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Curriculum Materials to support courses bridging the gap between GCSE and A level Mathematics
A report carried out by a team at the University of Bristol on behalf of SCAA (now QCA)
Jan Winter
This is a brief report of a research project carried out at the University of Bristol on behalf of SCAA in 1997. The brief was to examine the range of materials available to support the transition from GCSE to A level mathematics. The brief was interpreted broadly and the opportunity taken to look at other issues in this area.
Schools and colleges were asked to complete questionnaires about their intake, examination syllabuses used and results. The questionnaire then asked about how they perceived the transition to A level mathematics - did they feel there was a 'gap' and if so what steps did they take to support students through it? What did they feel were the essential pre-requisites for success at A level and how did they help their students to achieve them? The results from this study were used to identify a small number of institutions in which interviews were then carried out in order to examine some of the issues in more depth. These case studies produced interesting results which led the group of researchers to consider the issue from the perspective of the individual teachers' attitudes and to begin a small follow up project looking at teachers' 'stories' of mathematics and the impact these have on their teaching.
The major points of concern arising from the project related to the effects of factors falling in three areas: teaching strategies pre-16, GCSE examinations and teaching post-16.
Some of the main points we found were:
- How a teacher's 'end point' affects the way in which students perceive the mathematics they are learning. If a 'good grade' at GCSE is seen as the end point, at age 16, this can mean that teaching has not prepared the students for future further study. League tables of GCSE results are therefore clearly a concern as they put pressure on teachers to do this.
- The effect GCSE examinations themselves have. The content of the higher grades is not always a good preparation for A level but can sometimes lead to a discontinuity in students' experience of mathematics. This factor is somewhat reduced now, since the last changes to National Curriculum level content, but still needs to be recognised as an issue.
- Teachers varying views of what are 'essential pre-requisites' for success. While we emphasised that we meant mathematical pre-requisites, many teachers responded in terms of students' attitudes to their work as well as mentioning the process skills of Attainment Target 1. Of course, algebraic skills were still the single issue of concern to the greatest number of teachers.
- The greater emphasis in GCSE examinations on the 'processes' of mathematics can affect students' performance and attitudes positively. The kind of skills students acquire through more open and investigational activities were highly valued by teachers as important skills for success at A level.
- How teachers begin an A level course and the effects which this has. Teachers paid particular attention to students' early experiences and this was often closely tied to their views of mathematics and what were important foundations for further study.
- Curriculum materials did not seem to be a major concern for teachers - they felt they had, or could compile, resources to support students from within their departments' available materials.
This report on the project's findings is only a brief outline and anyone interested in the issues outlined would be welcome to contact me at the Graduate School of Education, University of Bristol for more details. This was a small scale, largely qualitative study which drew on the experiences of a small group of teachers and did not offer analysis of large amounts of quantitative data. It did however allow the issues to be explored in a way which offered important points for consideration when future reforms are being considered.