Key Developmental Understandings in Mathematics: A Direction for Investigating and Establishing Learning Goals

Although mathematics educators seem to agree on the importance of teaching mathematics for understanding, what they mean by understanding varies greatly. In this article, I elaborate and exemplify the construct of key developmental understanding to emphasize a particular aspect of teaching for understanding and to offer a construct that could be used to frame the identification of conceptual learning goals in mathematics. The key developmental understanding construct is based on extant empirical and theoretical work. The construct can be used in the context of research and curriculum development. Using a classroom example involving fractions, I illustrate how focusing on key developmental understandings leads to particular, potentially useful types of pedagogical thinking and directions for inquiry.