantly until this blip just really enjoyed it. So i've writen another note to the teacher explaining how cross and sad it made him and asking again whether he could write 34-20=14 instead of 30 semi circle with -20 on top 14 for now and that we could go back to number lines when the issue was less charged

The turning a subtraction into an addition is simply to show that subtraction is really counting on from the smaller number to the larger number and 'the difference' is the answer.
As has been mentioned, even if he doesn't need a numberline for this, they are a useful tool for some trickier maths such as division later on.

As for the subtraction; if it was 368-126, you would have 126 at the beginning and 'jump' in appropriate steps until you reached 368. So, they would start by jumping to the next multiple of 10, so 130 and record a +4 above the jump. Then it makes sense to jump to the next 100, so 200 and record a +70 above. Then jump to 300, then to 360, then to 368. Each time recording how much they have jumped. Then they add up the jumps, hence a suntraction becomes an addition. When children understand the concept they can make fewer, larger jumps.

That sounds quite hard method. My ds on year 2 not doing high numbers like that!!

Some Y2s will still be focusing on tens and units but the principle is the same. So for 56-24, you would make jumps up from 24 to 30 then maybe 30 to 50, then to 56. Thus leaving you with an addition of 6+20+6

It is not a difficult method and really helps cement what is actually happening in subtraction rather than this concept of borrowing or exchanging.

this counting on method is actually not what he has been told to do though. For 56-24 he has been told to jump 20 and then jump 4 but jump to the right not the left whereas I thought number lines had the smallest number on the left.

The smallest number would be on the left. For subtraction you would have the smaller number on the left and the larger number on the right. You would then jump to the right in steps until you reach the larger number.

For 56-24, children would start the way I described but as they become more confident they may make a first jump of 30 to 54 then another small jump of 2 to 56.

Oh God I'm dreading this with dd.

I spent most of my school life where maths was concerned in tears. Because I just cannot do maths the way you're 'supposed to'. I have a sort of synaesthetic brain and interpret numbers visually. I can't help it. And I can't write down how my brain does maths. It stacks the numbers up in coloured piles and then flips them about but all in a nanosecond. I'd cry and cry with frustration. Because I'd know the answer but I'd get told off all the time for not showing my method. My maths is very good actually, it just doesn't conform. I am absolutely dreading having to help dd with this.

SOH, you'll probably find the more modern versions much easier as the teaching and methods are largely built around the idea of visual learning. Children are shown expanded broken down methods and picture clues etc, then given a few different methods and allowed to choose which one fits them best. It really works very well and being an old gimmer who was teaching before the advent of the numeracy strategy and then watched it work over the years, I can tell you that far, far fewer children lack understanding now than they did then.

Witch, there is another method where you would jump 'back' to the left as you say. In this case (56-24), you would still set it out with 56 at the end but not put anything at the beginning. Then you would systematically take off chunks of 24. So you might take off 20 to get to 36 then take off 4 to get to 32.

That's just a different method but slightly more advanced because children need to be quite secure with place value and know how to subtract multiples of 10 etc. It also doesn't help to show subtraction as the difference bewteen 2 numbers in the way the counting on method does.