Yesterday’s post on the PISA ‘Ten questions…’ report left me with a nagging worry. I had plotted the PISA mean maths scores against “index of memorisation” rather than the “average percentage across 4 questions” measure that I thought PISA used in the graph that went across the internet (I now no longer think they used this*). It didn’t seem likely, but perhaps there was more of a correlation if we used this latter measure instead.
The R-squared for “index of memorisation” was actually marginally higher at 0.0095.
The data set that contained the average percentage measure also contained a number of other measures that were mentioned in the report. So I thought I would run these too. The first was the “average percentage across five questions” measure of whether teaching is “teacher-directed”. This seems to show a real, negative correlation with some interesting anomalies:
I haven’t examined the questions that are used to establish this construct (or the others below) in the way that I have done for memorisation so I am not sure exactly what this means.
However, one issue stands out as very odd indeed. PISA suggest that the opposite of teacher-directed is a “student-orientation” but look what happens if you plot that:
This is by far the largest correlation that I have found. And yet it doesn’t seem to get much of a mention in the PISA report. It is extraordinary that the authors highlight memorisation and teacher-directedness when this elephant is occupying the parlour, stamping its feet and trumpeting the tune of La Marseillaise.
And look at Ireland. It’s a massive outlier in terms of student-orientation but just a little below average on teacher-direction. So what exactly is happening in Irish maths classes? Who is in charge? What do they do?
For completeness, below is a graph of the other measure available – the use of elaboration:
So it seems that a higher score in any of the constructs – except for memorisation – is a bad thing, of which a higher score on student-orientation is definitely the worst.
Note: The data is available here.
*I now think they have used the ratio of teacher-directed to student-orientation. Some axes labels would be really helpful. This ratio is plotted in Part 3.