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?

For many years there was pressure on schools to follow, first the Numeracy Strategy then the Numeracy Framework which moved IMHO quickly from one aspect of maths to the next with no time for consolidation (the reasoning being that they would meet "it" again next term/year . Many schools found that this didn't work for their pupils, (we certainly did ) and looked for alternatives. As someone (icedfinger?) mentioned earlier in the thread we introduced Big Maths as part of our daily teaching approx 5 years ago as part of our Maths overhaul.

I think not enough practice, they do flit around. Doing a daily maths sheet of assorted questions is great. Also power of 1 and power of 2 book great for key stage one and key stage two parents wanting to ten mins a day which will be invaluable to their children for basic number bonds etc.

The blocks in the Framework were an absolute shambles. At least under the NNS the sample medium term plans blocked a week for place value or 2-3 weeks for addition and subtraction. What was worrying is the number of schools that couldn't see how much of a problem trying to cover counting, reading and writing numbers, place value and calculating in a two week block was. Or who could see it but felt they couldn't drop it despite the framework not being statutory.

I'm not sure the fear that practice/drill = killing enjoyment is restricted just to maths. I've got a feeling that a lot of phonics teaching might suffer from the same problem. Possibly other areas of the curriculum too.

I also have found my DDs seem to need more practice.

One thing is that in lessons the ones that 'get' a topic can fly through 20 questions, so they get loads of practice. But ones that don't 'get' a topic may only get through 3 questions by the lesson end, so if the remainder aren't given as homework, they never get the chance to properly practice and consolidate.

There did/does seem to be a thing in maths where if kids can do a question on a topic, then they shouldn't waste time doing more questions, rather move onto something else. If I look at the textbooks in my classroom, my utter favourites are the ones I used when I started teaching a decade ago. Massive exercises full of questions that get increasingly more difficult. Textbooks from about 5 years ago were colourful and friendly looking, each topic had a double page spread, but only 3-5 questions. After that there was a problem, or investigation, which were generally crap. We've now bought in some new textbooks which have long exercises again. Much less colourful but so much more useful.

I find especially at the bottom end, kids like doing loads of questions. They get a sense of satisfaction from a page of ticks, and with the repetition, actually have a chance of remembering the methods.

I agree about questions needing to get gradually harder.

eg Column subtraction, start with 2 digits take 1 digit, move to 2 take 2, introduce borrowing, introduce zeros, move to 4 take 4 digits, put in decimals etc.

A lot of the work I do with DD1 (y11) is to show her all the 'tricky' examples of things so she doesn't get thrown or fall into the traps. If she were more able she would maybe spot these herself, but she needs to do loads of questions in order to get more able to cope with unusual variations.

Again DD2 (y5) is great with column subtraction, but needs persuading that 5 digits take 5 digits really isn't harder than 3 take 3.

One question I would like to ask teachers on this forum is if any study is done, during teacher training, on how people learn? For instance, the ideas put forward by Tony Buzan on how best to learn new things and commit them to long term memory. Is any such study done on the technical aspects of how children learn during a teaching course?

Yes we covered mind mapping quite extensively and many schools did/do use the techniques even though some of the claims behind it have been discredited.

And a great deal of time is spent looking at learning theory

What about things like his ideas of repeating next day, then after a few more days to get things into long term memory? Has that too been superseded by subsequent research? I also still use his ideas of introducing new ideas by just going over them initially telling dd she doesn't have to understand them, just hear about them. Am I totally outdated in my teaching approach? (I do realise teaching a class of 30 is a whole different ball game than 1 to 1). Also is there anything to the idea of letting maths sink in by walking away when it gets too difficult, because it will be a whole lot easier when you come back to it?

Hi Richmal You can find the ideas you mention, along with the associated psychological research, covered in the cognitive psychologist Dan Willingham's excellent book Why Don't Students Like School. www.amazon.co.uk/Why-Dont-Students-Like-School/dp/047059196X

It's quite recent, so up-to-date on the research. This is the kind of thing that should be being covered in teacher training, but according to a lot of teachers isn't. The situation appears to be similar to the situation re phonics: university reading researchers in departments of psychology over the last 30 plus years produced a huge body of work supporting phonics using rigorous research methods, but a lot of education lecturers simply ignored it, preferring Whole Language ideas as more ideologically congenial, even though there was no evidence base for them.

I agree with the sentiment that not enough practice/consolidation is embedded in the curriculum. The rotation of subjects is ludicrous in the early years, by the time they get to fractions they have forgotten shapes, etc...

We found that the only way for them to remember anything was to practice nearly daily at home. Whenever we took the finger off the pulse at home they forgot stuff. This is true sadly in both sectors (private and state) as they both use similar style - even though in private they had more maths timetabled in the day.

I learned less maths at primary in my home country, but boy was it solid. I still remember stuff now and I haven't used it for 30 years.

Richmal, you may also find the posts on this teacher's blog helpful - he is very good on covering research findings pragmaticreform.wordpress.com/2014/04/06/3-apps-cognitive-science/

I completely agree that the maths curriculum is overcrowded and there doesn't seem time to consolidate things. I also think there seems alot of emphasis on finding a "quick" method of doing a sum such as 49+49. Of course there's nothing wrong if a child sees a quick way for themselves but I find that my own DD seems to expect to find an easy way and thinks that she is "thick" when she can't see it.

I wish there was less attention paid to momentary (and usually solid evidence light) fads things like mind mapping.

I have a mind map app. I like it for planning, or getting my initial ideas down in a "movable" fashion so I can tweak. I have used it with DS becuase it can be less intimidating than a blank sheet of paper upon which you are rewuired to make notes. So it can kick start the process.

But....

I think it is somewhere between "not as good as" and "no better than" creating notes in terms of improving retension on content. And teaching my son how to use evernote to his advantage took a fraction of the time that mind mapping did.

IME when DS was at primary school here and mind mapping suddenly got thrust into the mix by TPTB as a "must do" the end result was that teachers, parents and kids ended up bogged down in trying to deal with an unfamilar format that was over hyped as the solution to end all solutions in terms of retension, with little information to hand to help clarify how we were supposed to jump through the new hoop. Time dedicated to content was reduced as the format sucked up hours.

It wouldn't be the first time evidence light ideas got thrust into schools with fanfare and evangelic zeal. Anybody remember Brain Gym and the great fish oil fiasco ?

In the time since I went to school and now... a huge business of educational solutions and tools has evolved and grown beyond all belief. I think potentially that is more the primary driving force behind a fair few of the "new ideas in education" rather than any solid, evidence supported research.

www.danielwillingham.com/learning-styles-faq.html

www.danielwillingham.com/daniel-willingham-science-and-education-blog

I was wondering, Noble,if you could get yourself into the primary schools to see what they do teach? Lots of schools now have partner primary schools and they talk about issues such as this so the transition to secondary is smoother. Would this help?

We work very closely with our secondary colleagues. They join our lessons and our older children are taught by secondary staff one afternoon per week.
When they first visited they were surprised by what was taught in primary and said they had vastly underestimated primary teaching.

Hah, I'm a part time chalk face teacher. Chances of me being allowed out of school to visit primaries is zero. There's a primary liaison in our department who gets the occasional jolly.

"they had vastly underestimated primary teaching."

I've heard that before from a secondary maths teacher who became a governor of a primary and took a look i.e. they thought lots of their secondary peers underestimated..

Y7 DD's primary didn't work that closely with secondary for maths (they had an HLTA doing off-piste & L6 etc.), but the Y6 teacher assessment was confirmed when secondary did it's baseline testing which was very pleasing.

On blogs, another relevant teacher one I like for their sane approach to research is here (because of some up thread comments I've picked a link to something about mind mapping rather than the blog's home page):

evidenceintopractice.wordpress.com/2014/08/25/does-visual-mapping-help-revision/

It was me who sort of brought up mind mapping by mentioning Tony Buzan, but I was more interested in other ideas he covered in some of his books; like how often and when to repeat work in order to get students to remember it. (Which was more relevant to the OP)

Thanks for those who have given me more up to date things to read on the ideas of how to teach.

Singapore Maths makes good use of manipulatives, bars/visuals and so on to help children understand concepts, but they follow this up with loads and loads of practice, and a very strong emphasis on committing maths facts (number bonds, tables, algorithms) to memory. That's what makes it work.

Failing to use visuals and manipulative at all would be fault. But it's also a fault to have a maths curriculum where kids are spending too much time playing with manipulatives and getting very little practice in, which quite honestly seems to be a lot commoner in western primary schools. Western pedagogies do seem to have a deep rooted fear of memorization or intensive practice in general ("Death by worksheet! Drill and kill! It'll destroy their creativity!") It doesn't, of course; committing facts and procedures to memory actually frees up the "thinking bit" of your brain to concentrate on the creative aspects of the problem. Kind of like, spending lots of time learning scales and arpeggios and practicing intensively is essential if you want to be a creative and sensitive pianist.

The original blog post was excellent.

As linked above, some of Tony Buzan's stuff is not at all borne out by the data, esp. the mind mapping stuff. However, as far as I can recall he did have some decent advice about revising previous content at intervals to assist memory.

Overall, I think there are much better writers out there when it comes to evidence-based learning. Making It Stick is pretty good, although I think it is more aimed at older students.

www.hup.harvard.edu/catalog.php?isbn=9780674729018

There has so much incredibly exciting research done in the last 25 years about how the brain works and what is the best way to assist learning, but it's been a little bit slow to penetrate teaching; so much teacher training stuff (not to mention bloody Ofsted) still seems to be based on constructivist ideas (Dewey, Vytgotsky etc.), which includes a lot of very wrong ideas about the brain.

This

IMO it's the mistake Gove made with the new curriculum. He was clear it would tell teachers what to teach and not how. Singapore changed their maths results by very much focusing on the 'how' as well as the 'what'. If he had specified lots of practical work with lots of opportunity to draw/model/ practice and applyapply with a different model of differentiation, I think he could have had a very different curriculum to the one that I think a number of schools will end up teaching. I think there's a danger some schools are going down a didactic chalk and talk route with lots of rote learning without any of the other stuff because they think that's what Gove and Ofsted intended.