Three-way path with detours
Linton Waters examines the structure of a new tiered GCSEStandard Grade course. Heinemann Mathematics A and B is designed as a two-year course leading to GCSE and Standard Grade. The A publications reviewed here constitute the programme for Year 10. The B materials, for Year 11, will follow. The course is divided into three tiers from the outset and, although these are superficially similar in design, it is clearer to consider them as three separate courses.
The Foundation Course leads towards GCSE at national curriculum levels 4 to 6, the Central Course to levels 5 to 8 and the Upper Course to levels 7 to 10. The three courses have been developed by different teams and there is no attempt to match the programmes between them. This may lead to improved coherence within each of the courses, but it would be very difficult for departments using them to facilitate pupil transfer between the courses during key stage 4.
At each level there is a pupils' textbook and an Assessment and Resource Pack. The Central A and Foundation A textbooks are lively and have plenty of illustrations and alternate pairs of pages in full colour. The Upper Course A textbook has no colour and fewer pictures. The layout in each of the books is clear, but I suspect that the text in places in the Foundation book would be daunting for some users. A real effort has been made to present and develop ideas in realistic contexts and this is particularly successful at the Central Foundation levels. The books feature a range of problem solving and investigative activities although their style and designation varies between the books.
In the Central book, some of the best ideas are unhelpfully labelled "Detours", which is likely to devalue them in the eyes of pupils and some teachers. A number of the activities, some familiar, some original, lend themselves admirably to the assessment of ATI via GCSE coursework. Knowing that this is still an area of concern to many teachers, the inclusion in the teachers' notes of performance indicators which link the three strands of ATI to the specific activity is very welcome. These are provided for activities within the Foundation and Upper books but, incomprehensibly, not for those in the Central book.
The Assessment and Resource Packs provide photocopy originals of worksheets which accompany the text-book section and of test papers linked to the sections of the book. There is also a range of detailed recording grids, most of which will hopefully be rendered redundant in detail and in principal by the latest revisions to the national curriculum.
The resource packs also provide teacher's notes and, although they do identify the main context covered by each of the sections and list any equipment required, these are the most disappointing features of the whole scheme.
There are clearly dangers in text-book writers appearing to tell teachers how to teach. But if a group of curriculum developers are going to design "a complete GCSE course", they start with some basic principles about the way mathematics is learned and ideas about how the scheme is designed to promote that learning. Beyond that, many teachers value constructive suggestions, based on the authors' experiences, as to how the activities and the ideas in the scheme can best be introduced with pupils.
HMI and the Office for Standards in Education regularly criticise too heavy a reliance on textbooks in mathematics teaching. The lack of a clearly apparent philosophy behind the scheme and the absence of any significant advice to teachers on its use, risk reinforcing the all too widespread notion that all that is required is to issue the books and allow pupils to work through them. If the authors and publishers believe that teaching maths involves more than this, then they have a duty to say so load and clear.
To illustrate the point, Foundation Book A has a section on function machines in which small groups of pupils take it in turns to choose a number, turn up a card which shows a simple instruction such as "double the number" and then work out the answer.
It is the basis of good interactive groupwork which, through discussion, develops pupils' understanding of simple functions, can easily be extended to multiple functions, inverses, applications to fractions and so on. But none of this is suggested.
Instead, pupils work through a written exercise where the rules are explained, they are expected to imagine particular games described by the authors and, individually, work out the correct answers: a typical textbook approach which significantly undermines the potential of a good mathematical activity.
Overall, Heinemann Mathematics is a scheme whose sum is less than its parts. As a complete GCSE course, it has too many drawbacks to recommend its wholesale adoption. But there are useful elements within it, particularly the range of investigative, problem-solving and coursework ideas. As such, investment in reference copies of the Resource Packs could pay dividends.
Linton Waters is Shropshire County Adviser for Mathematics.