Tutoring·
There is a point in a session where the child is done. Not confused, not lazy. Done. There are twelve more problems on the page, all the same shape, and both of you can see them.
What I do at that point is take turns. He does one. I do the next. He does the one after that.
It halves the pile
Most of the dread in drill work is quantity, not difficulty. Twelve problems is a wall. Six is an afternoon that ends.
Nothing has been dropped from the lesson. The page still gets finished, and he still does his share of the thinking, some of it while watching me.
It reverses who is being watched
This is the part that matters most, and it has nothing to do with arithmetic.
For most of a tutoring session, one person is being observed doing something difficult and the other is deciding whether it was done right. That is exhausting in a way that is easy to forget once you are the one holding the pen only occasionally.
When it is my turn, he is the one watching. He checks my line, he decides whether it is correct, he tells me. For those two minutes he is not the one on trial.
Checking my work teaches as much as doing his own
It is a rest that is not a break.
To judge whether my answer is right, he has to hold the whole method in his head and run it against what I wrote. That is the same thinking his own problem asks for, done from the other side, and it does not feel like being tested.
Some of the best explanations I have heard from students came out while they were telling me what I had done wrong.
Say “let’s take turns,” and nothing more
I do say that part out loud. It is a practical arrangement and it needs no explaining.
What I never say is let us pretend you are the teacher, or now you get to check my work, as if I were handing out a treat.
Then I do my problem and ask him: did I do that right?
That question is the whole mechanism. It is a real question, asked the way I would ask anyone, and answering it moves him into the other chair without either of us mentioning that a chair has been swapped.
Name it and it turns into a game an adult invented to make a chore go down, and children can smell that from across the table. Left unnamed, it is simply how the two of us are working today. He is not being managed. He is taking turns with me.
What it is not
It is not a way to do his homework for him. The share is real and it is his page.
It is also not only for drill. New material is where children tire fastest, because the effort is highest and nothing is automatic yet. Taking turns there does something extra: my turn is a worked example. He watches the method being carried out, then carries it out himself, then watches again.
That alternation is one of the better-established findings in instruction. For someone new to a topic, a worked example followed by a problem beats problem after problem, because the example does the explaining while the effort is still expensive.
And when I get one wrong, I do not cover it up. He catches it, he enjoys catching it, and he sees an adult be wrong about something and simply fix it. That is worth more than the problem was.