King Edward VI Camp Hill School for Boys has placed problem-solving at the heart of its maths teaching, making widespread use of technology.
"Students wouldn't give up on a computer game just because they failed to solve it first time," says Paul Bruten, head of maths at King Edward VI. "This persistence is needed with mathematics problems as well."
The selective boys school in Birmingham has made problem-solving central to its work in maths, especially with gifted and talented pupils. The school uses a range of sources to find problems that are engaging and that lead students to experiment with different solutions.
One typical challenge involves pupils photographing each other throwing a basketball at a hoop, then using computer software to plot the parabola of the ball's path on a graph.
The boys are often guided to work in pairs or small groups to come up with their answers, which they sometimes display as posters. "Employers love this approach because students learn to solve problems, becoming more proficient at working in small teams and at communicating their ideas," Bruten says. "Collaboration and communication are vital to solving problems in mathematics."
Teachers describe the department as having a culture of "valuing incorrect answers" as they give an insight into pupils' thinking and unexpected angles to solving problems.
"Fermat's last theorem took centuries to solve," Bruten says. "And you would never just reach an instant decision in design and technology, so why should we ever accept a quick answer in mathematics? Mathematics also needs time to be savoured and enjoyed."
As well as mathematical computer software such as Autograph and GeoGebra, pupils have plentiful opportunities to use graphical calculators, and are increasingly taking advantage of the wide range of relevant smartphone apps now available.
Pupils are also encouraged to make and then upload YouTube videos explaining mathematical concepts.
King Edward VI is careful to avoid putting its pupils off maths by hothousing them, so does not allow them to take GCSE maths early, although they are encouraged to take a stand-alone qualification in additional maths alongside the main exam.
The five main sources the school uses for its mathematical problems are:
the United Kingdom Mathematics Trust, which runs maths competitions for 12- to 18-year-olds;
the Mathematical Association, which publishes books of problems;
nrich.maths.org, which contains a large number of searchable problems;
the National Centre for Excellence in the Teaching of Mathematics; and
the National Council of Teachers of Mathematics (of the US), which produces Mathematics Teacher, a publication that contains a good selection of problems.
Signs of success
The programme has been so successful that it led to the school being given a grade of "outstanding" in an Ofsted maths survey visit in 2011. More than three-quarters of sixth-formers study maths at AS or A level, achieving fantastic results, which is part of the reason why King Edward VI has been named the best state school in the country by The Sunday Times. Another sign of success is that the school sent two students to be part of the six-strong British team at the 2010 International Mathematical Olympiad.
What the inspector said
"Can high-quality results be achieved without turning our classrooms into exam factories? The experience of King Edward VI Camp Hill School for Boys shows that a focus on deep understanding and rich activities is the key to success."
Read the full Ofsted good practice case study at bit.lyO8z8ve
Name: King Edward VI Camp Hill School for Boys
Location: Kings Heath, Birmingham
Type: Voluntary aided, non-denominational, selective grammar school, for boys aged 11-18
Number of pupils: 720, including a sixth form of 243
Intake: More than 1,000 boys compete for just under 100 places each year, attracted by a state school that boasts the best academic record outside London.