Discussion in 'Primary' started by Rosiejohal, Apr 14, 2018.

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1. ### RosiejohalNew commenter

Hi all! I’m a primary school teacher and I've started a YouTube channel - the videos are going to be about Maths mainly. If you could watch, like and subscribe that would be great! And please share with any parents/kids who need help with Maths?

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2. ### Vince_UlamStar commenter

Thanks for posting these, Rosie, nice work.

One point which many Primary teachers miss is that a method which someone has to draw or write through is not in itself "mental". It's just another formal method even though it is not one prescribed by the DfE. It really is more efficient to use always the columnar methods as the repetition allows the construction of schema which will facilitate the growth of mental arithmetic.

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3. ### caterpillartobutterflyStar commenter

Lovely, but ummmm how do you envisage these being used?

I agree that 'mental methods' do not include numberlines and so using such a video would be counterproductive.
(I don't agree that many primary teachers miss this point. Or at least I've never met any, but maybe I've just been lucky.)

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4. ### RosiejohalNew commenter

I hear what you’re saying but during my training I was told the exact opposite... Informal methods to me don’t mean that everything is done in your head then the answer written down. And these videos aren’t intended as ‘I know everything you will too after watching these videos’ it’s about parents learning some of the ways their children may learn at school... so as to help with homework... or for a child to watch (if they’re bored I presume haha). But thanks for both of your feedback - I’ll try and be in clearer in my next video.

5. ### caterpillartobutterflyStar commenter

I think you misunderstand what we are saying.

Numberlines, bar models, part-whole, jottings, etc, etc are informal written methods and most certainly have their place.

Mental methods mean you might jot down key information, but then you do work out everything in your head.

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6. ### carriecat10Established commenter Community helper

I think the use of videos to support parents are really useful. I would suggest ensuring the numbers chosen are appropriate for the methods exemplified. I would expect that children should be able to calculate 34 + 152 mentally for example.
Perhaps making clear to the viewer the purpose of the videos would help - so the use of number lines etc could be representing the mental methods and not just being used to do the maths.

7. ### Vince_UlamStar commenter

Teacher training is not the best training for teaching maths. The ITT idea that a grab-bag of different methods should be made available to children is barmy. It's a waste of lesson-time which could be spent allowing children to practise the columnar methods, the most efficient algorithms, to proficiency, so building schema and developing their number bonds. Other methods hold children back throughout Primary and are anyway unsupported in Secondary.

In my first reply I addressed the issue of "mental" methods because you use "mental strategies for +" as a page headline in one of your videos. Really, nobody does mental arithmetic like this. It's too unwieldy, doesn't scale and doesn't accommodate R or Z. Not every way in which it is possible to do arithmetic is as efficient as every other way. The thing Primary teachers & their ITT tutors need to know is that the DfE prescribed methods are the best methods.

On formality: A method which is taught to candidate teachers during ITT and then taught to children in Primary schools nationwide is informal only in the bureaucratic sense. If a person is paid to stand in front of children and then teaches them a method then it's a formal method, children don't know any different.

They are good videos but I recommend you stick to the DfE prescribed methods, there is little point demonstrating to parents methods which their children are not supposed to learn. You speak clearly, lighting's fine and I like the sound of your Sharpies. Your contact grip, however, looks like it might be causing you some strain.

8. ### brighton56Occasional commenter

@Vince-Ulam Out of interest, are you still a secondary maths school teacher now? You always seem very passionate about the 'best' way to teach maths and how you feel primaries should focus on particular aspects.

To make assertions as to ITT's approach to training student teachers as being flawed is not fair. Talk to maths advisors from NCETM or from local authorities and they will not agree with you. Teaching columnar addition is pointless until children understand the maths behind it. Use of numberlines, counters, diennes or whatever else ensures children have the abstract understanding later down the line. You could teach Year 2 (some younger children) formal column addition but it's just the process they are learning. We need to go deeper than that to ensure children have the fundamental basics and understanding so each year the foundations can be built upon.

Furthermore, the DFE do not have prescribed methods. Schools no longer follow the National Numeracy strategy. The curriculum states, "By the end of year 6, pupils should be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages" - this does not say that children lower down the school should not learn other methods first. That said, surely the children who entered Year 7 in 2017 were the best you had seen with arithmetic in quite a few years? I haven't seen any schools under the new curriculum not putting a high emphasis on written methods.

If we were to go back and look at GCSE maths papers from the old curriculum year 2000 (foundation/intermediate) onwards I would say that they are not dissimilar to what the children are faced with nowadays at the end of KS2. As each year goes on we expect children to be able to do more and more by the end of primary. Instead of slating primary teachers constantly, go down and observe and see where we're coming from. I did 20 years ago and then moved to primary!

Remember @Vince-Ulam Primary teachers have 7 years to get children from not knowing what the number 1 is to mastering all the KS2 objectives. Secondary school have 5 years to build upon what we do. If you think about it, we're not too dissimilar in terms of challenges to get young people to learn our subjects. Your Year 7s do not start not toilet trained or unable to write their own name (well most).

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A great idea, hope you build up a good base of subscribers.

10. ### Vince_UlamStar commenter

@Vince_Ulam.

I am aware that many people have incorrect ideas.

No, this is an incorrect idea. Mathematical understanding, such as it is, has been communicated successfully for thousands of years without the incorrect idea that it is discrete from practice. This idea that understanding must precede practise is as sensible an idea as expecting children to understand grammar before they are allowed to speak.

No. You & many other people confuse the understanding of particular representations with the understanding of foundations. The foundations or arithmetic are beyond the vast majority of teachers. It took Whitehead & Russell over eighty pages to prove that 1 + 1 = 2. Primary pupils cannot be expected to understand this. All that you do with Diennes, lines & counters is teach pupils alternative representations.

They do. See The Mathematics Programme of Study: Key Stages 1 & 2.

I am simply pointing out that not all methods are equal and that there is no point teaching pupils methods that are inefficient, that they are not required to use and that they will not use once they leave Primary school. It's a waste of teaching time and hobbles children's mathematical skill.

I have not said otherwise and have previously acknowledged the incredible work carried out by Primary teachers. I only wish more of them were acquainted with their DfE prescribed responsibilities.

11. ### caterpillartobutterflyStar commenter

I took over a year 6 class one year and wasn't expecting much as I knew the year 5 teacher, having shared a year group with them a few years earlier. She sent them up absolutely confident they could all do column addition, no problem at all. Was happily telling the world that I'd have an easy time with them as they could basically do year 6 maths already.

When we get to addition, I start my lesson by asking a pupil to demonstrate. It was a sum where there was a need for carrying. The child added the units (we still called them units then!) and said something like "8 + 5 is 13, so you put the 3 there and put a dash here." The 'dash' was actually the 1, needing to be carried across but this had totally escaped him although he put it in the correct place. I asked another to continue, not mentioning my shock, and they added the tens with something like "7 + 9 is 16, so you put the 6 there and a dash over here in the hundreds." I then ask why they put a dash in the hundreds..."Oh because it tells everyone that it's wrong because you can't add to more than ten when using columns."
One of those moments when you have to work very, very hard not to say "What the actual F&*&!!!?"

Diennes blocks were essential to demonstrate the that you can most certainly add to more than 10 when doing column method!

And making the other year 6 teacher come and observe my first subtraction lesson later in the week because I was so scared of what the heck they would come up with.

12. ### brighton56Occasional commenter

Direct from the curriculum, "This appendix sets out some examples of formal written methods for all four operations to illustrate the range of methods that could be taught. It is not intended to be an exhaustive list, nor is it intended to show progression in formal written methods."

Maths mastery, although granted is often misunderstood, shows that children do need to understand what they're learning otherwise misconceptions arise further down the line. Concrete resources and pictoral are imperative to ensure children fully grasp what they are learning.

We don't teach dividing fractions by just saying: Keep-Change-Flip on its own. Young people need to understand why this is so. It's the same with adding or whatever it is you are teaching.

I certainly can't knock your passion @Vince-Ulam but be prepared to listen to other views.

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14. ### Vince_UlamStar commenter

As I said in an earlier post on this thread, there are other formal methods. The DfE, however, makes statutory the teaching of columnar arithmetic:

"Statutory requirements

Pupils should be taught to:

[...]

add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction
"
Mathematics Programmes of Study: Key Stages 1 & 2, DfE.

Not all methods are as efficient as the columnar methods. Primary teachers should be aware of this and teach the statutorily prescribed methods only. They would save themselves much time and their pupils would achieve higher mathematically.

Technically correct but practically speaking... I'd be interested to see you teaching maths to year R children and the processes you'd use.

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16. ### Vince_UlamStar commenter

Which is as correct as anyone can get.

EYFS is neither KS1 or 2. These teachers are not required to teach formal methods of arithmetic

I can see you trying to take a bottle of frozen water through airport security.

Didn't say it was, and I know they're not. I would still like to see your approach to teaching maths in year R, but now you mention it I'd be equally happy to see you teach year 1.

18. ### Vince_UlamStar commenter

Then you did not need to raise that issue in a discussion about formal methods of arithmetic in KS1 & 2.