Cadena De Valor

The development of A-level mathematics since its inception has seen a change in purpose, content, format and assessment procedure.

Initially its purpose was to provide a route to the study of mathematics-based courses at university. The syllabus was determined by Higher Education Institutions and the examinations were set and assessed under their control. The grades awarded to

students reflected their achievement in comparison to that of the other students, in that year’s cohort.

During the 1970’s the traditional format of Pure and mechanics components was expanded to include statistics. The number of syllabuses available increased and the lack of uniformity in their content led to the re-introduction of a core curriculum in 1983. In 1984 the first Qualification-awarding body was established to oversee course content and assessment. The A-level was re-focused to be the final, and most advanced part, of the study of mathematics in school as well as an entrance examination for the universities. In 1989 modular assessment was trialled and AS mathematics was examined for the first time and in 1993 the core curriculum was rewritten to include the study of AS maths.

From the mid 1990’s published research indicated that:

 Students considered maths and science subjects to be more difficult than other subjects despite mathematics grades being inflated to reflect levels of achievement comparable with other subjects (Fitzgibbon & Vincent,1994: Tymms Coe & Merrill,2005).

 The proportion of the A-level cohort opting for maths- based subjects was in decline and the proportion of these going on to study maths- based subjects in Higher Education was decreasing. [London Mathematical Society (LMS) & the Institute of Mathematics (IM) (1995), UCAS (1996), Gordon (2005)]

 Students lacked essential mathematical faculty (LMS&IM, 1995; Sutherland and Pozzi,1995: Standing Conference on Schools Science and Technology

(SCSST),1996]

 Higher Education Institutions were having to change their courses and had introduced entrance exams to respond to this phenomenon (Kahn & Hoyles 1997; Sutherland & Dewhurst,1999)

 Maths departments in Higher Education Institutions were under pressure to reduce, amalgamate or close altogether due to the lack of student take up of maths-based subjects (LMS, 1995: Middleton, 2001; Office of Science and Technology (OST), 2007).

These concerns led to a review of 16-19 Education by Ofsted & SCAA the results of which were published in 1996. It recommended a reformulated AS course, a more detailed specification of the new core curriculum, a move to modular assessment and recognised maths as more difficult than other subjects. It suggested other subjects be levelled up. The result of the review led to the introduction of Curriculum 2000 which introduced the separation of A-level maths into AS and A2 courses. Each course would entail the study of three modules, two pure and one applied, which would be separately assessed. The initial results of Curriculum 2000 were disappointing showing a high drop out rate from the A-level course and applications to study mathematics- based subjects in Higher Education dropping by 10%. The response by QCA was to revise the Pure content of the AS/A2 level renaming it Core maths. In 2004 the Shwartz report recommended that the proliferation of Higher Education entrance examinations be standardised into a single test.

The aim of modular AS and A-Level mathematics is to provide greater flexibility and to ease the burden of pressure that was a criticism of the traditional model that had a single assessment via two written papers at the conclusion of the two year course. By examining twice yearly it allows for one or two units to be studied and then assessed prior to moving on to the next unit.

In the first year two core components and one applied component must be studied and these are at AS level leading to an award of AS mathematics. In the second year two further units of core mathematics, which are dependent on knowledge of the AS core modules, and another applied unit are studied. These are at a higher level of mathematical knowledge and reasoning known as A2 level. Modules may be retaken without restriction and the best mark contributes towards the final grade. The final grade at A- Level is the sum of the best marks for the six modules. Synoptic assessment is expressly included to address the degree of drawing together that candidates have in knowledge, understanding and skills learned in different parts of the course. Trigonometry is studied at units C2, C3, C4 and in M1. Functions are defined at C3 though the word is used from the outset of C1.

In the face of this considerable upheaval to the A-level system in general and the mathematics A-level in particular, one reason for undertaking this study was to discover how students assess their learning experience and what they have, in fact, learned. To what extent does GCSE mathematics prepare the students for A-level

mathematics currently and moreover to what extent have the stated core skills of developing understanding, coherence and mathematical progression been achieved. These were issues that were fundamental to the planning of this research of a group of students as they study of trigonometry.

This study was undertaken in the years 2004-2006. The pilot study group studied the Pure modules and the main study group studied the new Core modules. The trigonometry component in Pure 1 and Pure 2 studied by the pilot study group was covered in Core 2 and Core 3 in the revised syllabus. Ultimately the trigonometry component of the Pure course was covered in modules C2, C3 and C4.

Having considered the way in which the content of the A-level syllabus has been modified since its inception and highlighted some of the reasons for the change in and structure we now turn to consider broader issues on the nature of mathematical understanding and on trigonometry in particular.

Chapter 3