Children's and adults' mathematical knowledge frequently appears to be in a state of crisis - a crisis of skills or a crisis of creativity. In the UK and the USA, there are now waves of enthusiasm for basic skills, mental arithmetic and target setting. Studies comparing England's performance in mathematics with other countries have shown England to be performing relatively poorly in comparison with others. For example, evidence from the Third International Mathematics and Science Survey (TIMSS) indicated that our Year 5 pupils (aged 9 and 10) were among the lowest performers in key areas of number out of nine countries with similar social and cultural backgrounds (Harris, Keys and Fernandes, 1997). A huge, multi-million pound National Numeracy Strategy is now underway in the UK and in its first report (DfEE, 1998), the TIMSS studies were cited as one reason for the new focus on numeracy.
At the same time, the news from the Pacific Rim reports rather different pressures for change. For example, Lew (1999) describes Korea, a country which scores very highly on most international comparisons of mathematics attainment, as being in 'total crisis' in mathematics. He illustrates graphically how most students seem quite unable to relate their well-developed manipulative skills to the real world. Lew argues that:
the direction of the mathematics curriculum in Korea should change from emphasis on computational skills and the 'snapshot' application of fragmentary knowledge to emphasis on problem-solving and thinking abilities.
Similarly, Lin and Tsao (1999) present a picture of test obsession in Taiwan, where college entrance examinations dominate students' (and parents') lives. Both of these countries are encouraging more 'open' curricula to include opportunities for mathematical creativity: that is, adapting their curricula to be more like those currently being vilified in the UK and the USA.
Other data from TIMSS suggest that English children are comparatively successful at applying mathematical procedures to solve practical problems and are generally positive about mathematics. Is it possible to retain these strengths while at the same time consolidating arithmetic skills and developing the ability to construct deductive