“My brain feels scrumpled,” one slightly dazed participant said midway through six days of grappling with the fundamentals of geometry, algebra and number games.

She was one of 80 selected to attend the first national summer school for maths teachers at Robinson College in Cambridge. All the participants were in their first 10 years of teaching and three-quarters were from the state sector.

They had given up a week of their holidays for what appeared to be a gruelling programme of 12-hour days of maths workshops, lectures, numerically orientated games and other activities. They even had homework.

Each day began at 8.45am with 90 minutes of working in teams on maths puzzles, before posting the results on the wall for colleagues to scrutinise.

Much of the work seemed challenging for the participants, half of whom had maths degrees. Formal Euclidean geometry, which has not been taught in detail in most English schools for more than 30 years, was to the fore.

The speakers included writer and broadcaster Simon Singh and Colin Wright, a juggling mathematician.

Among the other delights for the teachers was a tour of Cambridge landmarks of mathematical interest.

State schools received pound;450 for each teacher who attended the event, which was the brainchild of Tony Gardiner, a Birmingham University educationist, and supported by the National Centre for Excellence in the Teaching of Mathematics. It aimed to send the participants back to their classrooms buzzing with ideas.

The depth of maths teachers’ subject knowledge has been a worry, with the subject particularly hard hit by staff shortages.

Sophie Garnett, of Carlton-le-Willows school in Nottingham, who has a maths degree, said some of the content was too tough for her pupils. “I struggled with a lot of the ideas,” she said. “If I struggle with it, I know that 90 per cent of my kids will too.”

But the real strength of the week had been in developing her enthusiasm for the subject, she said. “It makes me remember why I loved doing maths in the first place. That has to make me a better teacher.”

Another teacher spoke for many when he said: “Events like this help to renew enthusiasm for the subject. You go back a different teacher.”

Karen Wright, of Highfields science specialist school in Wolverhampton, was even more effusive. “The summer school has been a life-changing experience,” she said. “I have returned to school on a high, fired up and overwhelmed with new strategies to try.”

Next year, Dr Gardiner plans to hold a similar event for heads of department and more experienced maths teachers.

* A.D.Gardiner@bham.ac.uk

Brain-teasers

Here are some of the simpler questions posed at the conference.

1. What is the angle between the hands of a clock at 2030 hours?

2. 4! = 4 x 3 x 2 x 1, so 4! hours is the same as 1 day, and 5! minutes is the same as 2 hours. How many weeks is the same as 10! seconds?

3. My grandma lives at the top of a hill. I went to visit her yesterday but she was out so I came straight home. On the way up I averaged only 2mph; on the way down I averaged 4mph. What was my average speed for the whole journey?

4. 20lbs of beef is cut into two joints. The small one costs 20plb more than the large one and sells for pound;8.20; the other costs pound;29.60. What did each joint weigh?

1 75 degrees 2 6 3 2 23mph 4 4lb at pound;2.05 and 16lb at Pounds 1.85lb