Opinions on primary Maths please.

Discussion in 'Mathematics' started by Anonymous, Nov 14, 2011.

1. AnonymousNew commenter

This debate has been had before but let's go.
FIrst - I am really tired of people saying "We don't do times tables". Let me assure that every primary school I have worked in, tables has been key and has been taught in a variety of ways including daily repetition, songs, inverse - here's 20 - how do I make it etc. A whole lot of different ways so children become familiar with them.
I am quite good at maths but I did find it hard at primary - especially long division. I just did not get it. We were shown a method but still did not get it. I would bet there are children who still do not get it - but chunking is another perfectly good way and the idea of counting up e.g. 10 tickets cost &pound;60 so 20 cost &pound;120 then 4 more cost another &pound;24 so thats &pound;144 buys you 24 tickets is a useful idea.
Same for multiplication - I have so many tutees who struggle to work out 34 x 6 without resorting to a method like the grid method. Both short multiplication and the grid method reinforce the concept of partitioning to multiply and it's not the world's hardest sum to work out mentally.
Numberlines, practical equipments etc - personally I think they are fantastic and very visual ways of seeing difference between, take away and addition. Not everyone is a numbers person so they do serve a purpose. This can then lead to columns.
A lot of people in this country lack numeracy skills - is this down to "trendy modern teaching methods in the 60s, 70s and 80s" or is it a problem spread through the entire generation including those who went to school in the 40s and 50s?

2. AnonymousNew commenter

Thanks for contributing Robyn and apologies if I am raking over old coals. I am a secondary languages specialist with an interest in maths but I suppose that I am posting here as a parent and as somebody who is concerned about the lack of basic skills that I see around me. I think a generational difference is that to get a grade A at 'O' level meant that you had to be very good at the basics and more. However, I know of A grade GCSE pupils that cannot do times tables or even long subtraction.

3. Mathsteach2Established commenter

I am not a qualifed primary teacher, I am secondary physics. However, my teaching experience covers the whole compulsory school age-range, 5 to 16 years. I am a firm advocate of Piagetian theory and methodology, and aware of recent developments from it.

For me with KS1, all mathematics needs to be experiential, practical and hands-on. Childen learn by doing, mostly through play. Some countries do not begin their formal education until age 7.

At the same time, they are, of course, learning to read and write in their first language and possibly a second language, therefore I would not burden them with the writing component of the symbolic language we call mathematics. We can begin that in Y3, which may then be a third language for them to study.

However, the grounding they have already had up to KS1, where they have being having hands-on experiences in counting and measuring, and talking and writing about this work in their prefered languages, the translation of their ideas and understanding into the symbols of mathematics has never, for me, produced serious difficulties.

To take a most simple example, at reception level the children might colour in on a worksheet pictures of two fish and three fish making five fish.

They need not be shown that in mathematics this can be written (omitting the units): 2 + 3 = 5 until Y3. However, in their language studies they may well be able to read and write the words "two", "add" or "and", "three", "equals" or "makes", and "five", and they will certainly have a sound conceptual understanding of these words. As their mathematics, taught as a symbolic language, proceeds from KS1 up to KS2, they will discover, or be shown, that the use of the symbols makes calculations much easier to perform, and algorithms can be taught.

In my experience, the move from pre-operational to concrete operational can be greatly assisted by using proprietary equipment such as Cuisennaire Rods and Dienes Blocks.

Well, that's my opinion, anyway, as invited by the thread title!

4. AnonymousNew commenter

Thanks for that Mathsteach. You suggest year 3 for introduction to more formal symbols. When would you suggest introducing times tables, longer multiplication, long division and long subtraction? And what would be your preferred methodology to ensure progression to the sort of maths needed for physics?

5. Mathsteach2Established commenter

As with the learning of languages, memorization can occur at the earliest possible age. My sister married a Welshman, and my nieces and nephews were bilingual by the time they started school. This, of course, came from usage of both english and welsh at home. Similarly with reading.

For those children not fortunate enough to have these opportunites at home, schooling must try to make up. A second language cannot succeed unless the children learn some vocabulary "off by heart". Poetry recital and speaking parts in plays are all taken on by infants. Done in an enjoyable way, learnings the times tables, as we call them, is not a different skill, and the understanding will come from the hands-on activities as the children realise they can count the number of items in an array (set in rows and columns - a matrix) by multiplying (which at this level can be seen as repeated addition) the numbers of rows and columns together.

In all of this work in the infant school, I say again, there is no need to burden them with the written side of mathematics involving its symbolic language nature. In wrtitng, many of them have enough difficulty correctly forming the 26 letters of our alphabet! Japanese children spend many hours practising the formation of Japanese characters, I understand.

I would have, and have had, great difficulty teaching physics to Y7 children who are not familiar with the symbolic language nature of mathematics (now beginning to require the use of algebra) nor with the basic numeracy understanding of the mathematical algorithms they are required to use (for Y7 physics, as a separate subject). For those children, I have often abandoned the mathematical side of physics, and just let the kids play with the apparatus (magnets, floating, lenses, springs etc.) practically for as long as they liked, very much infant school style.

Occasionally I have given them support in their mathematics by the practical hands-on activities especially Denes Blocks, or I trained the secondary mathematics teachers to do so, asking them to give less time to their exercises where they are only using the written symbolic forms. Not that I disapprove of repetitive exercises in mathematics, again to commit to memory the algorithms involved. This is like learning a second language or learning to play a musical instrument, practice makes perfect, they say!

It will be a longer post to answer all of your questions, existentialtyke! I will try again later.

The emphasis in primary maths is on mental methods. The grid method for multiplication teaches the children how to perform 16x6 in their heads easily. It would be a tragedy if children had to do as many adults do and reach for a pen to write it out in columns when it's just 60+36. Simples.

7. frustumStar commenter

Thinking ahead to "real life", I'd be disturbed if they were using the grid method: I'd much rather that they estimated and then used a calculator. That is the most reliable method.

8. jac1970

I can't claim to be an expert, but I am currently studying the Graduate Diploma in Mathematical Education, and completed the residential at Bath Uni in the summer, which was really interesting. We went through everything literally for KS3 Mathematical Teaching, and came up with 27 different ways of multiplication - only 3 for division. Times tables came in to virtually every one - in fact I am struggling to remember one where knowledge of times tables wouldn't have been essential or at least very helpful. The biggest thing that came out though with every subject part was that all the teaching had to be interesting, and fun. I know that seems very basic, but if you haven't got the students switched on and interested, and enjoying learning about maths in real situations, with not just reading and writing out experiments over and over, but getting up off the chairs, actively thinking as much as possible. If we get the children to really think, and understand then if they come across things they can't work out first of all we can give them the tools to work so much out for themselves. "What I know" and "What I have" and "Say what you see" are pedagogic strategies that work.

9. jklmn

I've been teaching maths in both secondary and primary settings since the early 1980's so feel able to comment. When I started teaching I taught the traditional methods I had been taught and able children could do them, less able couldn't, this I felt was unacceptable and have spent my career trying to get all children to be numerate. All the methods you describe in my view are staging posts on the way to a clear understanding of traditional methods. As a child the methods I used were all about repeating a routine but failing to understand why other than it give the right answer but i was an able child who could remember the routines.
the number line, a child has to have an understanding of place value, approximate answer size and calcuation to be able to calculate. 56 + 47 on a number line clarifies understanding of how the answer increases, a column method for some children is just a routine they follow hence why they write 913 as the answer as they fail to understand you carry the 10 from the 13. The same with subtraction however by Y9 and certainly by GCSE all children should have taken the steps to a column method.
Grid multiplication isn't it an ideally adaptable method for algebra? multiplying out a quadratic, (x + 3) (5 - x) or x(x-4)? Great method
Chunking leads into short division - and who needs long these days everything can be done by short!
These methods are not the end in them selves even able children should fundamentally understand what they are doing rather than just getting the right answer - that to me is the change in teaching of maths since I started teaching children really understanding rather than jus able to mimic a process they have seen.

Hope that helps