Picture the scene - teacher tells class of 11-year-olds: "I want you to work out the answer to 27 plus 37 plus 19." Pupils reach for their pencils. Teacher sees the body movements and adds: "No. In your heads - don't write anything down." Class groans audibly.
Eyes squeezed tight shut, children try to count on fingers and pencils. It is all difficult and painful. There are too many numbers, fingers get in a muddle.
Such scenes are commonplace. Too many pupils lack confidence. They are unaware of properties and patterns that will help them perform mental calculations quickly and easily. They do not know by heart simple number facts they could use for more difficult calculations.
For primary children, projects such as the Improving Primary Mathematics initiative (IPM) in the London Borough of Barking and Dagenham and the National Numeracy Project (NNP) have informed the national strategy being put in place to address these issues.
But what about secondary schools?
Picture this - teacher has been explaining to Year 10 how to estimate the mean from a set of grouped data. Class has answered and asked appropriate questions, and seems to have followed the procedure.
Numbers involved are deliberately kept simple so the arithmetic does not "get in the way".
Pupils settle down to work. A purposeful buzz as they compare and discuss answers. Teacher circulates, checking work. Looks over Simon's shoulder - Simon is drawing cartoon figures in his jotter. "What's up, Simon?" "Nothing Sir. I'm just waiting for his calculator (indicates neighbour). I forgot mine."
Teacher looks in Simon's book at neat columns of figures waiting to be multiplied (calculations such as 13 x 24 and 18 x 19). For the umpteenth time teacher launches into questions that will lead his pupil, albeit reluctantly, to the conclusion that he has no need of the calculator and he might as well give his brain some exercise and get on with it.
It is all too clear to teachers in secondary schools that many pupils lack confidence in handling numbers. They are insecure in their knowledge of basic number facts and their understanding of place value and number properties. Many expect to use calculators because it requires less effort than remembering or working out.
It is, of course, important for pupils to understand processes and apply procedures, but their ability to do this is greatly enhanced when they are confident in their knowledge of basic number work and place value.
Teachers in Barking and Dagenham secondaries are involved with the inspection and advisory service in a borough-wide key stage 3 project aimed at tackling this problem - the Axiom Project. The project aims to bring the whole-class interactive approach seen in the borough's primary initiative and the NNP into the secondary school.
Teachers' handbooks provide a lesson structure and detailed notes to help teachers involve pupils actively in thinking, talking and learning about number. As they work to develop pupils' confidence, teachers encourage them to explain mathematical processes and mental strategies, and to support each other and work together.
Strategies for carrying out mental calculations are discussed - for example, 30 + 40 + 20 - 7 for 27 + 37 + 19, and 18 x 20 - 18 for 18 x 19 - and practised. A supportive class ethos is built on clear expectations of all pupils.
Since September last year, all eight of the borough's secondary schools have been involved. Four units of number work have been used with two or three Year 7 classes in each school, and further work is planned for Years 8 and 9. Each unit of work consists of 16 lessons, and together the four units focus on number work at levels 3 and 4 of the national curriculum.
Through meetings and questionaires, teachers have been involved from the outset in helping develop project materials, and in evaluating the success of the teaching methodology and gains in pupil attainment and progress.
Training and evaluation sessions enable teachers to reflect on and develop their teaching. Pupils are assessed by means of a short teacher-administered test at the start and end of each unit, and an end-of-year assessment. Classroom observations by advisory staff, senior staff and project co-ordinators in schools also feed into monitoring and evaluation of the project.
Children enjoy the work and are striving to reach the standards set. These are early days and much work remains to be done, but many more pupils are becoming enthusiastic and confident in mathematics - prepared to tackle more challenging tasks, unafraid to get it wrong, talk about it, try again and learn from their mistakes and each other - instead of hiding away with their fingers.
Carol Singh is general inspector, mathematics, in the London borough of Barking and Dagenham.