The Pisa Test

The Pisa Test

Pisa, properly PISA, is the acronym for Programme of International Student Assessment. Maths, Reading and Science tests are served round the world to 15 year-olds (Year 10s). The results published at the beginning of December 2013 rank this year’s performance of UK students 26th, 23rd and 21st in the world for the three tests respectively. The Shanghai region of China, Finland and Poland all score notably better. Since 2006 the UK’s performance shows consistency – little improvement, little decline.
There has been lots of comment on the significance of the scores or the rankings. Personally I doubt one can read much from them that we don’t already know. But many people can’t resist league tables (so important to the enjoyment of sport). However, as a tutor I was more curious about the questions that comprise the Tests. Would I be able myself to get a good score? 

An article on the BBC website (‘Take-away Pisa for busy people’) provides a portal to a sample Maths test – six questions of ascending complexity.

Should you wish to try it for yourself go to  Don’t read on beyond this point – some of the answers are given away below in my discussion!  

I was relieved to find I was not stuck for correct answers – so then my interest turned to the structuring of the test items. Six questions, six levels – what makes one question slightly harder than another? 

What follows is my analysis of the sample:

Level 1 involved reading a fact off a bar graph. The danger here would be in misreading or not following the question: the difficulty, pinpointing the fact. Although this was Level 1, I am not sure it was for me the easiest question of the Test.  
Level 2 involved recognition of an equality – that  4 km in 10 min = 2 km in 5 min. This was the first in a series of speed, distance, time items. There was less information presented in this question than in the first, which might make it an easier proposition for some.   
Level 3 involved reading from a table. This one struck me as being about equal in difficulty to the Level 1 item, unless for the requirement in it to understand the system decimal places – to read correctly values on the right-hand side of the point.
Level 4 involved multipliers. Four quantities in a worded problem about people passing through a revolving door had to be lined up and multiplied to get a grand total (2 x 3 x 4 x 30). I would describe this as a test of simple systematic extension.
The Level 5 question returned to speed, distance and time again, and  the first of two compound calculations in the Test – in other words, calculations had to be combined to obtain the answer. An outward time at slower speed and a return time at a faster speed had each first to be worked out in order to find the total time the excursion would take – and hence  at what hour of the morning it should start.  
The Level 6 question would probably have equated with a GCSE Grade C problem. Data was given to work out a cyclist’s average speed. I analyzed it as a complex compound type of problem. Like the Level 5  item It required preliminary calculations (therefore compound); the preliminary calculations were slightly less straightforward than in the Level 5 question (therefore complex).

GCSE Maths above Grade C, I have long realised, crucially depends on the ability to manage series of steps. This has to be done, then this has to be done, and finally this has to be done, so that we can then do this to get the answer. If sentences of this nature, applicable to the Level 5 or Level 6 items, defeat or dismay a Year 10 student, then it is sensible to set aims lower and concentrate on calculating and reckoning correctly – and not on complex/compound  problem-solving.