© 2021 International Association for Cognitive Education and Psychology http://dx.doi.org/10.1891/JCEP-D-20-00005 Journal of Cognitive Education and Psychology Volume 20, Number 1, 2021 1 JCEP-D-20-00005.indd Page 1 31/08/21 5:28 AM Long-Range Impact of a Scale-up Model on Mathematics Teaching and Learning: Persistence, Sustainability, and Difusion Julie Sarama Douglas H. Clements University of Denver, Denver, CO Scaling up educational interventions in the STEM (Science, Technology, Engineering, and Mathematics) feld is critical but under-researched. We review and draw implica- tions from a series of studies investigating the long-range impact of an implementa- tion of an early mathematics scale-up model based on learning trajectories. Lasting efectiveness includes persistence, sustainability, and difusion. We conclude that persistence of the efects on individual children’s trajectories of learning is difcult to achieve, and support for children must be maintained through elementary school. More positive and perhaps more important, implementation of the scale-up model showed impressive sustainability with teachers as it increased their use of interven- tion components and their fdelity to high-quality instruction. Also promising has been indications of difusion. Keywords: learning trajectories; curriculum; preschool; early childhood education; ele- mentary education; mathematics; professional development; scale-up S caling up educational interventions is important but under-researched. A complete evalu- ation of scale requires not only high-quality implementation and immediate efects, but also positive impacts that last and dissemination of the intervention over broad areas (Dearing & Meyer, 2006). Lasting efectiveness includes persistence, sustainability, and difu- sion. Persistence refers to the continuation of the efects of an intervention on individual chil- dren’s trajectories of learning. Sustainability refers to the continued use of program components in the achievement of desirable student outcomes and professional practice over time. Difusion is the process through which an innovation is communicated through certain channels over time among the members of a social system and therefore widely disseminated (Rogers, 2003). Te purpose of this article is synthesize evidence on the long-range impact of an implemen- tation of an early mathematics scale-up model. Tis provides a unique view of the lasting efec- tiveness of one intervention and also a framework for other research programs. After a brief introduction to the model and the original research on its immediate efcacy, we synthesize Q1 Q2