Students' performance in reasoning and proof in taiwan and germany: Results, paradoxes and open questions

In different international studies on mathematical achievement East Asian students outperformed the students from Western countries. A deeper analysis shows that this is not restricted to routine tasks but also affects students' performance for complex mathematical problem solving and proof tasks. This fact seems to be surprising since the mathematics instruction in most of the East Asian countries is described as examination driven and based on memorising rules and facts. In contrast, the mathematics classroom in western countries aims at a meaningful and individualised learning. In this article we discuss this "paradox" in detail for Taiwan and Germany as two typical countries from East Asia and Western Europe.