This is a nice problem to have. Enthusiastic pupils are a positive statement that your teaching is interesting and enjoyable. However, there is a danger that the rest of your class will start to coast or, worse still, totally turn off.
It may be worth learning from the example of The Jo Richardson Community School in Dagenham, east London. It introduced a "no hands up" policy when it opened six years ago in response to exactly this sort of issue.
It recognised that the same few pupils always had their hands up. If the teacher ignored them and asked those with their hands down, the chosen ones felt picked on and ill-prepared, covering up their lack of knowledge with poor behaviour. Meanwhile, the old faithfuls who usually put up their hands started to lose interest.
There were also those in class, typically boys, who put up their hands without knowing the answer, simply to gain attention or waste time. Other bright pupils kept their hands down because they did not want to be labelled swots.
"These pupils may also be putting up their hands without really thinking through the answer," says Andy Buck, partnership headteacher of the Eastbrook - Jo Richardson Partnership.
Jo Richardson teachers now select at will. If pupils struggle with an answer they can always "phone a friend", which encourages the whole class to be alert in case they are selected.
"The pupils don't necessarily like it, because they know they all have to be thinking about the answer, but they know it's good for them," Mr Buck says. "They are also likely to listen to answers if they have been thinking it through themselves."
There is not a total ban. Keen pupils can still put their hands up for more challenging questions, which gives them a chance to shine while avoiding the danger of asking someone who really hasn't a clue.
But even less able pupils may be able to contribute when they are given more thinking time. "Remind pupils that this is not a race," says Dylan Wiliam, deputy director of the Institute of Education. "Teachers should be looking for the best answer, not the first answer. Slow down and ask a question that is worth asking."
Studies suggest that many teachers, keen to have pace in their lessons, leave almost no time before choosing a volunteer to answer. Instead, give the children two minutes to discuss possible options with a partner, before choosing a pair at random to give their verdict.
One teacher has invented a "pose, pause, pounce and bounce" approach: she poses a well thought out question, pauses for 10 seconds, pounces on a pupil and then bounces the answer off a second pupil, who discusses it further. It leaves the whole class on task and focused.
Another approach is to get all pupils to reply using mini whiteboards or handheld cards stating which multiple choice answer they agree with, says Professor Wiliam. "Don't dart from one question to the next," he adds. "Stick with a topic until pupils are really thinking it through."
Teachers at Jo Richardson ask the rest of the class to say whether they agree or disagree with an individual's answer in a show of hands. If they are in agreement they move on, but if there are dissenters, pupils are given the opportunity to further explain their views. "When it goes brilliantly, the teacher can step back as the pupils discuss the topic among themselves," says Mr Buck. "It's great to see the class learning together."
Next week: Girl bullies
Experiment with "no hands up" sessions, especially at the start of lessons or during question sequencing.
Ask thought-provoking questions.
Insist on up to 10 seconds "wait time" so that pupils can think through their answer before putting up their hands.
Get all pupils to agree or disagree with the given answer before asking them to explain why.
Rely solely on quick-fire questions - pupils may say the first thing that comes into their head. Instead, allow them to discuss and rehearse their answers in pairs or groups.