In their new book, The Teaching Gap, James Stigler and James Hiebert provide the answer. As part of the Third International Maths and Science Study, in the early 1990s, a representative sample of Year 8 maths lessons in Japan, Germany and the US were videoed. Stigler and Hiebert analysed the recordings. The results are fascinating.
The common characteristics within each country demonstrate that, compared to Germany and Japan, teaching of mathematics in the US is "extremely limited, focused for the most part on a very narrow band of procedural skills". Expectations of eighth-graders in the US were consistently below those in Japan and Germany, with the American students often a year behind their counterparts.
In Germany and Japan, teachers designed lessons so the concepts they introduced were developed and built upon while, in America, concepts were generally simply-stated. American lessons were more often interrupted and involved more frequent switches of topics. German and Japanese lessons had greater coherence, covering less ground but much more deeply.
Japanese and German teachers encouraged pupils to develop their thinking rigorously, often using students to present to the whole class. Japanese pupils, especially, spent far less of each lesson practising routines and far more applying or even inventing problems and solutions than their American pupils.
It is certainly possible to draw some conclusions. First, high expectations are crucial. Second, teaching young people to think raises standards.
Third, the failings of Americn teaching of mathematics cannot fairly be blamed on individual teachers.
American teachers reported that they were trying to change their practice but most of the changes they made were superficial or modest.
The system failed to set suitable expectations. It did not provide access to best practice advice in any systematic way.
This was left to individuals. Nor did it invest in professional development of sufficient rigour and quality to ensure teachers could adopt best practice when it was identified.
The data on which Stigler and Hiebert draw is several years old and, in many parts of the US, the education system has begun to apply the lessons of the Stigler and Hiebert analysis.
The UK needs to identify best practice across the globe. We need to invest in professional development of quality and depth. More will be spent this year than ever before on professional development but that is only a beginning.
We need a culture of continuous improvement. Last week, the Government published a consultation document on continuing professional development (CPD), which the press gave little attention. (It is The TES's Document of the Week, see page 21).
The most disturbing conclusion Stigler and Hiebert reach is that "the United States clearly lacks a system for developing professional knowledge and for giving teachers the opportunity to learn about teaching."
The same could have been said about Britain in the past. CPD strategy, in which every teacher has an interest, is designed to ensure that is not true in the future.
Michael Barber is head of the standards and effectiveness unit at the Department for Education on Employment
Maths criticism does not add up, page 18