Within the seemingly unrelated worlds of maths and music, creativity and logic can exist side by side. Just as reason alone could never have produced the theorems of Pythagoras or Pascal; so Beethoven's symphonies and Mozart's concertos are much more than the haphazard outpourings of creative geniuses. Today, popular musicians direct their talents with cynical logic towards the mass market; whereas in both industry and government, the creative application of mathematical concepts to the issues of the day is commonplace.
At Rochester Grammar School in Kent, Year 8 girls are finding out for themselves just how inter-related these two concepts can be. Their cross-curricular project, inspired by mathematical and musical creativity, is based on the famous Fibonacci sequence. Dubbed Phi-Factor, the project also involves elements of literacy, ICT and drama. Ges Hartley, deputy head at the specialist music and mathematics college, explains how in devising this particular project, traditional cross-curricular approaches have been spurned to ensure that no one loses sight of the process of learning itself.
"Abstract linkages between curriculum areas based on spurious similarities in content are of little value in developing independent, empowered learners," he asserts. "Of course we want the girls to think about applying their creativity logically and using logic creatively; but also for them to actually think about what they are doing and how they are doing it."
Working out how to fit 15 penguins on an iceberg might sound like something from an episode of South Park, but is actually the first stage of the Phi-Factor project. One of a series of investigations to help pupils develop their problem-solving; it is being led by tutors from the Happy Puzzle Company. The girls work out how to balance their small plastic birds on their equally small plastic iceberg. Put them on all at once, and the whole thing capsizes.
"For some students, planning and trying out ideas as a group, not to mention listening to other people's views, can be difficult," explains maths teacher Tracy Hinks. "Strategies for coping when things get tough are also crucial if ideas are to be followed through to a successful conclusion," she adds.
Although information about how the Fibonacci sequence can be applied in the real world is easy to find, representing it both creatively and logically in the form of a poster, as pupils are being asked to do, is not as straightforward. In deference to the original works of the man himself, rabbits, spirals and swirls, then more rabbits, dominate group portrayals.
However, subject matter is not the main point of this exercise. It is the logical creativity of the collaborative process manipulating the subject matter that counts. The girls have also developed the raw materials they need for the next stage of their project. So it is off to the drama studio and, you guessed it, more rabbits... Here, still imagery, movement routines and role-play are a few of the drama techniques used to transform what was once a hotchpotch of theoretical ideas into workable pliable material. Digital camera to hand, head of drama Richard Coe also makes sure there is something tangible for the students to take on to their next assignation. He explains: "In one representation pupils hop up like rabbits from below a fixed camera position and the Fibonacci sequence develops each time the camera pans away. When it returns the correct number of 'rabbits' are always on camera."
"Representation based around a clear cause and effect structure is the bedrock of all good drama," he adds. "Sequences in which one thing leads to another can shape events and actions whatever type of dramatic form is used."
Throughout the project, creativity is applied and logic directed towards something relevant to both the previous stage of learning and that which is to follow. It is an approach to which the great Italian scholar himself might have offered his approval - after all, many of Fibonacci's own mathematical theorems were devised as ways of understanding and interpreting the 12th-century world in which he lived.
"When we are dealing with an abstract problem we need to hold the idea in our minds in some form or other," explains Ges. "The symbolic language of maths, such as algebra, is one such holding form and the structures and notation of music are another."
"Our project is concerned with transferring problems between these different holding forms," he adds. "In order to do this, pupils need to think about the processes that they are using to solve different problems and to translate this from one subject to another."
As a specialist maths and music college, Rochester Grammar has a room full of music PCs. To devise a soundtrack for their class video, the Year 8s use Cubase - a program which allows both music and video footage to be edited on to computer so it plays back simultaneously. Cubase also facilitates more precise programming in milliseconds - rather than bars and beats, which are too large a lump of time to enable the music being generated to fit the video footage. One group's Fibonacci project is all about the relationship between the lengths of finger bones in the hand. Their music is a trilling effect, where the rapid, repetitive alternation of two notes creates a sort of multi-layered fluttering - symbolising the simultaneous waving of many hands. The rabbit group produces a bouncy rhythmical piece.
In both, an effective fusion of logical and creative thought is evident.
"All the time the students are making decisions," explains head of music Andy Millest. "Working out whether to keep or discard ideas is something even the very best composers have to think about."
As each group of students presents a synopsis of their investigation in front of the rest of their class, the Phi-Factor project comes to a conclusion. Many of them use PowerPoint and most seem engaged. The best groups from each class will get the chance to show their work at a special presentation evening.
Throughout the Phi-Factor project everything fits together. Summarising, analysing and communicating findings in a concise, coherent manner is as much a part of the creative process as is the manipulation of information about icebergs, penguins and rabbits.
"Whatever type of learner you are - visual, audio or kinaesthetic - there is something for you," explains one pupil.