A day trip to Windsor to work out the speed of the river flow and measure the height of trees can be really worthwhile for pupils, says Steve Coates. Windsor was humming with a large contingent of Japanese tourists and their cameras, augmenting the crowds. The high street was lined with people awaiting a procession from the castle.
Then three coaches packed with 140 Year 9 pupils from Chesham High School, Buckinghamshire, arrived. The pupils dispersed, accompanied by staff and sundry sixth-form volunteers, to six pre-arranged places in the town. The annual Windsor maths trail was under way.
Any trip like this takes a lot of preparation. Coaches have to be booked, parents written to and cash raised to cover costs. Pupils must be organised into groups which will work together before, during and after the trip. Staff and sixth-formers have to be briefed. Notes and workbooks sorted out. And, most importantly, packed lunches for staff must be ordered.
In maths lessons before the trip, each group of four pupils was given a group number between 1 and 35, a map of Windsor with a co-ordinate grid superimposed, and six clues - the solutions of which identified the six places where the work for the trail would take place. They had to recall and use their knowledge of co-ordinates, bearings and simultaneous equations.
After identifying the six centres, pupils had a cunningly disguised lesson in modular arithmetic. They had to work out their pre-assigned starting point by dividing their group number by six and taking the remainder. This always generates interesting discussions, particularly with those who have tried to use their calculator. "But look, Mr Coates, I've done 21.6 = 3.5 so it's remainder 5 - so we start at Centre E."
Some years ago, one of our advisory teachers told us about a maths trail based at a teachers' centre in a neighbouring county. We liked the idea of giving pupils a break from the classroom to do some "practical" maths in unfamiliar surroundings so we arranged a departmental visit.
The worksheets for the trail used the buildings and grounds around the teachers' centre - I particularly remember an unusual octagonal clock tower was a rich source of ideas. For three years, we took Year 8 pupils for a half-day outing. Ideally, we knew, the worksheets would have been tailor-made by us for our pupils and the work we had covered with them, but it was nice to have something different which we could include in our Year 8 programme.
Enter a new member of the department who had done some work on maths trails during her PGCE course and who volunteered to write one for us. This gave us the chance to think through what we wanted. We made three decisions: first, that although it would be possible to construct a maths trail on our school site, we wanted to take pupils somewhere unfamiliar. Second, by pitching it at Year 9 - the end of key stage 3 - rather than Year 8, it would allow us to include more interesting mathematics, (and it has provided a focus for the end of term). And third, we wanted to cover a range of mathematical ideas so that every pupil could be fully involved while still offering a challenge for the better ones. For example, one question asks pupils to find the volume of soil in a raised flower bed, and then to calculate how much soil would be needed if all the dimensions were doubled. We have found that this is an accessible question which also allows bright pupils to begin to consider the effect of a scale factor on volume even if they have not yet met the concept formally.
Back in Windsor, pupils studied the pattern made by the bridge railings. Others worked out the speed of flow of the river. In a children's play area, some measured swings, seesaws, or climbing frames before building a scale model at school.
Some considered the effect of perspective on the parallel lines of trees in Long Walk; others used basic trig, which they had just learned, with their clinometers to find the height of a tree. And so it went on.
A week after the trip, each group had to submit a neat, completed workbook based on work done on the day trip and in class. They also had to make a poster describing the work at one of the six centres and build their scale model. Maths staff marked the workbooks and posters. Models were judged and prizes awarded.
Was it worthwhile? Well, not surprisingly, our school inspector commented on the maths trail, and it was gratifying that the comments were favourable. But perhaps the most pleasing feedback she gave was how readily the older pupils were able to recall and talk positively about their memories of the maths trail when they were in Year 9. There are many criteria one could use to make an evaluation, but that seems a good one to me.
Steve Coates is head of mathematics at Chesham High School, Chesham, Buckinghamshire.