Kevin Lord and Jane White outline an initiative aimed at bridging the divide between school and undergraduate maths.
The changes to A-level mathematics arising from Curriculum 2000 will have significant effects on the undergraduate intake in universities throughout England and Wales from September 2002. They have prompted an initiative at the University of Bath in collaboration with a group of local schools and colleges.
Teaching-initiative funds from the university, together with a grant from the Thriplow Charitable Trust, are providing financial support for the project. Its aims are to develop greater familiarity with the teaching of maths in schools and universities among colleagues in the different phases, and to suggest ways to address the differences to improve the transition from school to university.
For several years there has been recognition of a gap between school and university maths, and some research has been undertaken to identify problem areas. Much of the work has focused on undergraduate subjects where maths is a service subject. Only limited time and resources have been invested in addressing the problems at the school-university interface for maths undergraduates. In the main, these have largely been attempts to evaluate student knowledge at intake based on the content of A-level syllabuses and through diagnostic testing.
Relatively less attention has been paid to the teaching and learning styles used pre-university, although these are significant in influencing students' perception of maths. Differences in the use of mathematical language and notation also exist across the institutional interface and these, too, are likely to present problems during the transition to undergraduate maths.
Essential to this initiative is the collaboration between local school and college maths teachers and university lecturers. For the first stage of the project, teachers were invited to the university to observe first-year lectures and tutorials and, in turn, university lecturers observed A-level lessons. Feedback from the visits was sought on the use of mathematical language, notation and rigour as well as pace, motivational examples and student involvement.
The comments were not entirely surprising: mathematical notation was used more precisely and consistently at university than in schools; rigour was essential in undergraduate maths but less so at school; examples in school typically involved numerical calculation, in contrast to large numbers of abstract examples at university. However, the visits promoted better awareness of the teaching styles and demands in each phase, and helped to establish a useful dialogue between the two groups.
The second stage involved meetings between teachers and lecturers discussing different approaches to teaching A-level and first-year undergraduate maths which might help to narrow the "gap". Language, notation, rigour and proof were identified as areas that could be usefully developed. Students often experience difficulties when they arrive at university with changes in language and notation.
In addition, aspects of proof have been reintroduced into the A-level core (and, more recently GCSE specification). A series of results and theorems were selected to be "proved" by teachers and lecturers to compare the rigour and notation used. For the teachers, this provided sample proofs to use in the classroom and offered suggestions on increasing the level of rigour. For lecturers, they could better appreciate the style of work students had experienced at A-level.
In addition to the meetings and visits, the project has surveyed a group of first-year maths undergraduates on the differences and similarities in the teaching style, mathematical language and notation used in lectures during the first semester compared with their A-level courses. The students completed a weekly journal focusing on these areas. Comments are still being compiled, but initial reading suggests the formalisation and abstraction of mathematical ideas can be challenging, as can the new mathematical vocabulary used in undergraduate teaching. The responses obtained will help to inform developments in the use of tutorial sessions and learning resources provided for students at the university.
Teachers of maths at A-level are relatively restricted in the content they teach by the Core and A-level specifications. However, they are able to use different teaching styles and could place greater emphasis on rigour and precise mathematical language. The initial stages of this project have found that teachers are keen to liaise with university staff and are receptive to new approaches and ideas. The lecturers have also taken an interest in the content of A-level maths and the way it is taught.
Through the meetings, there has been useful dialogue and collaboration and an increase in the understanding of the problems faced by both schools and universities. It is this mutual co-operation and partnership between phases that will ensure smoother transition from school to university maths in the future.
* A booklet outlining the findings of the University of Bath project will be available to schools and university departments from January. It will include examples of proof and provide guidance on improving the use of rigour and notation at A-level. If you are interested in receiving a copy, e-mail Jane White at firstname.lastname@example.org. A small charge may be made to cover postage and packing.
Kevin Lord is head of mathematics at King Edmund Community School, Yate, South GloucestershireDr K A Jane White is a lecturer inApplied Mathematics, Department ofMathematical Sciences, University of Bath