Number lines

[LemonRedwood]

I started at a new school this year, teaching year 5 having been in year 6 for forever the past 7 years.

Pretty normal start to the year in maths - place value recap, followed by addition & subraction, mental and written methods. Although it's year 5, most of the children are working at a borderline year 3/4 level.

When teaching mental addition and subtraction, I've been encouraging the children to either draw or visualise a number line to help them with counting on and counting back methods. If they are visualising the number line in their heads, great, I ask them to write down their thinking - so essentially just jotting down the calculations they are doing in their heads. Then compare strategies to find the best one for particular calculations - partitioning, rounding & adjusting, counting up or back etc. I used, and encouraged the children to use, number lines throughout my time teaching in year 6 (in a school where 95% of the children were working at at least ARE), even with more and most able children, as it helped them understand their own thinking a bit clearer (rather than the "I just know it" that you get when you ask children to show their working).

I've just been told by the maths subject leader in my new school that there are to be absolutely no number lines in KS2. Apparently, there was training for everyone last year and this is what they do now. Compensating/rebalancing only for mental methods as this is "what the children need."

Does anyone else have this in their school? Am I right in thinking this is bollocks? Surely a number line, especially for those that are struggling and are way behind ARE, helps children to understand what they are doing when calculating in their heads? And compensating/rebalancing isn't the most efficient method for every type of calculation - surely we should be teaching children the most efficient strategies?

I feel a bit like I'm going to be told soon that we should only teach them written subtraction as that method "always works and they'll need it for SATs" even for something like 5000-4995!

Am I not seeing something? Should I challenge this?

[LemonRedwood]

Sorry, that was a bit longer than intended

[noblegiraffe]

I'm a secondary maths teacher and we all have number lines up in our rooms. We mostly use them when doing negative numbers - so many children struggle with the idea of addition being movement one way and subtraction the other and fall apart at -3-7 even at KS4.

What's compensating/rebalancing?

Written methods always work but you're right that it can be a sledgehammer to crack a nut. You end up with kids doing a column method to multiply by 100.

[LemonRedwood]

I've not heard of compensating/rebalancing in over a decade of teaching! I am assuming it's another way of saying rounding and adjusting (but could be completely wrong!). I could ask the maths subject lead but I'm still fizzing a bit over the patronising email containing the no number lines instructions, so best not to reply straight away

[Ekphrasis]

I think that's nuts but I'd wouldn't be surprised it's the sort of thing they'd cook up.

But really, they'll be wanting us to drive cars without wheels next.

I think the sage at which your children are at they absolutely need number lines.

My maths was appalling due to reliance on column methods, me not understanding them and a lack of more visual methods like number lines.

How do they expect a child to develop the internal visual system needed for mental maths without number lines?

[LemonRedwood]

I like that last sentence, Ekphrasis. I'll add that to my argument, thanks!

[toomuchicecream]

This sounds like a misunderstanding of the 2014 curriculum, which says that children should be encouraged to use formal written methods as soon as appropriate (paraphrased by me). I've also heard it explained that number lines are a transitional method on the way towards understanding and being able to efficiently use formal written methods, and if you use a transitional method too long it gets stuck - like the children who default to dividing by drawing circles and putting marks in.... If sufficient work has been done on fluency and number sense in earlier years, in my opinion UKS2 children should be able to decide when to use a number line as an informal jotting of a mental method, and when it is most appropriate to use a formal written method. However, the children currently in UKS2 won't have had the same emphasis on fact fluency in the way KS1 children now should do, so they are likely to need more support through the use of number lines than hopefully subsequent years will.

Last term we reviewed our calculation policy and adopted the White Rose Hub model policy (the original version). I was really surprised to see the absence of number lines in KS2, then I realised that they've been replaced by the use of concrete apparatus like Dienes and place value counters. When I was in years 5 & 6 I taught using number lines a lot, especially for division, so I wasn't sure I liked the change. Then when I thought about it, I realised that there's a better conceptual link from the use of, say, p/v counters to compact written methods, so it will help the children to understand what they are doing.

Don't know if any of that helps your argument....

[monkeysox]

Secondary classes have them on the wall......

[thecatfromjapan]

I've come across a school like this. I think toomuchicecream has hit the nail on the head for the thinking behind it when she mentioned the whole "formal methods" thing.

Thing is, isn't there an emphasis on problem-solving now? Number lines have their place in a child's repertoire and an over-reliance on column-method isn't going to help with all problem-solving, is it?

[thatdearoctopus]

DH lectures on a Master's course in teaching primary mathematics and he said this is just plain wrong.
What training did they receive (and from whom) that led to this gross misunderstanding?

[thatdearoctopus]

Many years ago, when KS2 SATs were first introduced, there was a question on the maths paper that was along the lines of what someone has referenced above: 6004 - 4996. Over 2/3 of children nationally got the answer wrong, because they attempted to use the column subtraction method and they weren't sufficiently proficient to cope with the two zeros in the Tens and Hundreds columns. Had they used a number line/counting on method, they would have had a much better chance of arriving at the correct answer.
Since then, we have always been encouraged to teach a variety of methods to suit a range of situations. That hasn't changed since the 2014 curriculum was brought in.

[LemonRedwood]

Well, screw it. I've been using the number lines anyway for counting up and have even put one up on the working wall.

The world has not imploded yet.

[ProfessorCat]

Give them rulers.

Yes, it's nuts.

[showergel1]

Just had maths training which insisted on using written methods as a last resort. Number lines are a jotting which enable children to do calculations mentally.
You are correct in thinking this no number lines rule is bullshit.

[Noodledoodledoo]

Another secondary teacher here who has a numberline up on the wall! As before used a lot for negative numbrs!