Gerald Haigh examines a surprising theory about test scores.
National test results will be arriving in schools next week. As you study them, ask yourself if any children have earned lower scores than you expected simply because they haven't noticed some of the questions on the paper.
Findings from a study by external markers Wauton Samuel - who analysed more than 1,800 papers from Lewisham - suggest that this is actually happening.
Obviously, children often leave some questions alone because they seem too hard, and there are questions towards the end of any paper that children simply don't reach, and Wauton Samuel's analysis takes account of that.
However, after a close look at the scores on one optional paper - Year 5, maths test B - Wauton Samuel's managing director David Waugh realised that some questions were being left alone more than others - and, significantly, that some of these were questions which were fairly easy. In other words, children who did answer them had a high success rate. It's reasonable to conclude that at least some children accidentally miss out questions they might well have got right.
Analysis of question one on the paper, for example, reveals that 1,343 children got it right, 388 got it wrong and 148 (7.88 per cent) missed it out. It indicates that the very first question on the paper, an easy one, was missed completely by nearly three children in an average class.
A look at question two, by contrast, shows that although fewer got it right (1,279) and more got it wrong (566), a comparatively tiny number (35, or 1.86 per cent) did not attempt it.
The same pattern of an unusual number of "misses" applies to at least three other questions on that paper: numbers four, eight and 12.
One explanation is that it has to do with the position of the question on the paper. The most "misses" come when there are two questions on a page.
Where a question takes up a whole page, far fewer children miss it.
A look at the paper itself reveals that those most missed questions consist of just one line, and share the page with a question that takes up more space and which, in three cases, has some graphics. It becomes possible to speculate that some children are drawn to the most eye-catching section of the page, and then move on without noticing that they've missed something.
David Waugh has all the figures, and the Qualifications and Curriculum Authority, which hasn't done this sort of analysis, is looking at them. It rightly points out, though, that this is just one paper - and Waugh himself is tentative about drawing conclusions, especially about cause and effect.
"I'm sure this is a complex picture," he says. "It really deserves to be properly analysed by a statistician who has knowledge of education. In fact, I wonder if anyone has done it already."
You don't need to dig too deep to realise that there's a pointer here for the classroom teacher. As Waugh says, "It does make you wonder whether a school could improve its test results by simply teaching children not to miss questions".
As you'd expect, many schools do this already. "We tell them simply to make a list of the question numbers and check them off as they do them," says one Year 6 teacher. "You still can't guarantee it'll work for everyone, but it should go a long way to solving the problem."