I was prompted to start this investigation of the recent PISA “Ten questions…” report by the graph below:
Specifically, I wondered what had been plotted on the axes for memorisation and teacher-directed instruction so that I could compare them with PISA 2012 maths scores. It would have been really helpful if PISA labelled the axes in reports like this – this is one of the first things we teach children to do in school science.
I first plotted PISA’s “index of memorisation” against 2012 mean maths scores but the ranking was different to the y-axis above. I then tried plotting a different measure from the report data that was based upon the percentages of memorisation-type responses to the questions that PISA asked (although we must treat this construct with caution – see my first post). Yet again, this did not reproduce the ranking. I have now figured out that PISA used a ratio. They have plotted the percentage of memorisation-type responses to questions divided by the percentage of elaboration-type responses. This now explains why the axis goes from “more memorisation” to “more elaboration”.
If you plot this ratio against PISA 2012 mean maths score there is, again, little correlation:
The x-axis on the PISA graph is similarly a ratio of teacher-directed responses to student-orientation responses. This is where we find our first positive correlation with PISA 2012 maths scores:
So there you have it. Correlations do not necessarily imply causal relationships but clearly a higher ratio of teacher-directed activity to student-orientation is associated with better PISA maths performance. Again, it would be necessary to look at what these constructs are.
Here it is with the PISA axis superimposed on it:
The PISA report does nothing to highlight this relationship.
Note: You can find all of the data for the three posts here.