Prospective Teachers’ Knowledge of Children’s Multiplicative Thinking: Learning Trajectory—Based Instruction in a Mathematics Course

Responsive teaching requires teachers to have knowledge of children’s thinking. Prospective teachers need support in developing such knowledge because they often enter teacher preparation programs with fragile mathematical knowledge and anxiety about teaching mathematics to children. We designed a learning trajectory–based intervention to support prospective teachers’ development of their knowledge of content and students in the area of children’s multiplicative thinking. The intervention was a four-lesson unit that scaffolded prospective teachers’ knowledge development according to a trajectory of children’s multiplicative reasoning. Results indicate improvements in prospective teachers’ anticipation of children’s multiplicative strategies and knowledge of the range of multiplication strategies to which children have access.