When maths and science collide
A. I put a posting on the science forum at www.tes.co.ukstaffroom in order to "open up the discussion on algebraic skills and science among school pupils and with support teachers".
Here are some of the responses: Science Guy: "The area that causes the most trouble is rearranging equations. We need to do this in Year 8 when we look at speed and try and get them to change the formula around. When we ask if they have done this in maths they always look at us blankly (as they would not come across this until Year 10). The other area in maths that annoys science teachers is graphs and lines of best fit. In work from Year 11 which involved plotting a graph from a rate of reaction (which had a nice curve), every single pupil drew a straight line of best fit as 'Lines of best fit are always straight'. What makes this worse is that this year on the SATs paper was a question that asked the kids to plot a line of best fit which was clearly a curve, take readings from it and ignore an anomalous result. I showed it to the maths teacher responsible for producing the cross-curricular numeracy booklet and he has decided to encourage the maths department to look at this."
Woozle: "The science teachers at my school invigilated GCSE maths and were stunned at the questions. The level of mathematical ability required for foundation maths (up to grade D) is way below what we expect our foundation students to do. In maths they are asked to draw a line 120mm long, shade in 34 of the boxes and calculate simple areas etc. In science we demand line graphs (best fit included) and formulas rearranged!"
Teachers attending a Specialist Schools Trust science and maths seminar at Warwick University also selected transposition of formulae and lines of best fit as topics that should be addressed earlier in the maths curriculum.
A pupil who is in a higher science group might be in a foundation group in maths. Such pupils need to be identified and a support mechanism put in place. Support staff may be encouraged to mentor individuals or small groups of pupils once they have received training in these aspects of maths.
The technique of using a triangle to provide a mnemonic for solving speed, distance and time problems encourages this lack of ability in transposition of formulae. Revision guides are littered with these triangles for different science formulae.
This formula is for speed-distance-time calculations, which may entice you to put the s at the top of the triangle. This is all very well if you can remember where to put the s, and can lead pupils to think that you need a different formula for each calculation, instead of being able to rearrange a formula. I avoid using this triangle and begin by using words they know.
Then, in stages, I show how the words transform into the algebra.
* Speed is in miles per hour (or kilometres per hour).
* Speed = miles per hour (emphasise this means miles travelled in an hour).
* Speed = miles V hours (for "per" read "V").
* Speed = distance V time.
The variables speed (s), distance (d) and time (t) should be defined with their symbolic notation so that pupils develop the good practice of defining notation.
In symbols we get s = d V t. Pupils should write this as a fraction so they get used to the arrangement: s = dt .
Ask them to transpose the formula for t (this may be asked as "rearrange for t", "make t the subject of the formula", "isolate t").
To transpose the formula, pupils should be reminded of the balance method of solving equations: "What you do to one side of the equation you must do to the other side to keep the balance."
Then ask: what operation is being performed by t? (answer: dividing d); what is the inverse (opposite or undoing) of dividing? (answer: multiplying).
Encourage them to get rid of the fraction first by multiplying both sides by t. Point out that t V t = 1 and d x 1 = d, leaving s x t = d.
Using colour makes the process easily identifiable and mistakes are easier to track.
Again, ask pupils to identify the operation being performed by s and ask for the inverse operation, leading to dividing both sides by s. Point out that s V s = 1, leaving t = ds . Thus the formula is transposed for t.
Wendy Fortescue-Hubbard has been awarded a fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses.www.nesta.orgEmail Mathagony Aunt at email@example.com Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX