Many school-leavers look back on the maths classroom as a place of mystification; a place where they are shown a method and told to repeat it. It's a place where nobody asks questions and nobody explains anything," says Paul Scruton, director of the School Mathematics Project and driving force behind SMP Interact, its major new course for key stages 3 and 4.
"Yet most people agree that learning occurs most effectively when you have a chance to interact with the subject matter and engage with other people about it: to ask questions, to put forward your own ideas for others to comment on. We wanted to develop a maths course which, as well as the very useful and necessary heads-down working through exercises and examples, included approaches and activities which allowed pupils to do these things."
The first tranche of SMP Interact books are now being used by key stage 3 pupils, following classroom trials that began in 1997 and included a last-minute rewrite to adjust to the government's secondary numeracy strategy published last Easter.
So how different are they, both from their SMP workbook ancestors, the maths market-leader of the 1980s, and from maths courses which have been published since? Very different, says Shabana Nazli, maths teacher at Pudsey Grangefield, a 1,150-pupil school for 11 to 18-year-olds on the outskirts of Leeds which has introduced SMP Interact into all its Year 10 and 11 sets, and its mixed-ability Year 7 classes too: "In a lot of books I have used before there has been an explanation, a bit of information, and streams of exercises. These books are applicable to real life. When I was doing standard form with the Year 10s we were talking about going to the moon or calculating the size of DNA. We were talking about careers and because they're going on work experience they were saying 'where can you use this? Where can you use that?' " The course is written in separate books for each of three ability-based strands from the second half of Year 7 onwards (the first half of the year comprises all-ability foundation and number-work texts), but Pudsey Grangefield and other schools manage to juggle pupils throughout Year 7 between the same topic in differentiated books alongside each other, says Paul Tierney, head of maths at Pudsey Grangefield.
To achieve that, the maths department had to sit down with the different strands and work out where material overlapped and where they would need to make time or opportunities to teach more able children something extra (the least able in each class are withdrawn to a special support group, using the lowest ability coursebook).
Initially they did the same type of time-consuming mapping to fit topics which appear in one order in the course into the different order in which they appear in the key stage 3 strategy, says Tierney. Then they decided not to bother: "Originally we intended to follow the medium-term numeracy strategy plan, but we found we couldn't do that topic by topic and use the books because it became very bitty. So we decided to use the books as they should be used, because that worked very well."
Ironically, keeping to the combination of activities and exercises as written brought the school's lessons closer to the overall aims of the national strategy, which - as Paul Scruton explains - were foreshadowed in SMP Interact's planning stage: "In some ways we were ahead of the game: we were advocating the central role of the teacher when we started writing nearly half a decade ago. When the strategy was published we had to change some topics around: we brought material on speed from Year 8 to Year 9 and indices were brought forward to Year 8. But the three-part lesson, the teacher-led and student-led activities are essential to the course, just as they are in the strategy."
Despite the separate ability strands, the initial "filter" exercises in the introductory books and the self-assessment sections at the end of each topic, SMP Interact has been criticised for under-challenging able children, and underestimating the general improvement in primary maths since the National Numeracy Strategy.
Some of Pudsey Grangefield's most able year 7s commented that although they enjoyed maths they learned nothing new in the early weeks after they arrived in September. Several of their classmates, however, felt their maths had improved since primary school: "Mr Tierney explains things in more detail and I understand it more" said Emma, 12.
Worcester maths inspector and Mathematical Association secretary Robert Barbour admires the inventiveness and reliability of the course, but does think its pace is slow: "Authors like to write things that are a bit easy, because then children can do them and teachers don't complain and everything has a tendency to sag.
"The numeracy framework is trying to pull things up, but textbooks are tending to pull in the opposite direction, to get market share. I'm disappointed that people writing textbooks don't seem to have understood what the primary strategy has done, and that includes SMP."
However, where children do undoubtedly work harder in using the course is for homework, says Tierney. His department has included experienced teachers without maths qualifications, and a newly qualified teacher; all of them feel confident not only using the well-designed teacher's books, but also in setting consistent homework, using their own slim pupil practice books that accompany each ability strand: "It's really good to be able to set homework fairly easily, fairly quickly, and not on bits of paper that get crumpled or lost. We find the more able students want to do even more, but also that if students have forgotten to do their homework or haven't brought their book in, you can say: 'These are the specific homeworks you owe me.'
"Of course, students like different things. I have some who say to me: 'Are you going to talk at the beginning of the lesson or can we just get down to some work?' Some like to cut things out, some like to work in groups, some like to work alone and not talk. But I think there's a variety of approach in this which suits all of them some of the time at least."
SMP Interact is published by Cambridge University Press. Pupil practice books cost from 55p to pound;1.95, pupil books from pound;3.95 to pound;6.95, teacher's guides pound;7.95 to pound;9.95. Tel: 01223 325588Fax 01223 325152Email: email@example.com