Maths, for the primary teacher, is one of the most difficult subjects to teach. Many primary teachers, with no more than a maths GCSE themselves, lack confidence in the subject, and many tend to rely very heavily on their school's chosen maths scheme to get them through. But how good are these schemes? And how can teachers best use schemes without becoming over dependent on them?
Key stage 2 maths schemes are the subject of a recent report by the School Curriculum and Assessment Authority (now the Qualifications and Curriculum Authority), part of its rolling programme of educational resource analyses. Although directed mainly at publishers, the report also yields some useful tips for teachers on the strengths and weaknesses of maths schemes in general.
The four schemes on which the report was based are Cambridge Primary Mathematics, Collins HBJ Mathematics, Heinemann Mathematics (SPMG), and Nelson Maths 2000; none is mentioned specifically, however, because of QCA's desire not to kitemark, commend or condemn particular schemes. They were analysed using a checklist developed at QCA and refined by a group of (anonymous) teachers, advisers and publishers.
One of the chief characteristics of primary maths schemes is their sheer bulk, which can make them tricky to manage. Of central importance is the teacher's handbook, a hefty tome offering the teacher support and guidance, ideas and activities.
QCA reports that these handbooks are generally of high quality. The problem is that too many teachers lack the time to read them properly, shove them away in a cupboard, and then attempt, unsuccessfully, to operate the scheme without their assistance.
So first of all you need to read the handbook. One option would be for a group of teachers to work on the handbook together and draw up detailed schemes of work incorporating its best ideas.
The handbook should help you to lead the class, rather than simply let pupils plod through their own workbooks individually and in isolation.
"Too many teachers rely uncritically on these schemes ... to provide excessive amounts of individual work, and give too little attention to teaching the whole class or groups of pupils," reports Her Majesty's Chief Inspector in 199596.
Many handbooks do contain ideas for whole-class work. Grouping children by ability as they work on the scheme can also be a way of ensuring a certain amount of mathematical discussion between them. But there is no substitute for the teacher discussing topics and ideas in depth with pupils, either individually or in groups.
However good a scheme is, only the teacher knows the true range of abilities in his or her class. QCA criticises schemes for not stretching pupils sufficiently at any level, aiming questions at the middle and bottom of each attainment level. Some schemes have little to offer the most able, or make no provision for low achievers. This is where the teacher needs to step in with supplementary work.
None of the four schemes analysed provides full and adequate coverage of the national curriculum, according to QCA, despite attempting to do so. Only a thorough knowledge of the handbook will tell you what is there and what isn't.
The best advice to teachers is to be as flexible as they can in the way they use the scheme, and even be prepared to miss bits out, if they can see a better way of covering a topic. Teaching should be scheme-assisted, rather than scheme-driven.
Don't stint on other resource material. There is plenty out there - from books of investigations and classroom activities, to radio and television programmes, CD-Roms, puzzles, games and kits. If you don't have time to make games and workcards yourself, you may find parents are willing to help.
Make sure that pupils are getting away from the page, particularly when it comes to topics like three-dimensional shape, mass and capacity.
Whether you are using a scheme already in place or thinking of investing in a new one, the QCA report lists important points to note. How well, for instance, does the scheme handle the progression from one concept to another (say, multiplication to division)? Does it help with diagnostic assessment by advising teachers on the sorts of questions to ask to further mathematical discussion?
Are computers and calculators properly integrated into the work, or are they just tacked on? Does the scheme provide meaningful, or merely silly contexts for the practical application of maths, and does it have ideas on links between maths and other parts of the curriculum?
Most schemes, according to the QCA report, fail to give pupils sufficient experience of open-ended mathematical questions, as opposed to those with tick-box answers, but these are crucial in developing their understanding of mathematical processes. This is an area many teachers find difficult, too, where other publications can usefully be brought in.
The development of mental strategies, so high on the agenda these days, is also poorly covered by most maths schemes. Here, schools need to take a stand independently of their chosen scheme, and create their own policy: five to 10 minutes of mental maths a day, with targets set for each half term, is already working wonders in many classrooms.
Key stage 2 mathematics schemes, Pounds 1, available from QCA,Newcombe House, 45 Notting Hill Gate, London W11 3JB.