The occasion of the present outburst of primary-bashing is the publication of Laying the Foundations of Numeracy, by Helvia Bierhoff, for the National Institute of Economic and Social Research. The research "reveals that 10-year-olds this side of the Channel are two years behind those across the water". It turns out that this refers to the capacity of pupils in Germany and Switzerland to do "relatively sophisticated sums". These pupils tend to work from one book, officially approved, and "an eight-year-old in these countries will have six times the number of exercises on a topic as an English child".
I have a nasty feeling that this is a recipe for disaster. One day the children (and their teachers) will rebel, as they did in this country 30 years ago, and demand intelligibility and applications for their work. I once received a high-powered delegation of German mathematics educators. They asked if I could show them the wonderful schools in Germany which they had read of in this country. They added ruefully that they had come here to see good primary practice and they had not been disappointed. As for Switzerland, this was the home of Jean Piaget, the pioneer of developmental psychology. His methodology has come under attack, but his conclusions about how children learn and in what order have proved uncannily right. I was amazed to learn that the local authority of Geneva would not allow his students to teach whole classes in their schools, for fear of corrupting them with his ideas.
This is not to say there is nothing in the report to make us take notice.
First, mental arithmetic clearly needs vital encouragement. Second, textbooks: most of the primary series are slip-shod and second-rate. There is a lot to be said for Government censorship, perhaps in the form of having to be on a prescribed list. This has worked well in some states in the US, notably California.
Third, we need more research into primary mathematics. What concepts and skills should children learn and in what order?
Fourth, in-service training is vital. The Secretary of State is proposing to open 50 centres for the improvement of mathematics and science teaching. She might do worse than consult the Nuffield National Mathematics Committee. This body was set up when the original Nuffield primary mathematics project finished its job and is still flourishing a quarter of a century later. It oversees a nation-wide network of regions, with names such as NORMAC (northern mathematics council). These in turn provide courses and publications and could re-activate the associated Teachers' Centres, which have been put on ice for lack of funds.
If the Bierhoff paper can act as catalyst for these developments, it will have been indeed worthwhile.
Geoffrey Matthews is Emeritus Professor of Mathematical Education at the University of London and an Honorary Research Associate of the University of Greenwich