"You'd be amazed how many don't know how to ride a bike safely," he says. "They can balance, but few know how or when to change gears or which gears to use in different circumstances, not to mention how to brake. With them it's all speed and very little emphasis on handling skills."
These lessons are an attempt to put that right. The 17-year-old girls in S6 get one lesson a week riding and have become quite adept on the tricky terrain in the BMX park and on nearby Cumbernauld Glen.
The 14-year-old boys in S3, meanwhile, are just starting out, learning basic skills in the playground. Some are practising their balance by going round a slalom of coloured markers, others are involved in a slow bike race using only their front brake over 20 metres - the winner is the one who comes last. Later the boys practise breaking at speed within a small defined area.
"Just like in any other physical activity, you're looking for balance, co-ordination and awareness of body shape and position," says Bill, one of Abronhill's PE teachers who have undergone an adapted version of Cycling Scotland's teacher training module.
A purpose-built mountain biking trail on Cumbernauld Glen is to be created for the school by the end of this year by the Scottish Wildlife Trust. This will give the pupils more adventurous terrain.
"Eventually I would like to see the same sort of progression throughout the school as we have with more established sports, with pupils learning basic skills in the school and then refining and consolidating them at first at the BMX park and finally the new trail. Here is where they can become more experienced and discerning."
The S3 boys' first trip to Cumbernauld Glen seems to prove Bill's point. One of the more able riders has just negotiated a slope with decent speed and good control. Eager not to be outdone, a less talented rival of equal ego has tried the same thing and barely managed to stay in the saddle. It neatly demonstrates an important point - there's more to being a good cyclist than speed www.cyclingscotland.org.