Developments in A-level syllabuses must avoid a return to dull rote-learning, insists Jeff Searle.
I was finishing marking a set of coursework scripts by A-level maths students at the end of the first year of their course. The work was of an investigative, problem-solving nature in which students had a free, but guided choice of problems to work on. I came to the end of one student's work, an investigation into the minimum number of moves in the Tower of Hanoi problem and saw he had written: "I have thoroughly enjoyed this investigation and may pick it up at a later stage in my mathematical education." I had never seen a comment like that at the end of a routine textbook exercise in more than 20 years of teaching A-level maths.
After one result, where this student had checked a formula he had devised against a computer program, and the results matched for 400 discs on four pegs, he wrote: "Astonishing". This student was quite typical. He and many of his colleagues have shown enormous and genuine enthusiasm for their work, way beyond what might reasonably be expected as a course requirement.
These students have used every resource available to produce their work, including each other, the maths staff and computers, in particular the Internet, where they have found a wealth of material to help and encourage their research. Have they cheated? Not at all. They have worked as any good research mathematician would and have produced write-ups which are clearly their own and show they have a good understanding of what they have done. They have a right both to be pleased with their work and to feel proud of it. They will receive recognition of their efforts in the course assessment. Some of these students will take the interest and enthusiasm generated by their coursework with them into higher education maths courses.
This is all surely partly the outcome of an enlightened way of teaching A-level maths that we should be taking further n this new century. Those responsible for Curriculum 2000 would appear to be killing this approach stone dead. The scope for any coursework looks very limited, and far from encouraging the use of modern calculators and ICT, it seems assessments are being devised that prohibit their use. What message is that giving to A-level students? My credibility has certainly been on the line during the past few years when telling students they cannot take their much-loved and used graphics calculators pre-programmed into an examination.
A look at some of the proposed syllabuses suggests we will not have time to allow our students all the benefits of an investigative approach in which they can make full use of technology. The time allotted looks as if it will force us back to the situation where a lot of students learn mathematics by rote, with little understanding, and little opportunity to develop the ability to use it in problem-solving. Valuable teaching and learning time will be taken out of year l of the course to allow for the AS examinations. I fear that soon we shall have students who are qualified, in that they will have passed some exams, but will be able to do very little with their maths.
Good results might be very pleasing for government ministers, and schools and colleges when it comes to performance league tables. However, I have yet to see a satisfactory answer to the questions: "What is A-level and AS-level maths and what should we expect the holder of an A-level or AS-level in maths actually to be able to do?" Being able to show mastery of a technique by doing a routine example in exam conditions is part of the answer, but a much larger part is the ability to use maths creatively, through investigating problems. I cannot see that this could ever be achieved in a formal examination system that prohibits any interactive discussion and use of modern technology.
Jeff Searle teaches maths at Tynemouthsixth-form college