Although basing instruction on a learning trajectory (LT) is often recommended, there is little direct evidence to support the premise of a "LT approach"--that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child's present level of thinking. The present report serves to address…

It is not yet understood how children acquire the meaning of numerical symbols and most existing research has focused on the role of approximate non-symbolic representations of number in this process (see Piazza, ("Trends in Cognitive" 14(12):542-551, 2010). However, numerical symbols necessitate an understanding of both order and…

Design research studies provide significant opportunities to study new innovations and approaches and how they affect the forms of learning in complex classroom ecologies. This paper reports on a two-week long design research study with twelve 2nd through 4th graders using curricular materials and a tablet-based diagnostic assessment system, both…

This paper discusses how implementation of Lesson Study (LS) has brought about evolving changes in the quality of mathematics classroom teaching in one Chinese primary school. The Japanese model of LS was adapted as a teacher professional development to improve mathematics teachers' teaching practices. The LS group consisted of five mathematics…