Peter Hughes: Criticisms of maths skills don't add up

Practice, practice, practice is an invitation to extinguish creative and lateral thinking. Photo / Getty Images

While poor in some areas, NZ kids' results rank highly in international report evaluating real-world relevance.

Recent debates about learning the basic facts and the ability of our Year 9s in basic subtraction was kicked off in the media by New Zealand's results in Timss (Trends in Mathematics and Science Study) that showed we were doing poorly in maths.

In fact very different interpretations are possible if data from Pisa (Programme for International Student Assessment) 2009 is used.

The 2010/11 government report on Pirls (Progress in International Reading Literacy Study) and Timss show that in reading our Year 5s come 23rd out of 45 countries. In science Timss places our Year 9s at 31st out of 49. For mathematics the media reported that Timss places our Year 9 students 34th out of 53. In fact this is the Year 5 result. The correct figure for Year 9 is 16th out of 42.

This misreporting has had an important negative effect on the debate about mathematics learning. It has opened the door to a flood of criticism in the press and talkback radio about learning the tables and doing standard pen and paper calculations. Yet the Timss report for Year 9 does not mention these things: "New Zealand's Year 9 tended to be very strong in data and chance (ie statistics and probability) and to a lesser extent number compared to their overall performance. They were very weak in algebra and to a lesser extent geometry." It points to alarming weaknesses in algebra and geometry; we urgently need to work on these areas rather than number.

All these results are very depressing. Yet are they correct? Pisa suggests they may not be: according to Pisa our 15-year-olds are near the top of the world in all three subjects. Out of 65 countries, New Zealand ranks seventh in reading, 13th in maths, and seventh in science.

The countries that are ahead of us in Pisa when reading, maths, and science position are combined are China (Shanghai) first, Hong Kong second, Finland and Singapore third equal, Korea fifth, Japan sixth, and Canada seventh. And we come in at eighth in the world. This data will be used later. So how can Timss and Pisa produce such wildly contradictory results for New Zealand?

The student assessments are constructed from quite different perspectives. In essence, Timss starts with the curriculum and assesses how well the students are achieving, whereas Pisa starts from the opposite end and asks how well students can utilise their mathematics in the real world. While it would be unfair to say which of the two we should prefer - and there is a lot of research on this that highlights the major difficulties in making such judgments - we might well choose Pisa because of its links to real world problems.

George Lim in his opinion piece on March 20 explains why children in the highly ranked Asian countries do so well in school maths - quite simply they do lots of practice. Does this suggest a way forward for New Zealand in the teaching of maths? Evidence from the United States is useful in answering this question.

In both Timss and Pisa the US always rates poorly, and every time a new report comes along their politicians react hysterically. Voucher schemes, merit pay for teachers, and charter schools are among the tired old non-solutions they resurrect to solve the problem. Yet, as an American colleague has repeatedly pointed out, if the US education system is so bad, how do they dominate the world in such things as university rankings and number of Nobel Prizes awarded?

Comparing the US with the five Asian countries above on these two criteria we get some interesting results. Of the top 40 universities in the world 25 are in America, China has none, Japan one, Hong Kong one, Korea none, and Singapore one. Looking at Nobel Prize winners since 2000, the US has 64 (or 85 if the 21 born outside the US are counted), China has four, Japan 11, Hong Kong one, Korea one, and Singapore none.

Readers can draw their own conclusions from this data, but I for one cannot infer that New Zealand should imitate the Asian countries' relentless emphasis on practice in learning maths. Until there is any evidence to the contrary the best assumption is that "practice, practice, practice", as George Lim puts it, is an invitation to extinguish creative and lateral thinking in maths, things which our best students currently are rather good at.

Peter Hughes is a lecturer in maths education at the University of Auckland. He is co-author of 51 maths textbooks published in New Zealand, the US, Australia, and the UK.