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A Review and Comparison of the Mathematics Gcse Syllabuses Offered for Examination in 1988

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A Review and Comparison of the Mathematics Gcse Syllabuses Offered for Examination in 1988 A REVIEW AND COMPARISON OF THE MATHEMATICS GCSE SYLLABUSES OFFERED FOR EXAMINATION IN 1988 by PETER DAVID MORRIS B.Sc. A Master's Dissertation submitted in partial fulfilment of the requirements for the award of the degree of M.Sc. in Mathematical Education of the Loughborough University of Technology, 1988. Supervisor: Mr. P. K. Armstrong B.Sc. M.Sc. ~ by PETER DAVID MORRIS 1988 ABSTRACT In September 1986 the first groups of children began courses which will culminate in the award of the General Certificate of Secondary Education. From November 1987 (January 1988 in the case of London University Examinations) the General Certificate of Education and the Certificate of Secondary Education are no longer available. The Department of Education and Science and the Welsh Office have published GCSE: The National Criteria - General Criteria (9) in which the rules and regulations for the development of any GCSE courses are detailed. This includes a commitment to 'Criteria Referencing' as opposed to 'Norm Referencing' for the award of GCSE grades. The seven grades defined will eventually be awarded for reaching 'pre-determined standards of performance specific to the subject concerned'. The publication: GCSE: The National Criteria - Mathematics (10) sets out the essential requirements which must be satisfied by all syllabuses for examinations entitled 'Mathematics'. Within the criteria specified the Examining Groups are responsible for devising their own syllabuses and techniques for assessment. The Subject Criteria for Mathematics specifies fifteen ~ims' and seventeen 'Assessment Objectives' which should be adopted by syllabuses on offer. The mathematical content is defined by List 1 which has to be included in ~ syllabuses; by List 2 which has to be included in all syllabuses on which a candidate can be awarded a grade 'C'. Grades 'A' and 'B' will only be awarded to candidates who have completed a syllabus well in excess of that contained in List 1 and List 2. The dissertation studies the background to GCSE and the Subject Criteria specific to Mathematics. Methods of differentiation are discussed together with a general section concerning coursework. The main part of the the work details the schemes of assessment specified by the Examining Groups; each has submitted a scheme including a school based component and a scheme examined entirely by end of course written papers. In addition to these syllabuses the dissertation includes details of other nationally available schemes, namely SMP, KMP and MEI, together with all of the Mode 2 and Mode 3 syllabuses (none from LEAG and NEA). Schemes which are based. on 100% coursework are also reviewed:- ATM/SEG, MEG and GAIM (not available in 1988). Syllabuses which are undertaken in one year, usually on offer to 'mature' students, are also reViewed. The dissertation ends by posing questions about GCSE and Mathematics which have become prominent since its inception. ACKNOWLEDGEMENTS I would like to express my thanks to the following people: My tutor, Hr Peter Armstrong, for his invaluable help, 8lidance and constructive critism during the writing of this dissertation, my wife, Geraldine, who typed and corrected the manuscript and whose help was indispensible. DECLARATION I, Peter David Morris, declare that the contents of this dissertat1on, 'A Review and Compariscn of the Mathematics GCSE Syllabuses offered for Examination in 1988' are entirely my own work. CONTENTS Chapter Abstract 1. Introduction 1 2. The Mode 1 Syllabuses 12 3. Nationally Available Mcde 1 Syllabuses 26 4. Mode 2 Syllabuses 31 5. Mode 3 Syllabuses 39 6. Mature Syllabuses 51 7. Other Schemes 56 8. Conclusion 66 Bibliography 75 Appendices 78 CHAPTER 1 Introduction 1 1.1 General Introduction. The summer of 1988 will see the first staging of a single system of examining pupils at 16+. The G.C.E. O-level and C.S.E. examination dual system will be replaced by the General Certificate of Secondary Education (GCSE). The main aims of the GCSE are: to improve the quality of education to raise standards of attainment to produce a system that is fairer to candidates to motivate teachers and pupils to enhance the esteem in which examinations are held to promote improvements in the secondary school curriculum to remove the need for schools to enter candidates for O-level and C.S.E. in the same subject.' (8) The GCSE is to be administered by six Examining Groups: The London and East Anglian Group (L.E.A.G.) The Midland Examining Group (M.E.G.) The Northern Examining Association (N.E.A.) The Southern Examining Group (S.E.G.) The Welsh Joint Education Committee (W.J.E.C.) The Northern Ireland Schools Examinations Council (N.I.E.C.) The Examining Group's work is to be monitored by the Secondary Examinations Council (S.E.C.) and in particular the S.E.C. have the right to sanction or veto any syllabuses submitted according to whether the National Criteria and the 2 Subject Specific Criteria have been followed. The Examining Groups have to abide by the National Criteria, published in March 1985, when they are :- drawing up examination syllabuses devising assessment procedures conducting examinations awarding grades and issuing certificates. The National Criteria are set out in two parts, General and Subject Specific. 1. The General Criteria set out rules and procedures which govern the practices of the Examining Groups over all assessment matters. The General Criteria lay down guidelines for all syllabuses in all subjects. 2. The Subject Specific Criteria determine a framework for each of twenty (approximately 85% of total entries are made in these) subjects in terms of aims, objectives, content and assessment procedures. The change from the dual system of G.C.E. and C.S.E •• to the single system of GCSE has been prompted for a variety of reasons which the aims of the GCSE mirror. A criticism aimed at a Joint 'a' level and C.S.E. system concerns the proliferation of examination titles and syllabuses, the number of which has increased year by year. The Examining Boards, of which there are 20, had by 1984 developed almost 20,000 different syllabusus. It was not unusual for neighbouring schools to have been undertaking different syllabuses in mathematics. Many schools were also dealing with many different Examining Boards because different departments would be attracted 3 to syllabuses from different boards for a variety of reasons. Confusion was apparent amongst pupils, teachers, parents and employers. Difficulties arose when pupils transferred schools and employers found difficulty in understanding why one syllabus would include an item which they considered important whereas pupils from another local school, following a different syllabus, would not have covered the same ground. 1.2 The Need for Change. The majority of schools are now comprehensive and it seems logical for all comprehensives schools to follow a single examination system. The '0' level, introduced in 1951, was aimed at the population who attended grammar schools although many pupils who entered secondary modern schools gained considerable success in the examination. The C.S.E. examinations, introduced in 1965, were meant to be nationally available for all pupils and the 'average' attainment target was grade 4 with grade 1 being perceived as equivalent to a G.C.E. '0' level grade C. Many people, parents, pupils, teachers and employers never really gave the C.S.E. examination the credit it was due. Quite often it was more difficult to achieve a grade 1 at C.S.E. than it was to achieve a grade C at '0' level in the same subject. C.S.E. examinations also introduced the idea of coursework in examinations so that the final grade awarded did not rest on the candidates performance. in one or two final timed written examination papers. The performance of a pupil over an extended 4 period, usually two years, was assessed. However, in mathematics, coursework was often a misnomer. , Coursework , consisted of a series of timed written, formal tests. Pupils who were neither truly '0' level standard or truly C.S.E. standard were placed in the difficult position, as were the teachers, of having to enter two examinations. More often than not they would be expected to follow an '0' level course in preparation for both '0' level and C.S.E. examinations. A single system of examinations, therefore, with a seven point (eight really if. one includes ungraded) attainment scheme should cater for the majority of pupils in a comprehensive school. 1.3 GCSE and Mathematics. In the introduction to The National Criteria for Mathematics (10) it states that the 'criteria should be so interpreted that any scheme of assessment will:- (1) assess not only the performance of skills and techniques but also pupils understanding of mathematical processes in the solution of problems and their ability to reason ma thematically; (ii) offer differentiated examination papers so that, by choosing papers at an appropriate level, pupils are enabled to demonstrate what they know and can do rather than what they cannot do; (iii) encourage and support the provision of courses which enable pupils to develop their knowledge and understanding of mathematics to the full extent of their capabilities, to have 5 experience of mathematics as a means of solving practical problems and to develop confidence in their use of mathematics; (iv) have regard to the need for examination tasks to relate, where appropriate, to the use of mathematics in everyday situations.' The National Criteria of Mathematics document lays down fifteen Aims (see Appendix A) and seventeen Assessment Objectives (see Appendix B). The Syllabus Content is divided into List 1 and List 2 (see Appendix C). The content of List 1 has to be included in all syllabuses called Mathematics and candidates expected to achieve grades E,F,G will not be expected to know more.
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