The same tasks, different learning opportunities: An analysis of two exemplary lessons in China and the U.S. from a perspective of variation

• Comparison of two exemplary lessons from a theory of variation.
• Reform-oriented mathematics instruction in China and the US.
• Different learning opportunities in terms of patterns of variation.
• Designing and implementing mathematical tasks in classrooms.

This study examined the learning opportunities afforded in two exemplary lessons based on a theory of variation. Implemented in China and the U.S., the two lessons focused on the same topic of patterns in a calendar and were carefully developed through a lesson study approach. Both lessons set similar learning goals but enacted these goals differently. When compared with the U.S. lesson, the Chinese lesson provided more learning opportunities through high cognitively demanding tasks focusing on different identities within patterns. However, the U.S. lesson, which featured fewer tasks and focused on a single pattern identity, may have better supported students in discerning the critical features within the objects of learning. The implications for task design and implementation for effective mathematics teaching are discussed.