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?

That was supposed to be This about New Statesmans Singapore post.

Though I did make sure dd knew times tables I do not think large amounts of worksheets are necessary for children to understand maths. I remember dd getting thoroughly bored by Mathletics; endless repletion of things she could basically already do. Also arithmetic is not mathematics; only a part of it. I used the method of go over something to introduce it, go over it again to understand it and go over it again to remember it, partly from what I read, but partly from my own ideas and because it worked. Once a child has done a three or four multiplication sums and recalled the method, doing further sums is only adding tedium.

There is sense in making sure children know why they are doing something, not just how to do the method and for that children do need a good understanding of how sums work. To take the example given in the blog: 376*9. I asked dd, Y7, how she would do this and she replied: times by 10 and take away 376.

It does seem odd that so much has been learnt in maths, but we still have no idea of the best way to pass on that knowledge to students, only the whims of politicians of what method is going to be in this year.

Dave Gorman,, talking on the Infinite Monkey Cage brought up the idea of doing trials of different methods though schools to see which worked, the only problems being it would involve a politician admitting they did not know something and parents preferring all children to have an equally bad education than half of them getting an education that possibly worked.

Also some failing schools in America are now getting fantastic results by letting their students loose on Khan Academy to work at their own pace and just having small tutorials in class specific to the areas in which the students are struggling or to add more depth and interest to their work.

My wish for the new year would be for a trial of flip learning in maths in a failing school.

I find my DD (6)is being moved on in maths so quickly that while she can remember what she's just been taught (division)she quickly forgets the basics(adding, taking away simple numbers such +1). She was falling behind at school as they seem to move so quickly. I have enlisted a tutor to help and she gaining a much better understanding at the basics but it's with my help as well doing daily practise of simple sums, only 10 a day, takes about 5 mins, without this I think she would be lost.

"it's made clear that if the children aren't constantly using manipulatives or carrying out projects like creating bridges or something they aren't learning,"

It's the constant pushing of views like these, for which there is in fact no proper evidence base, that is a huge part of the problem. For years now, the academics in university teacher training/education departments have been doing badly designed "studies" which have foregone conclusions, in order to "prove" their philosophical/ideological ideas on how children learn. I recently read a particularly outrageous one: the author filmed primary maths lessons in Finland, and discovered that Finnish teachers use chalk and talk, whole class questioning, no group work and lots of practice in workbooks. His conclusion? That Finland's exceptional PISA maths scores must be down entirely to something in the culture, because such "bad" teaching methods couldn't possibly be having a positive effect.

We're very good at that sort of 'evidence' in education. Properly carried out RCTs are rare I think.

I'm midway through my PGCE at the moment and I agree. Most teachers come from a humanities background and we rocket through the maths topic.
That doesn't necessarily mean your two points are related. It also doesn't mean that this is how it works in all schools. We certainly don't "rocket" through any Maths topics...and I hate uncontrolled mess, so there's no stupid bridge building for the sake of it, either. Teachers from other schools have come to observe our maths lessons and commented on the quite extensive practice our children are getting. (I think they were a bit shocked...) I rarely do "group work" in Maths, although my pupils are allowed to work together, if they so choose.
It depends on the year group as well. We'll be starting preparation for the tests in May after the holidays, so some things will be revision and others will be an extension of what they've covered before. I've just spent ages creating the workbooks for my different groups. The one for my Level 4s consists of 150 pages. They need lots and lots and lots of practice and quite a bit of exposure to everything we are covering. This will be supplemented with problem solving activities as needed.
I've come from a humanities background (my degrees are in History/Anthropology and Linguistics), but my A-Levels are in English, Economics, History and Mathematics. I'm not that great at teaching History, but I'm rather good at teaching Maths and English.
Perhaps it would be an idea to talk to your class teacher about why you appear to spend so little time on each Maths topic.

Just tonight, my year 6 DD attempted a word problem involving exchange rates and choosing which country in which to buy a jumper. The best way to work the problem was using fractions. (Much easier than dividing decimals without the aid of a calculator.)

She understood what she needed to do, which steps she should take, etc. the whole thing fell apart because she didn't know how to manipulate fractions. To work the problem out she needed to move between mixed fractions and improper fractions. She needed to know how to divide one fraction by another. It was the rote technique that she lacked.

Without being able to do the "mindless" arithmetic, one cannot go on to solve the more interesting problem. I am sorry to see her fall on the first hurdle. Her teacher plans for her to sit the level 6 maths sat in the Spring. I've never seen her do the sort of practice that I had as a child. I've been waiting for years for them to get down to business. I now assume they never will, and the aims of math education are very different to what I exoerienced as a child.

To work the problem out she needed to move between mixed fractions and improper fractions. She needed to know how to divide one fraction by another. It was the rote technique that she lacked.

I disagree that these things should be taught by rote. It is easy to tell a child that to divide by a fraction you turn it upside down and multiply and then get them doing several such sums. It will give them no insight into why they are doing this. Drawing a number of circles and asking how many halves, quarters or thirds they can get out of them will not only help them remember but will build their confidence in manipulating fractions.

Of course a child needs to know the why but they also need the rote so it becomes automatic.

As in many subjects it isn't a case of "either or" ...both are necessary.

Agree. You teach a concept through activities that allow them to develop an understanding of what's going on. But they also need to know skills, number bonds and times tables to automaticity so they can focus on higher order problem solving skills not reasoning their way through a written algorithm.

IMHO that means they can carry out a procedure quickly, with a high level of accuracy in a lesson where it hadn't just been taught. The number of repetitions that will take will be different for different children but it would be a rare child that only needed 5 questions to be that competent.

Some really good points raised and I like the consensus of a mix of 'rote'/ experience of calculation with application (especially to new problems extending knowledge).

Interesting idea to try flipped learning in a failing school - JustRichmal. In a way DD1 did precisely this.

It's only 1 child - so only anecdotal evidence - but for us getting DD1 to follow an on-line maths programme (Mathsfactor) outside of school which was structured, which included clear explanation & visual demonstration of concepts & offered lots of opportunity at practice (homework/ on-line games/ away from computer games) was a game changer as far as we were concerned.

Well put mrz that is exactly how I feel as a parent.

Of course I want an understanding, but understanding isn't the same as being able to execute the problem. Both are needed. It is the practice which is missing.

Just to take an example. Suppose a child were just starting 2 digit long multiplication. Would they learn better by working through a sheet of twelve sums until they really had the method for say 40 minutes or would they learn better by doing 3 sums for 10 minutes every day four days in a row? Which would they find easier? Which would they enjoy more? which would best increase their understanding and by which method would they retain the information on how to do such sums?

I basically use the later with dd, but is there anything more than anecdotal that one method is better than the other?

"There is sense in making sure children know why they are doing something, not just how to do the method."

This is an utterly tedious straw man argument. Absolutely nobodyon this thread or elsewhereis advocating making children memorize procedures without understanding them. Nobody. Singaporean teachers teach children how multiplication works and how to use it--but they also give them lots and lots of practice.

I really don't understand why advocates of constructivist approaches to maths seem to think that "understanding how multiplication works" and "knowing your tables down pat" is some kind of mutually exclusive binary choice.

As others have said, yes, there is value in making children do lots and lots of problems, even when they seem to know how to do that kind of problem already. Later on they will be tackling algebra, trig and other things where you have got fractions and powers and negative numbers and multiplication all going on at once in the same problem. They need to be absolutely pat on each of those types of basic operation, so that they can devote the "thinking bit" of their brain to focusing on the algebraic or trig. part of the problem.

If you are still having to fumble about in your brain trying to remember how to multiply 10 to the power of 3 by 10 to the power of 5, and going "Oh, is that what you do to divide a positive number by a positive number...? Erm...." "Let's see, what are seven nines again? Hang on, wait while I faff about doing a gimmicky trick on my fingers to help me remember...." then your "working memory" simply has no space left over for focusing on the higher-order part of the problem.

What's more, if you make a mistake, you will have no good way of giving yourself feedback on your errors or working out why you went wrong--"Well, maybe I made a mistake with the multiplication... or perhaps I arsed up the fractions bit like I do sometimes..... I've never been quite confident with those..."

It is very intimidating and discouraging for students. That is why students who have not been really well drilled on operations during the primary stage have a tendency to scrape through during the early secondary school, but then collapse when they start doing things like algebra.

This thread saddens me. I love maths and despair at the idea of my DCs not having a proper foundation.

So I've taken it upon myself to talk about numbers etc all around us - much in the same way as we do with reading and writing. My maths teaching at primary school left me unable to do mental arithmetic but I excelled at maths when it came to A levels and university. I will be keeping a close eye on their teaching.

As others have said, yes, there is value in making children do lots and lots of problems, even when they seem to know how to do that kind of problem already

Not an approach which would have worked with my dd. There were lot more productive ways of dd spending her time when learning maths. I'm not surprised children take years to learn what they could learn much quicker. By children finding maths difficult, they probably just mean they are finding it tedious.

JustRichmal, I am very happy with the "little and often" approach you outlined earlier. What I am getting is the "little and not very often" approach from my DC's school.

ToomanyChristmasPresents, like PastSellByDate, I too taught dd at home taking this little and often approach. By the end of year 4 she was so ahead she was learning nothing in maths at school and we decided to home educate.

This is not a "teachers are no good at teaching" post. Teaching 121 is very different from teaching 30 students and anyone who can do it has my admiration. All I can say is what I found worked for dd. I just wish a more scientific approach to looking at what works and what does not were adopted by schools; rather than politicians either harping back to the good old days of endless drilling of facts, or the "in with the new" approach of giving children blue tack and string to work out trigonometry for themselves.

After decades of compulsory education we know what to teach, but still have not the slightest idea of the best way of teaching it.

But why only three problems For four days, why not 10? It might work for your dd but some will need much more repetition than that. Half my year 4 class would have sworn blind they had never done column addition on day two if they'd only done 3 examples on day 1.

I'm not sure anyone was advocating lots of examples but only on one day anyway.

Three problems for four days was not meant to be prescriptive, just a way of breaking up 12 questions into a 'little and often' grouping. Is 12 questions the right number anyway ? Nobody knows!

Do children need lots of repetition and lots of examples to work through or do they need to do a lot less and repeat next day then a few days later? How much and how many days later? What is the optimum way of teaching children? Or are they so different it would be best to go over to flip learning and let them all go at their own pace? There is no research so no one knows. There just seems to be opinions and fads as to what will work best. All I had was what I had read and intuition, but I don't think anyone knows. At least Tony Buzan did ask the question of how best to teach.

Some children will remember after one or two repetitions others will need many more

I think the idea that nobody knows and there is no research isn't entirely true. Pretty strong evidence from cognitive psychology supports the idea of "spaced practice" where you leave gaps of time between practice. What probably can't be specified is how many problems to be done in each practice session, but that probably varies between individuals anyway, and also probably differs for whatever it is you are practising.