Not every teacher can do this. A lot of people, though perfectly adequate and in no danger of failure, would have to push their presence in a much more overt way if they were put in that position. I know, because for most of my 30-year career, certainly until I became a head, discipline was something which I had to work at consciously. I could do it, but it was hard work.
So I think I know what might happen in a similar dining hall with someone like me in charge. It goes like this.
The teacher stands up. Children close by look up and begin to settle down. But not all respond, so the teacher has to decide whether or not to shout - which, as Kate Abbott points out to me, is not only undignified but courts failure. "It's a large hall. The last thing you want to risk is not carrying to everyone."
So, no shouting. Instead the teacher, remembering B F Skinner's principle of contingent positive reinforcement, points to the children who are being quiet and says, "Well done - here are some people who are ready."
More children pick up this cue and settle down. The teacher, feeling things coming under control, walks towards the more remote tables and may use the time-honoured formula: "I'm waiting!" And so, gradually, the room comes to order. There is still a risk - the dreaded Steve Higgins might drop his cutlery on the floor, provoking an outburst of giggling, for example, and causing his fan club of admiring girls to look up expectantly to see what the reaction will be.
Kate Abbott knows what to do. "The most sensible thing is to judge the intention of the youngster who causes the disturbance. If it is a deliberate attempt at disruption, you don't have a confrontation there and then, but you isolate the culprit from the others and make sure everyone knows that you intend to deal with him or her later."
I hope I would have done the same, but something inside says that I might have heard the crash and the giggles, seen red and yelled, "How dare you, Steve Higgins!" Kate Abbott, remember, just stands up.
The current discussion of school discipline is strongly focused on regimes, systems and sanctions. All of which, obviously, are important - any school which does not have a consistent,across-the-board policy for dealing with troublemakers is likely to lurch from crisis to crisis.
What is missing from the debate, though, is the place in the jigsaw of the person with natural authority, the rock upon which so much of the school's ethos is founded. All teachers know and admire such people. Heads rely heavily upon them. Kate Abbott, clearly, is one.
Jim Ravenhill, a senior teacher at Coundon Court Comprehensive in Coventry, whose work I have watched for nearly 25 years, is another. "I have never had any worries at all about that side of the job," he told me.
Where does this natural authority come from? The word that everyone uses, perhaps inevitably, is confidence. Good disciplinarians succeed because they know, without any shadow of doubt, that they will succeed. (Less effective disciplinarians are subliminally fearful that The Great Bluff will be called. So they back off, change tack and give confusing messages.) The teacher who has this self-belief can build on it in ways that continuously enhance his or her ability to impress pupils - so things get better all the time. Confidence, for example, provides freedom from the worry that pupils will interpret explanation as weakness. "I'm never afraid to discuss with a child why I have the right to tell them what to do," says Jim Ravenhill.
"I believe that I have the right as a grown-up to set boundaries, and this is qualified by my belief that children want boundaries. Children are grateful for an adult who is being an adult, and not an adult who is being a kid."
Maureen Cruickshank, principal of Beauchamp College, a Leicestershire comprehensive for 14 to 18-year-olds, also homes in on this. "I'll say: 'Come off it. We have to submit to the rules for the sake of the whole community. None of us wants a breakdown'."
This succeeds, Jim Ravenhill explains, because children respect fairness. "In my experience they want three things of their teachers - they want them to be fair, to be kind and to be strict." Fear, obviously, is nowhere.
Really effective disciplinarians like children too much to want to frighten them. "I'm backed by my own assurance that what I am doing is of value to the child," says Jim Ravenhill, "I prefer talking to children. I find a lot of grown-ups are less emotionally mature than many children."
Kate Abbott feels the same way. "You've got to want life to be good for these kids, to move them on academically; to make them feel secure, and you're not going to do that if you're putting them down continously."
Both Kate Abbott and Jim Ravenhill talk of role models, but in different terms. Kate Abbott recalls a woman teacher she met when she was on teaching practice. "She'd been a model and had this brilliant slow, deliberate feline walk. She'd go menacingly towards trouble and it would defuse before she got there. I thought 'I'm going to do that'."
Jim Ravenhill recalls the firm example set by his mother, and ("remember I was born in 1946") by Gary Cooper in High Noon. "I still admire that honourable, courageous thing - Alan Ladd in Shane."
Each of these three teachers had lovely examples of the power of their self belief. "At my last school," Maureen Cruickshank says, "we had a walk-out of pupils, and I went to fetch them back. I could actually hear some kids muttering about picking up stones, but I stuck at it and rounded them up like sheep."
Kate Abbott started early. "When I was 17 I broke up a fight between two Hell's Angels while everyone else was standing and watching. I just believe that if I want to do something I am able to do it."
For his part, Jim Ravenhill remembers a moment that will be familiar to many sports teachers. "I was refereeing a football match and some of the parents on the touchline were so abusive that I asked them to leave." And, of course, they went- "though the worst case scenario hardly bears thinking about."
What there is here, suggests Kate Abbott, is "a kind of naivete that spurs you to the belief that you are in charge, and that this will communicate itself to others."
There is recognition that some of these enterprises might be risky. Maureen Cruickshank who regularly, like many other heads, goes out of the gate to deal with groups of youths. ("I go out and hassle them") made the obvious link. "Now when you're sticking your neck out, you remember Philip Lawrence."
Confidence, though, cannot be the only thing - a person can be both confident and stupid, after all. At least two other qualities seem to be present in the good disciplinarian. One, Kate Abbott explains, is good basic classroom management. "You have to have all the admin right - the paper and the books. All that's got to be very tight so that none of the organisation gets in the way."
The other necessary quality is a highly-tuned ability to deal successfully with other people - to pick up signals, to read attitudes, to select the correct responses. Suppose, for example, you rebuke a child in class, then realise that you have been a little unjust. Kate Abbott's explanation of how to deal with this sort of thing points up just how elaborately wrought is the school pupil's concept of fairness.
"It's always important to put it right very subtly, so that the child feels that you have been fair but have not pandered too much. You might say, 'I'm sorry I misunderstood you,' but you make sure the rest of the class knows that the child is still doing what you wanted by saying, perhaps, 'Now, have you got everything you need?' It's non-confrontational, but nevertheless there's a clear signal going out."
From all that Kate Abbott and the others say, it is clear that confrontation - "do it because I say so" - although it might have its place, is rarely the preferred option of the good disciplinarian. "Teachers who make a song and dance about their authority," says Jim Ravenhill, "do so because they're insecure."
At this point you wonder how on earth the student or newly-qualified teacher is ever going to learn all this. Wally Rutter, who manages student and newly-qualified teachers at Matthew Moss School in Rochdale, in partnership with Manchester Metropolitan University, recognises that experienced mentors to whom class discipline comes easily may have forgotten what it's like not to feel in control.
He knows, too, that classroom control contains so many subtleties that even when new teachers observe lessons, they may not actually know what they are looking for - "the apparently aimless walk to the back of the room; the meaningful eye contact".
So, among the many sessions that the school runs for new teachers, "we help them to be aware and to try to look for the things that may not be obvious at first". The school also shares out the mentoring task across a range of experience, and does a lot of work on the basics of classroom management and teaching and learning styles ("right down to the arrangement of furniture").
There was a time, not so long ago, when that degree of support did not exist. The reverse was the case - too often, the successful disciplinarians, far from sharing their skills, basked in the schadenfreude created by the failure of their less able colleagues. Now, though, there are whole-school policies which support the learners and enhance the qualities of those more experienced. Kate Abbott says she feels "genuinely proud" to be working in an environment which is providing stability for pupils. "I go along with our head, whose motto is 'a disciplined school is a caring school'."