Michael Bawtree's Year 8 students have made models of the Arc de Triomphe, and now they are beginning to triumph over the task of rotating their cubework masterpieces by 90 degrees. Getting to grips with shape and space may be a challenge for young mathematicians, but these students remain firmly focused, with the help of software that he has created to boost productivity and eliminate the distractions that are the traditional bugbear of maths lessons.
Michael is head of maths at the Yehudi Menuhin School in Cobham, Surrey.
The school teaches gifted 8 to 18-year-olds from all over the world who have exceptional talent for piano and strings. Half of their school day is spent studying music, half on academic subjects, and his students span the entire range of mathematical ability.
Today's aim is to help the class to understand how to represent three-dimensional objects in two-dimensional form - a topic he says is sure to feature in key stage 3 testing. He begins by giving each student a set of Multilink cubes for model-building and some isometric paper with dots laid out in a grid of triangles that help pupils to represent the depth of 3D objects.
Attention is focused on the whiteboard - a wipe-clean board which he uses as a projection screen for his software. It displays three views of a simple L-shape which has been made from cubes. Colour-coding helps with orientation, picking out the top, left and right faces of the object in each view. The pupils' first task is to construct the shape. Then, orienting it on the desk to match what they see on the whiteboard, they must draw each of the three views on paper, complete with colour-coding.
Freed from the need to draw on the board, the teacher moves around the class, helping anyone who is finding things tricky. For those who finish quickly, there are another five shapes to choose from, including the Arc de Triomphe, a little staircase and a wide-headed dog - all revealed by Michael at the click of a mouse.
Typically it takes between 40 and 50 minutes before the class is ready to move on to the next concept: rotation around an axis. The dog reappears on the whiteboard, and the students position their model dogs in the same orientation. He talks them through the task of rotating the model 90 degrees anti-clockwise - it must be spun round the vertical axis that is clearly indicated on the board.
A glance round the room confirms that his pupils are getting the idea, and he asks them to draw the new view on paper. When it is time to reveal the answer on the whiteboard, he clicks through the transformation step by step, rotating the dog's head, body and legs in three separate stages. Five more shapes can be tackled before the class moves on to 180-degree rotation - again with half a dozen examples, a luxury that Michael says was impossible back in the days when he had to draw everything during the lesson.
"Before, I might only have had time to draw one example," he says. "Now the children can see many more instances, so they get a better idea of the principle we are talking about. I can give them a choice of simple and more complicated examples, so differentiation is much easier than it used to be.
And I never have to apologise for the quality of my drawing, or say 'Imagine if the diagram was like this'. " It is not only the 3D topic that has been given the Bawtree treatment. His software, The Virtual Textbook (TVT), spans the entire maths curriculum for KS3 and 4. The teacher spent two years creating it in his spare time, and today TVT is used by more than 80 schools around the country.
The project began when Michael discovered the potential of Excel, Microsoft's spreadsheet software, which he used to create TVT. "When I saw what it was capable of, I got very excited," he says. TVT can do much more than just present information. Bawtree has used Excel to create mathematical models for the topics being taught. That means TVT can work like an engine, churning out new examples of questions - complete with answers - on request.
"If we are doing 'brackets - removing and collecting like terms', for example, I simply click the 'new' button and it generates a whole bank of new questions, with the answers hidden until I reveal them. It saves so much time spent working out answers, which textbooks often don't provide."
Michael, who has taught for 33 years, now delivers 95 per cent of his lessons with the help of TVT. He says: "Nowadays, I never turn to a textbook unless I absolutely have to. Productivity has risen considerably - I am getting through much more material than I did 5, 10 or 15 years ago.
There are no distractions, such as, 'Sir, I haven't got my textbook.' All the attention is focused on the whiteboard.
"Few teachers have really immaculate board handwriting, and we tend to write in monochrome blue or black, seldom picking up a red pen to underline or highlight something. Everything on the TVT screen is clear, colourful and precise - and in a topic like 3D representation a good picture can speak a thousand words."
The industrious teacher has also created an extensive electronic collection of 436 maths homework sheets - an exercise that began 10 years ago, long before the advent of TVT. "It seemed so unprofessional to bring home a plastic bag full of 30 exercise books," he says. "So I decided to invent my own homework system."
He began emailing the sheets to those pupils with email addresses - others received printed copies - with everyone filling in the answers in the boxes and handing in their sheets the next day for marking. "Pupils focus much more on the maths, rather than worrying about presentation details such as headings and underlining," he says. "And the teacher's versions of the sheets include the answers, quickly brought up on screen when marking."
Classes at Yehudi Menuhin are unusually small, sometimes with as few as two, and at most 15, pupils. But TVT was trialled by Michael at his previous school, Winston Churchill comprehensive in Woking, with a class of 33 students. "I had my best ever results in my last year there, and I don't think it was just co-incidence," he says. "With the exception of three girls, none of the students in my top set took home a textbook in two years. They learned exclusively from The Virtual Textbook and the homework system. Every one of the 33 students obtained grade A, 14 of them with an A*."