James and Abigail are celebrating Abigail’s 8th birthday today. They notice that James is exactly the same height as Abigail. When is James’s birthday?

At first glance it might seem like one of those unsolvable puzzles, or perhaps you’re thinking that there’s some missing information. But of course, the answer is clearly: in two months’ time.

Still not persuaded? Perhaps you’ve missed out the key information. According to the Royal College of Paediatrics and Child Health, the average 8-year-old girl is 127cm tall. You can find it from the UK growth chart; perhaps you remember seeing your own child’s height plotted on the graph? By contrast, for boys, 127cm is the height typically reached at the age of 7 years and 10 months. Therefore, the conclusion is obvious: James will be turning 8 in exactly two months’ time.

Now, you might be thinking that this is a complete nonsense: nobody can sensibly work out somebody’s age to the nearest couple of months just by their height. And you’d be right. That’s why medical practitioners talk about centiles. Heights can easily range by as much as 30cm at that age, and nobody bats an eyelid at it.

You might think it would be equally foolish to try predict a child’s age from an example of their work. Imagine being shown three pieces of work by an anonymous child and then being asked to guess their age. You might estimate what year group they were in, absolutely - probably based as much on your knowledge of the curriculum as anything, but nobody would sensibly try to estimate their age down to the nearest couple of months, surely?

Six isn’t the magic number

And yet, that seems commonplace in reverse. Somehow, it has become acceptable to consider progress through the academic year as a series of six steps, as though every two months will see an identical change in attainment for everyone. It seems perfectly normal these days to look at a child’s work and judge them as being one step below their expected attainment.

Just think about that for a moment. That’s like looking at a child’s work in April and deciding that it’s good, but that it’s more like February writing. Or taking a maths test and deciding that a child has scored enough marks for a nine-year-old, but that because their birthday was two months ago, they are falling behind.

There’s no sense in sitting there smugly if you’re proud of your three-step approach, either. It’s no less laughable to imagine that you can describe a child’s level of skill as though it were a series of four-month steps each year. Just as 127cm might be the height of a very tall five-year-old, or a very short 10-year-old, so we should expect a range of attainment at each age group.

And that’s before we even get into puberty. Just as paediatricians know that children’s growth spurts can come early or late, slow or fast, so it is that teachers know that children’s academic growth can be erratic at best. In truth, for 20 per cent of girls who are exactly the average 127cm at the age of 8, they’ll end up being in the top or bottom quartile of adult heights. And we know that the same is true of education. Getting exactly the expected score at the age of 7 is no more likely to lead to average results at 18 than it is to an average height.

Six points of progress each year - or three, or 10 for that matter - is no more useful an indicator of children’s success than expecting to grow exactly 5cm between birthdays. We’d do well to stop pretending otherwise.

Michael Tidd is deputy head at Edgewood Primary School in Nottinghamshire. He tweets @MichaelT1979