In many ways they are model pupils: they do not hurl abuse at the teacher, they do not start fights in lessons and above all, they are quiet.
These pupils - the ones who do not cause trouble but rarely participate - are not often at the forefront of teachers' minds. When staff are just trying to get through a lesson with no one setting light to the curtains, there will be some quiet, average pupils who become "invisible".
During their careers, most teachers will have experienced that feeling of guilt about a pupil they never really got to know because they kept their head down and stayed off the radar.
Although it is possible to be a low-profile child and go on to achieve academically and in life, they are also vulnerable to lagging behind and falling through the educational net. And such pupils may simply fail to reach their potential.
Quietness and non-participation can also mask more serious issues, such as abuse, mental illness or special educational needs.
So more and more schools are realising that the average, quiet students - just as much as the swots, the prima donnas and the troublemakers - need your attention.
One of the key problems with pupils who never put their hands up to answer questions or take part in class discussions is that it is hard for the teacher to know if the pupil has understood the lesson. Teachers and educational experts will agree that talk is fundamental to learning and to assessing where your students are at.
"As a probationary teacher, you don't have the energy or brain space to be concerned about these pupils, but it is something people should be concerned about," warns Dr Janet Collins, a leading researcher and writer on issues related to quiet children.
"Nursery school teachers are always looking out for whether children are developing linguistically, but as you go through the school teachers are less concerned about it," she adds.
Spotting the invisible pupils
Inexperienced teachers may well ask: how do you know when you have an invisible child on your hands? Just how elusive are they?
"They are very difficult to spot," warns Collins, "They sit very still and are very quiet. They put their hands up a split second after the teacher has asked another pupil to answer the question.
"The teacher would perceive that the child knew the answer. They often haven't been learning anything."
She stresses that part of the reason pupils become invisible is that other pupils and teachers stop talking to them because of the lack of feedback. A vicious circle then starts.
In her Open University paper Playing Truant in Mind: the social exclusion of quiet pupils, Collins outlines the various ways in which children can be physically present in lessons - behaving well and not causing trouble - but failing to take part mentally.
She believes truancy of the mind is "more detrimental to learning" than physical truancy, as the child's physical presence in the classroom can mask serious problems.
Collins' paper highlights the case of a girl who had high marks in her French book but did not speak in lessons: "She was asked to read (out loud) but she said, 'I don't speak French, it confuses me.'"
"Her physical presence in the classroom and positive statements from the teacher reinforced her image of herself as a successful student," Collins writes. "In one respect she was a model pupil. Unlike some of her more vocal peers who seemed intent on disturbing the lesson, she did not cause the teacher any discipline problems.
"She handed her neatly completed work in on time. However, in other, far more serious respects she was a failure: she had learned nothing of the spoken language."
So what can be done to spot potential problems and engage pupils in their tasks and in classroom talk?
Getting to know your pupils is obviously key - although far easier said than done with large classes and a full teaching timetable. Making a point of learning names very early on is vital. Then give pupils the chance to speak in a number of different contexts.
"Teachers should not set out to change students' personalities," Collins says. "You don't have to turn a quiet person into a talkative person, but you need to help them build a wider repertoire of behaviours."
She adds that a key issue for teachers to be aware of is peer pressure: many pupils do not raise their hands to answer questions for fear of getting the answer wrong and being judged by their classmates and the teacher.
That is why, she explains, it is essential to vary the way you group pupils for discussions. Many students who would not talk in front of the whole class would happily speak to another pupil on a one-to-one basis.
It is also essential for teachers to see the vital part teaching assistants can play. They often sit among the pupils and come from the same community as the children, making them a less threatening conversational partner than the teacher, Collins explains.
Ditching 'hands up'
Varying the standard "hands up" approach has also borne fruit for some teachers and researchers.
In 2010, Professor Dylan Wiliam, emeritus professor at the University of London's Institute of Education, conducted televised research at Hertswood School, a Hertfordshire secondary, in The Classroom Experiment. The BBC programme involved testing a variety of innovative ways to get all pupils - rather than just the usual suspects - to take part fully in lessons.
On a very simple level, Wiliam banned pupils from putting their hands up and picked who would answer by randomly selecting lollipop sticks with their names on from a pot.
In other instances, the whole class was asked to "vote" for the right answer to a question by holding up their fingers or writing their answers on mini whiteboards.
Wiliam also used low-tech "traffic light cups" to check understanding. Pupils placed red, yellow or green cups on their desks depending on whether they were certain they had understood, were unsure or had not got what was being taught at all.
But aside from these practical tricks, Wiliam says the key is to help children have the confidence to make mistakes. Fear of getting things wrong and being judged is a key reason many "invisible children" may not take an active part in lessons.
"We had a pupil called Sid who said he didn't raise his hand because he was afraid of being ridiculed for getting the wrong answer," Wiliam tells TESpro. "You need to lower the stakes of failure and show that it is normal, an essential part of learning. If kids are getting all the questions correct you're wasting your time."
But he is keen to point out that there is "no magic formula" for getting pupils to participate.
"During The Classroom Experiment we had a nice moment when the teacher picked on a pupil who said 'I don't know' and he had to be pushed for an answer. But it is all about the teacher's sensibility: sometimes pushing them to answer is the right thing to do, but sometimes it's the absolute worst thing to do."
Wiliam says that the different techniques used during the experiment created a more "cohesive" classroom, which allowed even the quietest pupils to share their thoughts.
He points again to the archetypal "quiet kid", Sid: "He was average, he never raised his hand, but he was an extremely thoughtful guy. He was asked 'What's a domestic servant?' He replied 'I have no idea, but it doesn't sound very democratic.' You would never have got a response like that under the usual set-up."
Talk to the puppet
Other techniques to help invisible children emerge from the shadows include conducting lessons using puppets.
Research funded by the Nuffield Foundation into the use of puppets in primary science education found that they could help shy children open up. Teachers were also able to assess children's understanding more effectively.
The idea is that the puppets, animated by the teacher, have childlike personas. The puppets ask the children questions using simple vocabulary, and the pupils explain what they have learned to the puppets.
The report, which analyses the use of puppets in classrooms in London and Manchester, says: "The puppets seem to allow children freedom to talk when they are not sure about things. They know the teacher knows the answer so why bother explaining?
"However, the puppet doesn't know so their explanations are fuller."
One of the researchers, Dr Jane Maloney, now primary programme manager at the University of London's Institute of Education, adds: "The puppets provide a role model of how to discuss things. They can say no, yes and they can change their minds. Children learn that it's OK to put forward what you think and then change your mind."
Above all, the puppets provide pupils with a reason to talk.
"The puppets break down barriers, because the pupils are talking to a child who doesn't understand," Maloney says, adding that talking to an adult can be intimidating.
And if puppetry is not your thing, then put the pupils completely in charge: "One teacher didn't like using the puppets but he got the children to talk to him via the puppets - he posed questions and argued with them. It made them laugh a lot," Maloney recalls.
Puppets can be effective beyond primary level as well, Maloney says: they have been used effectively in most year groups, even sixth form.
There is also the whole-school approach. Introducing a house system with roles and responsibilities for pupils of all abilities can give children a sense of belonging and more individual attention. Heads have reported success in giving roles and titles to pupils for good attendance and behaviour as opposed to outstanding academic performance.
Mentoring is important, too. At Conisborough College in Catford, southeast London, head Bob Ellis has introduced a system where every member of staff is assigned 15 students to mentor. It is their task to get to know the pupils really well, and to be up to speed on their academic tracking data and extracurricular activities.
Instead of a traditional parents' evening where parents meet each subject teacher for a few minutes, the mentor sits down to review progress with the pupils and their parents twice a year.
"By having a faculty system with mentors it reduces the scale of the school so relationships are a bit closer," says Ellis, who is also a mentor himself. "With a traditional parents' evening, there's a danger that the parent speaks to lots of teachers who don't know the pupil very well.
"This way, there should be no child who is invisible."
So there are lots of techniques to try, most of them simple and above all inexpensive. But experts agree that much of it comes down to simply getting to know your pupils as well as possible. Only then can teachers find a way of communicating with their pupils and understanding if they are progressing properly.
And can teachers expect help from policymakers any time soon? Do the powers that be care about the "invisible child"?
"My strong feeling is that these average children do not receive enough attention in research or policy," says Dr Peter Rudd, reader in education at the Institute for Effective Education at the University of York. "The focus is on children on thresholds such as the CD borderline, in an era of league tables. But those children not on a threshold risk missing out. What about the E-grade pupils who could get a D grade?"
But as many schools have already proved, just because average, quiet kids have been neglected by policymakers and intervention schemes, this does not mean they must also be neglected by their teachers.
TOP TIPS FOR ENGAGING INVISIBLE PUPILS
Know your pupils. Spend as much time as possible talking to them and learn their names quickly.
Think very carefully about how you group children and make it clear what you expect of them. If you set up an expectation that everyone will speak by the end of the lesson, they are more likely to speak.
Value spoken communication as much as written.
Teach pupils the tricks and strategies of conversation, such as playing devil's advocate.
The earlier in the day a pupil speaks, the higher the chances of them speaking again. Try group activities where everyone has a chance to speak, such as circle time activities where pupils take it in turns to hold a teddy bear and say their name and how they are feeling.
When putting children in pairs for discussion activities, put the quiet ones together and similarly with the noisy ones.
Make the most of your teaching assistants. Children may find it easier to talk to them.
Give pupils a chance to think before they answer and share their thoughts without a large audience, using simple techniques such as Think, Pair, Share in which pupils think about a problem alone, then discuss in pairs before sharing with the group.
Encourage the whole class to answer, not by raising hands but by writing their answers on mini whiteboards, or by holding up their fingers to "vote" for an answer.
You can try picking on pupils to answer questions by drawing names from a hat - but be aware that not all children will respond well to being "picked on".
Lower the stakes of failure - help pupils understand it is essential to make mistakes in order to learn.
Once you have identified invisible children, give them roles and responsibilities - they may thrive on it.
The Puppets Project:
training, advice and resources on using puppets in science teaching
teaching techniques encouraging discussion and whole-class exploration of concepts
Keeping Up: pupils who fall behind at key stage 2 (2007). Former Department for Education and Skills
Collins, J. Playing Truant in Mind: the social exclusion of quiet pupils. Paper presented at the 1998 British Educational Research Association annual conference
Collins, J. The Quiet Child, (1996). Continuum International Publishing.