It’s been a pretty full on term so far, as it always seems to be, so it was lovely to have a break yesterday evening and do some maths for ourselves! We were fortunate enough to welcome Trevor Starbuck to the first Birmingham and Solihull Further Maths Support Programme network meeting hosted at John Willmott School. The intention of these network meetings is to bring together teachers from across the city who have an interest in meeting with other teachers to explore issues relating to the teaching and learning of mathematics and further mathematics at A Level.
Trevor had spent part of the afternoon talking with some of the higher achieving Year 11s, and then turned his attention after school to a small but very enthusiastic group of willing maths teachers. Not having had the privilege of teaching A Level, and still holding a passion for all the mechanics modules I chose at Uni oh so many years ago, I was really looking forward to this session.
The classroom we were meeting in had been transformed into a den of mechanics experiments. Trevor’s enthusiasm for the subject was radiating from him as he introduced the two experiments we were to undertake. These involved, amongst other things, half pipes, marbles, clamp stands, metre rulers and timers.
Firstly, there was timing a marble rolling some given distances. The metre long pipe, marked into 20cm segments, was kept as shallow as possible for the marble to roll. It was then timed 3 times each for rolling each distance from 20cm to 1m and the mean value taken. Results plugged into Autograph and the following graph was produced:
The second experiment involved the the rolling of a marble across a tilted table. Our job was to track its path as accurately as we could, to gather data on its path, distance and time. We first set the pipe and clamp stand so the marble could travel a decent path up and across the tilted table. Next was to identify the end point of the path, which crated the x-axis. This path was timed (at least 5 times, and a mean value taken) and the axis was then split into 8 equal parts. Rolling the marble as consistently as possible, we tracked when it passed each division (again, 5 times for each, taking the median of the points we had plotted on the division lines).
We ended up, as you would expect, with a lovely parabola. The final two measurements to take were the height of the middle division – the point where the marble started its downward journey, and, using a bit of trigonometry, the degree of inclination of the table.
These experiments were reminiscent of those undertook by Galileo in the late 16th Century. Ofcourse, he didn’t have electronic timers, so we were quite relieved when Trevor didn’t insist on use using a water hour glass timer, similar to what Galileo would have used. As well as rolling balls across inclined planes and measuring their distance, Galileo also used the Tower of Pisa to give him a vertical height from which to drop objects. He was able to demonstrate that a body dropped from height starts at zero velocity and increases his speed over time (rather than the constant velocity, that was larger the more the body weighed, assumed by those before him). This also involved his discovery that the velocity of a falling body is independent to its weight and the mathematical expression that, the speed of an object increases as the square of the time, hence our quadratic graph from the results of the first experiment.
Fast forward 100 years and armed with Newton’s Second Law of Motion, we are now able to form some calcualtions from our data.
And so we have it; practical experiments and calculation enabling us to derive a (very approximate) value of gravity. There is of course discussion time here for all the aspects not taken into consideration, the main one being air resistence, but our time had come to an end.
The Birmingham and Solihull FMSP network hope to meet at least termly. It was a really enjoyable, practical session; a chance for us teachers to focus on mathematics, from those of us who would like to brush up on our A Level to those who have been teaching it for many moons! Each meeting will have a specific focus such as this, but there will always be time for discussion of other matters according to teachers’ interests and concerns. I do encourage any local teachers who are interested in A Level maths (you don’t have to be teaching it) to get involved with the network. For more information, please contact: