Discrete investigations

Linton Waters


FOUNDATION ASSESSMENT AND RESOURCE Pack B. Pounds 29.95. -O435 52981 1.

By David Kent, Keith Pledger and Roy Woodward.

CENTRAL BOOK B Pounds 7.99. - O43S S2983 8.

CENTRAL ASSESSMENT AND RESOURCE Pack B. Pounds 29.95. - O435 52985 4.

By The Scottish Secondary Mathematics Group (SSMG).

UPPER BOOK B. Pounds 8.99. - 0435 52987 0.

UPPER ASSESSMENT AND RESOURCE Pack B. Pounds 29.95. - O435 52989 7.

By John Hackney, David Kent, Graham Newman, Keith Pledger and Roy Woodward Heinemann Educational.

Linton Waters looks into the latest texts from Heinemann Mathematics.

Heinemann Mathematics provides three GCSE and Standard grade courses labelled Foundation, Central and Upper, reflecting the tiers of GCSE examinations. They have recently been completed with the publication of the B books designed for pupils in Year 11. These follow the same format as the A books designed for Year l0. Heinemann suggests the Foundation Course leads towards GCSE at national curriculum levels 4 to 6, the Central Course to levels S to 8 and the Upper Course to levels 7 to 10. The differences in the approaches taken by the authoring teams remain apparent. This could be a significant issue for the many schools forced to teach pupils entering for different tiers in the same group, even in Year 11. It would not be straight forward to switch between two adjacent tiers if working through the books as presented.

As with the A books, the Central B and Foundation B text books are lively with plenty of illustrations and alternate pairs of pages in full colour. The Upper Course B 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 and Foundation levels.

The books were clearly written before the latest revisions to the national curriculum for England and Wales. The detailed assessment recording grids in the Assessment and Resource packs are likely to be less beguiling post-Dearing. In my review edition the national curriculum references in the teachers' material were all to pre-revision Statements of Attainment. More significantly, the Upper Course students' book contains many sections which most teachers will now choose to omit from their teaching, such as Critical Path Analysis and Matrix Transformations. This at least would allow opportunities for revision and exam practice which are not provided for in the Upper Course.

This is another contrast with the Central Course which includes sections called Recap and others including Mixed Problems which reflect typical GCSE examination questions. The problem-solving sections remain a strong feature of the series presenting a wide selection of open, investigative starting points which could be used as the basis for assessed coursework.

Inexplicably, as with the A series, guidance on their assessment is omitted from the Central Course teachers' notes.

There is little attempt to use and develop the learning skills of national curriculum Attainment Target 1 in the other chapters. Typically these offer brief explanations and examples along with a series of closed questions. To be successful they will need effective mediation and interpretation by the teacher. The absence of advice on how to achieve this is, for me, a serious omission.

Opportunities to promote essential practical activities are missed. For example, the Central Course has a section on cubic functions. It includes pictures of cubes built up of smaller cubes and talks about Zoe's investigation into the number of smaller cubes in each picture. This perpetuates the presentation of maths in a second-hand, abstract manner, when undoubtedly most pupils, particularly those following the Central Course, would learn far more by handling, building, counting, dismantling, comparing and discussing real cube models.

Schools buying new teaching materials, particularly large, expensive schemes, need to know that the investment will help take their teaching forward.

Although Heinemann Mathematics has a number of strengths it has too many deficiencies to recommend its wholesale adoption. Nonetheless, investment in reference copies of the Resource Packs could offer some useful ideas, particularly for discrete investigative, problem-solving and coursework activities.

Linton Waters is Shropshire county adviser for mathematics

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