Teaching with procedural variation: a chinese way of promoting deep understanding of mathematics

In mathematics education, there has been tension between deep learning and repetitive learning. Western educators often emphasize the need for students to construct a conceptual understanding of mathematical symbols and rules before they practise the rules (Li, 2006). On the other hand, Chinese learners tend to be oriented towards rote learning and memorization (Marton, Watkins & Tang, 1997). One aspect of the criticism is that rote learning is known to lead to poor learning outcomes (Watkins & Biggs, 2001). However, Chinese students consistently outperform their Western counterparts in many international comparative studies on mathematics achievement such as TIMSS (Beaton, Mullis, Martin, Gonzalez, Kelly & Smith, 1997; Mullis, Martin, & Foy, 2008) and PISA (OECD, 2004; OECD, 2010). This paper aims to contribute to an understanding of the “paradox of the Chinese learners” (Marton, Dall‟ Alba & Lai, 1993) by exploring the procedural variation and its place in the development of mathematical understanding.