What makes a great mathematician?
Lack of motivation in pupils is the main reason maths attainment has remained static in Scotland and performance in national and international studies has been disappointing, according to inspectors.
HM chief inspector Kenneth Muir says: "Lack of motivation in maths classes is the major reason maths attainment at the end of S4 has remained largely static," and this is endorsed by the Trends in International Mathematics and Science Study, and the Scottish Survey of Achievement.
"The message from Timms and the SSA also calls into question the motivation of some students. Our pupils are not as strong applying mathematical skills as we would like them to be."
Pupil motivation was influenced by two main factors - the home environment and teachers, he continued: "I've seen some stimulating maths classes, but I've seen a lot of dreary teaching too."
Mr Muir made his comments at last week's HMIE and Learning and Teaching Scotland conference on "Mathematics in Curriculum for Excellence: motivated teaching, motivated learning", which highlighted good practice.
In 2005, Brechin High's maths department was slated by HMIE. Inspectors identified "major weaknesses in learning and teaching". Teachers' explanations were "often unclear" and "in almost all lessons, most pupils lacked motivation and rarely stayed on task for any length of time".
Last week, however, the department's work was being flagged up by the inspectorate as an example to follow, with the spotlight on its work with transition teacher Vivien Rose.
Together, principal teacher of maths Alastair Mills, who arrived at the school in 2006, and Ms Rose, a trained primary teacher, have introduced co-operative learning, swapped single desks for circular tables for groups of pupils, and introduced mixed-ability classes in S1. Even Ms Rose's elaborate wall displays are beginning to catch on.
"I think our primary colleagues are better trained for mixed-ability and group work," said Mr Mills. "They have better ideas for cross-curricular - their bread and butter. As maths teachers, we can be a bit too focused on the mathematics. If Vivien had not been in the department, I don't think we'd have been able to put these things through so quickly."
After more than 20 years in primary, Ms Rose admits that teaching S1-2 maths was a daunting prospect. But great mathematicians are not necessarily great teachers, as Mr Mills pointed out: "It's about good teaching."
Angus Council introduced transition teachers to schools in August last year. There are five. Ms Rose teaches a half timetable at Brechin High and visits one of the school's feeder primaries every week. "I would like the focus in primary to be more about how they learn rather than what they learn," she said.
"As Robert Fisher (author of Teaching Children to Learn) put it, I think it's about learning to learn."
Active learning has been the key to success at St Timothy's Primary in Glasgow. A visit seven years ago to a partner school in Spain, where textbooks were banned and all learning was contextualised, caused the Scottish school to embrace active learning fully. Now active approaches have infiltrated upper primary maths.
When Katrina McDonnell had P7 last year, she taught maths for three hour- long sessions every week and on a Friday did a mental maths test.
"I like my bit of tradition as well," she said, laughing.
Other aspects of Ms McDonnell's approach are far from traditional, however. Last year, the pupils chose what they wanted to learn about in maths. She said: "In maths, some concepts follow on from each other, but there are other things like time and area, where pupils have a certain amount of choice."
When the topics had been confirmed, the class recapped what it knew and progressed its understanding, finally breaking into five workshops - measure, numbermoney, shape, information handling and problem solving - where what they had learnt was cemented. When a workshop was complete, the children moved on to the next one.
"If they are used to a more traditional setting, group-work skills have to be taught," Ms McDonnell pointed out.
In her classroom, groups were mixed-ability but it became clear that if workshops were pitched in the middle, they suited no one. So for each workshop there were three outcomes - a revision outcome, a level D outcome and a challenge task.
Pupils self-assessed, indicating if they needed longer to work on specific outcomes. Ms McDonnell assessed progress through observing the class, and pupils fed back how they had got on during a plenary session at the end of each lesson.
Eventually, pupils began to ask if they could work on workshop tasks during golden time. "If maths is fun and more game-like, then the pupils are more motivated to learn and they realise their ability in maths is not fixed," she said.
Rewards like "Mathematician of the Week" also helped to keep pupils motivated, as did the encouragement they received from their parents. Parents receive a maths newsletter, see what's going on in maths when they visit for enterprise day, and as homework children tell their parents what they have learnt in maths and the parent feeds the information back to the teacher.
"It's about parents, pupils and teachers - it's a three-way process," said Ms McDonnell. "We need each other to be successful."