Primary maths teaching - not enough practice?

[noblegiraffe]

Interesting blog post here on primary maths teaching

thequirkyteacher.wordpress.com/2014/12/06/put-down-that-measuring-cylinder-and-step-away-from-the-pond/

The gist is that "My point is that the children are struggling with formal methods because they have not committed to memory the basic number bonds and multiplication facts required. Those that have committed the above to long term memory certainly won’t have used that knowledge to then perfect subtraction and division fluency/facts in order to become competent at column subtraction and short/long division. My hypothesis is that children just do not practise anything enough, ever."

As a secondary teacher I certainly get frustrated year after year with Y7s who have forgotten how to do long multiplication by any method, can't remember (or were never taught) the bus stop method of division and struggle to borrow when doing subtraction. I'm thinking that children should be coming out of primary as likely to forget these methods as they might forget how to read. My suspicion is that they spend a week doing long multiplication and then it's done, on to the next topic. But, I don't actually know what goes on in primary schools. This blog seems to confirm my fears, what are your experiences?

Not a British primary school, but when my son was in that age group they seemed to flit about from one thing to another very quickly with no overlap between topics, like say... fractions then suddenly area, then attributes of triangles. The move seemed to be before he'd really achieved the "muscle memory" required not to have to look up examples (via looking helpless and put upon) the next time it came around in the following year.

He did get shitloads of questions to answer. But they were in one big "holy mother of god we have to drag him through this mountain of homework tonight, hopefully getting him to bed before 11 cos it has to be done by the morning" sort of megablobs. Whereas I think if had it been split down into several blocks of questions, to be done and handed in periodically over say a few weeks, with sme left over for memory jogging over the next few months... he might have remembered it better. Especially if one topic had the previous one melded into it on some level.

Revision was less revision and more "try to stuff the entire curriculum into him at warp speed nine cos he's forgotten everything aside from they've done this week".

I'm not sure, but I think the NC here borrows heavily from the American one.

Certainly it seemed like there was an awful lot to cover, in the time available some of it going right over the kids' heads and no time to really concentrate on getting the foundations into a non-hole ridden state.

I'm an ex primary teacher and now a tutor and totally agree. There is so much packed into curriculum that nothing is consolidated, or covered so infrequently that it's easily forgotten. The amount of Yr 8s that say they 'haven't done area' Oh yes, you have!!

Around here we heard a lot of "Big Maths" e.g. a nearby primary inserted the daily number facts routine into the timetable at the expense of French etc. DD's school didn't take it that seriously, but they still ended up doing lot of the 72 questions in 100 seconds things.

So, no they actually got them committing those basics to memory in the few Middling State Primary schools I know around here and that was also encouraged by the calculator ban in the former calculator-allowed second SATs L3-5 paper.

I found this comment interesting: "I am of the understanding that Maths questions that are really testing English Comprehension will no longer dominate." I thought that was one of the significant differences with the L6 paper i.e. it looked much wordier than the not very wordy L3-L5. PISA maths is of course wordy, multi-step stuff so if this change is the case it may well come back and bite.

Another part re. working memory we can probably sum up with one name: Jo Boaler, who was on that TV program the other week suggesting that instead of knowing 7x8=56 a child could work out (7x10) - (7x2)

I think that the problem is that children don't understand what they are doing. They do not spend enough time working with malipulatives like counters or multi link cubes or lego an abacus or base 10 blocks. Children do not actually know what a sum like 8*3 means even if they can learn it off by heart. Often children do not fully understand place value.

My five year old can work out a mutiplication sum like 8*3 if you give her a large bag of counters. she organises the counters like

**
**
**

and then counts the counters.

If a child uses counters they can see why your method of finding 7x8= 56 by working out (7x10)-(7*x2) would work. I feel children need understanding rather than magic tricks. Once a child has understanding then they can apply methods like long multiplication.

I think that the new primary school maths curriculum is crap. Its too much too soon. I am doing singapore math with my daughter because I don't trust her school to teach her.

My post has not shown the counters right. I am not sure what has happened.

Oh its mumsnet bold! lol....

This is what it should like

########
########
########

Well, with the emphasis on rapid progress, new learning every ten min etc, no one will ever get to consolidate any learning - let alone get to the point of rapid recall!

In singapore they go at a very slow pace in their equivalent of reception and key stage 1. They then fly like the wind when their children have outstanding number sense.

This web page has a picture ot show cuisaire rods being used for multiplication and division as well as loads of text about maniplulatives.

nrich.maths.org/10461

56 = 7 x 8 works for me : 5,6,7,8 as a memorising trick.

However I agree with the point on physical counters (my school had those rods too) for the early stages and then colouring in squares on graph paper later, these gave me a good sense of number rooted in physical experience. I do a lot of maths through visualising this sort of thing to this day.

We spent a lot of time with balances and weighted numbers to get the number bonds too in the early years.

I was disappointed to see really weak kids at 5 made to do written maths sums in our local school when they clearly had not "got" it. Then a quick 5 min attempt at rescue with some counters before it was time for something else.

My suspicion is that they spend a week doing long multiplication and then it's done, on to the next topic. But, I don't actually know what goes on in primary schools. This blog seems to confirm my fears, what are your experiences?

I teach Year 6 and my entire first term is blocked for place value and calculation methods (regardless of which year group I teach). We've spent about two weeks on long multiplication and two on long division this year so far. They still knew and were happy with grid multiplication and short division from last year, which had taken them ages to get to grips with when they were in Year 5. Most of them can multiply and divide decimals by a whole number. My more able ones are happy multiplying and dividing by decimals as well. They are generally confident expressing remainders as fractions; they understand fractions as a form of division and are beginning to use decimal notation for remainders. Addition and subtraction doesn't tend to cause them any problems (even my SEN kids are ok with these). Calculation methods crop up in all sorts of topics and we revise them frequently. The majority of my class score on the Level 5 and 6 range when it comes to calculations and number skills. This has taken quite a bit of hard work and constant revision since I started with them in Year 5. (They are dire with measures, though, and the word "algebra" scares them... ) I'd be a bit annoyed, if their secondary teachers then told me that they don't know anything.

What I found more scary were the secondary PGCE students, who visited us last year towards the end of their training and seemed less skilled in Maths than my class.

I have my class for the second year, though, so I know what they have covered last year and what they should be able to do. There's no way they can tell me that they haven't done something, because I know whether I've taught it or not. They tried that in Year 5. Unfortunately for them, I had seen their Year 4 Maths books, so knew what they'd covered.

We do Big Maths at our school and have really seen a huge impact. Every day the children have a 20 min session which covers:
Counting
Learn its (addition facts/ tables/ bonds)
It's nothing new (putting learn its into another situation)
Calculation (practising a method)

It works if it is used daily. Children get to know a method properly. The old strategy had teachers teaching a method then not returning to it for some time.

I'm not sure it is lack of manipulatives that is the problem, ReallyTired. A lot of teachers went wholesale down the practical activities and understanding route in the belief that it wasn't important to know number bonds and tables and that sitting and doing worksheets was boring and would turn children off maths.

Singapore didn't really do that. They place equal importance on knowing number facts as well as understanding them. Every concept is introduced with concrete activities but they move that on to pictorial and then abstract. There is a balance between the two, it's not either or.

BTW if you are the poster using Singapore Maths with your DD, maths no problem are no longer going to be supplying the books. They're selling what they have then that's it. I'm not sure there's another UK supplier.

So nice to see a thread about maths teaching.
I don't have much to add at present, except school seem to have very little focus on maths so far (Year 1). Everything that comes home seems to be about reading and writing.

There are singapore math style books for the UK curriculum that are being produced by Mathsnoproblem

www.mathsnoproblem.co.uk/mathematics/primary-key-stage1-and-key-stage-2/maths-no-problem.html

In many ways it makes sense as there is no point in my daughter learning about foreign currencies at the age of five. The author of the book has written the same state textbooks as used in singapore.

I have to except the UK national curriculm as I live in the UK.

"Singapore didn't really do that. They place equal importance on knowing number facts as well as understanding them. Every concept is introduced with concrete activities but they move that on to pictorial and then abstract. There is a balance between the two, it's not either or. "

I agree. It is the age that primary schools in the UK move on the abstract. In singapore children start counting physical objects. They draw the physical objects in a grid. The physical objects are replaced by counters and then by coloured in squares. The number of the coloured squares are labelled with curley bracks an a number.

Singapore children can use the bar model to solve some quite complex probolems like simulateous equations.

Maybe the UK was/ is poor at the transition from malipulatives to the abstract. Personally I think that year 1 maths is far too formal for five year olds. Singapore allows children to enjoy foundation style learning for much longer than the UK.

I am pissed off that the only malipulatives that my daughter gets to use in year 1 is her fingers! I would rather she used counters as it can be really hard to get a child to stop using her fingers for maths.

If you are happy to switch over to the UK version it's fine. Just wanted to give you a heads up in case you were thinking of sticking with the old series. It does sort of make sense for them to produce a UK aligned version.

I think it's rare for children not to be able to use manipulatives in year 1. Especially at this stage. I wonder if they think she's able at maths so doesn't need them.

I completely agree with the blog writer. English primary maths is amusing to say the least. I am following Russian maths curriculum with my DS. There is just much more practice, and every lesson when you learn something new, you're still asked to practise four basic operations (which get more difficult and are related to new topics). Next lesson, you always do a bit more practice on the previous one. Over time, things become automatic, mistakes decrease and you can build on this knowledge in all future maths.

There is great fear of abstraction too. Teachers go a great deal avoiding using abstraction, and fail to explain some things as they try to simplify everything.

As previous posters say, in other countries you start later, but learn profoundly and move steadily on. No point announcing you're learning times tables to Y1 (there is no learning X1 or X10, it takes only understanding) and then by Y5 many children still don't know their times tables.

There are just jumps between topics with no connections between them, no deep and logical coverage of topics, no real practice and omission of maths as soon as there is RE, D&T, meeting with someone, etc, etc.

Yes, it's my experience with my two DDs that there is too much flitting around from topic to topic and not enough practice or consolidation.

I was taught maths by modern methods of playing number games and looking at patterns. I swapped schools for upper primary and found myself far ahead for those being taught by the traditional "maths means doing lots of sums" method.

I still see maths as playful patterns rather than difficult arithmetic. It is this outlook I used hen teaching dd maths.

Just as one example, dd had to do 278, so I just reminded her that she knew what 258 was.

The more visual, colourful and fun you can make maths, the easier a child will learn.

I think everyone is raising a lot of good points:

practice can help (I've posted enough about how much improved DDs were thanks to mathsfactor on-line tutorial - which isn't just sums - but includes instruction & playing games & has resources for games away from the computer).

maths teaching can seem patchy - jumping from topic to topic with little 'join' between topics (ye oldie building blocks approach is clearly very out of fashion)

there is institutional antipathy toward solidly learning number bonds/ times tables (regardless of method). My impression was 'appreciation of numbers' was being taught rather than understanding - so more important to notionally know what should be done than to actually be able to solve a problem (real world or just numbers on a paper). By way of example in Year 2 I had a row with DD2 who firmly believed 2 + 2 was 5. She said her teachers had told her this was right. I said were you estimating - she said NO! I WAS ADDING. 2 + 2 IS 5! and burst into tears. To be honest so did I - it was so heartbreakingly depressing and absolutely upset me that she didn't understand the fundamental difference between adding actaul numbers and estimating.

I also think pre-specified new national curriculum - there was a bit of confusion about whether 'long' methods of mutliplication/ division should be taught in primary school. Certainly our primary SMT were dead against these being taught, children were forced to use chunking/ grid methods only and I was repeatedly told long methods of mutliplication/ division were for secondary (which runs entirely counter to many foreign educational systems)

What was interesting for us as parents was that anyone who had been educated abroad at our primary at some point just gave up and did their own thing at home. Schools hugely benefit from this in the short-term - but I do wonder about the long term - it's generating a lot of bad feeling. Many of us went part-time because we felt we had to help at home.

I think the reason parents try so hard for grammars is that they hope (perhaps more than believe) that the standards and quality of teaching will be much higher than they've experienced in primary. That's why pupils take the 11+ in their thousands in Birmingham at least - it's about escaping crippling mediocrity.

Teaching maths in secondary I agree with you all.

The pressure comes from the government /ofsted who need to see progress in each 10 minute slot. What about good old fashioned practice?
The Dutch education system is also interesting, they block out 3month for fractions and teach the understanding to begin with, spending weeks on equivalent bar fractions etc. So when pupils come to the abstract, they understand why they are doing something.

I have a bottom set year 7 who quite frankly have been let down by primary school in terms of maths. They don't know their bonds to 10, times tables and don't see the impact this has on their work.

appreciation of numbers being taught rather than understanding

Yes, yes, yes PSBD! This is certainly the feel I am getting.

And, yes, yes, yes, to people with experience outside the British state primary system being shocked into action and making difficult far reaching choices to deal with it.

I don't think this is a reflection of "quality of teaching" so much as it is about what teachers are taught in their training. "drill and kill" (practice = kill enthusiasm for learning) is still a very current idea in Teacher training institutions, among Ofsted inspectors, etc. Many education lecturers have for years followed their own ideologically-based notions about how children learn, rather than paying any attention to what their colleagues in university departments of psychology have discovered through properly conducted experiments.

They don't know their bonds to 10, times tables and don't see the impact this has on their work.

See this was another thing that annoyed me. In the country where I live there is no horror of learning by rote. If anything its primary failing is that churning out parrots appears to be the goal. Becuase virtually every test (of which there is a constant flow) is about mindless regurgitation. Maths got the same treatment as everything else, learn by rote for a test (in a cramming fashion), vomit it on demand for the teacher, thus purging memory banks for next chunk of short term memorisation.

Remembering long term requires regular refreshing, recycling and reusing. Without long term memorisation there is no solid foundation to build upon. No point trying to stick a fancy roof on a house with wobbly walls due to a foundation full of gaping holes. It will fall down. And it is much easier to remember something you understand, becuase then it has meaning.

I'd rather they put less in the maths NC curriculum here and focused on getting a solid foundation. If they want to put more topics in then maths needs more timetabled hours. Actually, I still think they should focus on teaching less, cut out the obession with going at warp speed nine AND give over more of the timetable to maths. It's too important a subject to risk screwing up. Ditto national 1st language. I'd happily take an axe to the subject creep that has happened here. And make it LAW that maths and 1st language are taught daily, plus for the first three years at the very least make them the only subjects that have homework/testing.

It was so frustrating having to give up any hope of spending a few extra hours a week supporting maths learning becuase the (deranged) RE teacher had given our (still not reading yet) first years a complicated research project on an obsure thing god said, that required even the most devout catholic parent to spend half the week on google with an increasing sense of desperation.

Blimey. DS has been in the British secondary system for three years now and all is well, but the resentment and frustration with those primary years here is still rather fresh.

The pressure comes from the government /ofsted who need to see progress in each 10 minute slot

I think the single greatest improvment to schools globally would be to instigate a worldwide law that requires all those moulding, shaping, training, researching and inspecting education have a teaching timetable of no less than one full day a week (so they too can understand how it feels to be running on fumes after a particularly crappy day, with one lesson still to go). And not just with nice, easy classes of well behaved, clever kids. They also need the classes with Kevin the persistant bogey flicker and Mary&Micheal who turn any bogey drama into a full blown drama.

Let's see their progress in that ten minute slot.

edit

Mary&Micheal who turn any bogey drama into a full blown crisis .

I have kids who know what a dodecahedron is, but can't find an equivalent fraction. My yr3 DD is sure that the times tables are just another passing fad that she can ride out until a topic she finds more palatable comes along.

As a parent, I wish they learned their times tables, and then remembered them because they were learning new topics that build on them and use them. Say, common denominators, equivalent fractions etc. Or even, gasp, long division!

Everything seems to be just a few days, there is no mastery. And the children think it's all disjointed and therefore you can ignore the bits you don't like because there will be a new lucky dip next week.