Preservice Elementary Mathematics Teachers’ Emerging Ability to Write Problems to Build on Children’s Mathematics

It has become increasingly important for mathematics teacher educators to assist elementary preservice teachers (PSTs) in leveraging the knowledge of children’s learning of mathematics during instruction. Professional noticing (Jacobs et al. J Res Math Educ 41(2):169–202, 2010) involves the interrelated skills of attending, interpreting, and responding to children’s mathematics. Responding with problems that build on children’s mathematical thinking is a skill that is both difficult to learn and a critical practice in teaching elementary mathematics. We present our analyses of PSTs’ responses to a sequence of three increasingly complex methods course activities designed to scaffold PSTs’ engagement in professional noticing, and to develop their abilities to write problems that build on children’s mathematics. Supported by our series of activities, PSTs demonstrated a strong foundation in attending to and interpreting children’s mathematics. In comparison, however, these experiences did not result in comparable gains in responding to the children’s mathematical thinking, a result with implications for mathematics education.