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What Counts in Teaching and

Learning Early Math? 

Learning Trajectories for Young Children

To realize the surprising capability of young children to learn math, research suggests using Learning Trajectories. Learning trajectories have been placed at the core of some standards, curricula, and approaches to teaching. We will introduce why learning trajectories are so important and then do a “deep dive” into a learning trajectory for counting. In so doing, we will also (a) feature how daily activities and routines can be used to promote mathematical understanding and introduce a new, powerful resource:  Based on 20 years of research, the Learning and Teaching with Learning Trajectories (LTLT or [LT]2 ) tool helps trainers, teachers, and families to promote high-quality teaching and learning and equity.

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Doug Clements

Douglas H. Clements, Distinguished University Professor, Kennedy Endowed Chair in Early Childhood Learning, and Executive Director of the Marsico Institute for Early Learning at the University of Denver, is widely regarded as a major scholar in the field of early childhood mathematics and STEM education, one with equal relevance to the academy, to the classroom, and to the educational policy arena.  He has published over 160 refereed research studies, 27 books, 100 chapters, and 300 additional works, including the development of new mathematics curricula, teaching approaches, teacher training initiatives, and models of “scaling up” interventions.  He has served on the U.S. President's National Mathematics Advisory Panel, the Common Core State Standards committee of the National Governor’s Association and the Council of Chief State School Officers, the National Research Council’s Committee on Early Mathematics, the National Council of Teachers of Mathematics national standards committees, and is and co-author each of their reports. A prolific and widely cited scholar, he has earned external grant support totaling over $25 million, including 36 major grants from the National Science Foundation, the National Institutes of Health, and the Institute of Education Sciences of the U.S. Department of Education.


Julie Sarama is the Kennedy Endowed Chair in Innovative Learning Technologies and Distinguished University Professor at the University of Denver.  She conducts research on young children's development of mathematical concepts, implementation and scale-up of educational reform, professional development, and implementation and effects of software environments (including those she has created) in mathematics classrooms. These studies have been published in more than 80 refereed articles, 7 books, 60 chapters, and over 100 additional publications.  She is Principal Investigator on her latest IES award, “Evaluating the Efficacy of an Interdisciplinary Preschool Curriculum (EPIC),” which evaluates a curriculum produced from grant from National Science Foundation (NSF) on which she was also PI, “Early Childhood Education in the Context of Mathematics, Science, and Literacy.” In total, she has directed 36 externally funded projects from IES, NSF, and the National Institute of Health (NIH). Another project, funded by the Heising-Simons Found and the Gates Foundation, Scalable Professional Development in Early Mathematics: The Learning and Teaching with Learning Trajectories Tool, is updating and disseminate a professional development software application ( empirically supported in previous projects. She has taught secondary mathematics and computer science, gifted math, and methods and content courses for elementary to secondary teachers.

Julia Sarama

California Early Math Project