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Secondary Magazine - Issue 30: From the editor

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Created on 19 March 2009 by ncetm_administrator
Updated on 27 April 2009 by ncetm_administrator

Secondary Magazine Issue 30

Mathematics and science

I'm running some physics training later this month and have a request to explain the best way to teach the algebra of re-arranging equations with three variables like speed/distance/time or density/mass/volume. Could you give me the thinking on this from a maths perspective? I know the 'triangle' is not popular - but still used a lot by science teachers.

I was really pleased to get this email recently from a colleague in the science department. What a nice opportunity to start a dialogue with a colleague about the relationship between science and mathematics. I wonder what pupils think that relationship might be? In the importance statement for mathematics it says that:

Mathematics is fundamental to national prosperity in providing tools for understanding science, engineering, technology and economics.

It is clear that there is interdependence between mathematics and science, so the opportunity to make connections both within and between them is invaluable. Various ‘Numeracy across the curriculum’ initiatives have completed curriculum audits and made colleagues from both subject disciplines more aware of the demands from each subject, but can you imagine the experience of groups of pupils as they encounter mathematics within science? Does it make sense to them? Do they see the connections? Pupils seem to find it hard to make links within mathematics so it is necessary to make some of these links explicit – making connections explicit across the two subjects is even more fundamental to enhancing pupil understanding.

The recent Ofsted report Mathematics – Understanding the Score says:

secondary pupils...know the difference between being proficient at carrying out techniques and understanding the underlying mathematical ideas. They recognise that they often learn methods by following teachers’ illustrative examples and working through many exercises, obtaining correct answers without really understanding why.

I worry that using ‘the triangle’ will only re-enforce pupils’ experience of achieving correct answers without understanding – and will that benefit their learning of either mathematics or science?

So how will I answer my colleague?
As we know, algebra is generalised arithmetic and so my response will be to refer my colleague back to some arithmetic and the ‘facts for free’ scenarios.

If I know that  2 x 5 = 10, what else do I know?
   5 x 2 = 10
   10 ÷ 2 = 5
   10 ÷ 5 = 2

The main task is to give pupils the opportunity to become totally familiar with the relationships between this family of number facts, and then extend this to another family of number facts which are not so intuitive.

For example, if  24 x 35 = 840
then    35 x 24 = 840 
   840 ÷ 24 = 35
   840 ÷ 35 = 24

Having got to grips with some specific facts, I can start to generalise:

If I know that  a x 5 = b, what else do I know?
   5 x a = b
   b ÷ 5 = a
   b ÷ a = 5
And finally, if  s x t = d
then    t x s = d
   d ÷ t = s
   d ÷ s = t

It would be appropriate to make some links between pupils’ mathematics lessons and the mathematics that they use in science. It would be relatively easy for the mathematics department to spend time in their starter activities to focus on number relationships before and during the time when the science department will be using and needing to rearrange formulae for speed/distance/time or density/mass/volume or acceleration/speed/time. An ongoing dialogue is vital so that these opportunities can be exploited.

If you have collaborated with colleagues in your science department – why not tell us about it here?

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