Number lines explained....

Maths is certainly not what it used to be. For one thing, its name has changed; your child no longer learns "sums" or "maths", but "numeracy". For another, the way maths is taught is completely different. And that can be confusing for parents.....

Today there have been suggestions of "family maths classes" to help not just children, but their confused parents too. In the meantime, School Gate is here to help with at least one aspect of primary school maths - the number line.

For those who are desperate to know just what a number line is, Judy Sayers, senior lecturer in Mathematics Education at the University of Northampton, is here to give us our very own lesson. But before she starts, you should take a look at this excellent example of a number line courtesy of the website from Ambleside Primary in Cumbria.

Now, over to Judy:

"I have seen children who struggle with calculation transformed by the use of number lines. We have probably all used them in some form or another, for example, using a ruler to help us add one number to another. Today all children learn with a number line - first encountering them in reception when counting on, adding on or taking away.

If you look at this example from the Primary National Strategy calculation advice, you'll see that number lines can then be adapted for all sorts of things...

Number lines are what they say they are - various numbers all laid out on a line. Once children work with them, they'll soon learn that if they start at any number, then add or take away another, it leads to a different number.

The beauty of using the number line is that children have a mental image of moving along it, and this can help those who struggle with abstract ideas.  Many children soon grasp what is happening and no longer need the graphical image to support their thinking.

Teachers also introduce empty number lines when children are ready to make the leap - this is when they have a good understanding of the number system and know exactly what number comes before or after any other. This is where the use of a number line can become really exciting...

You just need a question and a line, and  you can do all sorts of things, not just addition or subtraction, but multiplication and division too - this example from the ATM website is somewhat more advanced...

Once children have developed their understanding and use of the "empty" number line for their own "toolbox" they do not need to use the number line, because the visual image becomes abstract and they become far more efficient, effective and most importantly confident, in their abilities to manipulate numbers.

The old methods of calculating were introduced far too early in the English schooling system and were only good if you were accurate and had a pencil and paper to hand. They did not necessarily develop mental strategies that are explicitly taught today. The methods today all help to develop mental strategies and agility and therefore develop mathematical thinking in ways we were never taught. The number line is just one of the tools which support children's thinking and understanding about the number system. Gone are the days of boards or worksheets full of "sums" to plough through, children are provided with the opportunity to explore the number system in more interesting, exciting and meaningful ways."

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Comments

[Nancy]

I was pleased to see the headline of this article as I struggle with explaining maths to my 7-year-old and have been 'reprimanded' by her teacher for teaching her the wrong techniques.Unfortunately after reading it I'm still none the wiser. I'm not the most natural mathematician so perhaps I'm not the best person to comment, but I feel all these number lines and 'number sentences' (what's wrong with 'sums'?) make things more complicated than they need to be.Maybe I'm just stuck back in the eighties...

[S Atan]

Its all greek to me

[Kim]

Hi Sarah - you should tell them! Just so you know I'm not talking out of my hat, here's the link to the primary national curriculum on the govt's own site:

http://www.direct.gov.uk/en/Parents/Schoolslearninganddevelopment/ExamsTestsAndTheCurriculum/DG_4015959

As you can see, it talks about "maths" rather than "numeracy".

[Glen Thomas]

The terms 'numeracy' and 'mathematics' are not interchangable:

Numeracy refers to a sort of quantative literacy, so it is contextual, concrete and practical, and is useful for survival and daily living. It covers number sense,
logical thinking and data interpretation, for example.

Mathematics is rather more ideal, abstract and pure, adding to numeracy areas like algebra, statistics and calculus.

Those who remember maths classes at secondary school may remember the rote drilling, but forget the important foundation building done by the primary schools.

Some of the techniques taught may not look efficient, but they may be better at illustrating basic principles.

Glen

Education blog: click on name below

[Whimsey]

Number lines are useful, especially when you get in to negative numbers (teachers tend to introduce negative numbers by talking about temperatures, as it's much easier to understand the idea of 'minus five degrees' than just 'minus five')

One thing I don't approve of at all, is doing sums 'horizontally' instead of vertically, as if they are done horizontally, viz:

45 + 87 + 107 = xxxx

it's impossible for the child to see the decimal/place arrangement, and impossible to mark the 'carries' and 'borrows' effectively.

[Sarah Ebner]

Hello Kim,
They call it numeracy at my daughter's school. Maybe I should tell them!

[Kim]

Just one small point - a couple of years ago it was decided to rename "numeracy" as "mathematics". So the second sentence of the post isn't completely accurate.

[PIPKIN]

My yr 2 daughter had an explanation of the calculation strategies she was being taught sent home with her numeracy homework. Initially, it seemed wierd to us 80s kids. Then when I thought about how I do mental arithmetic esp using money/working out change, or dates and ages, I realised that I use similar strategies, even though I was never taught them. I still write columns to add or subtract "big" numbers or do multiplication or long division if I can't be bothered to use a calculator. But then I got 2 As for Maths/FMaths A levels then did an engineering degree, so maths doesn't faze me.

[DAVID VINTER]

We started arithmetic aged four, and knew all tables to 12x12 by age 6. Then did mental arithmetic every Fri morning. I can still do it 60 years later.

SAY 17X19--= 340-20+3 = 323, I think my old method is easier.

[IK]

wow, just what I needed for my 4yo daughter. thanks!