At the STEM Innovation for Inclusion in Early Education (STEMI2E2) center, we are developing and validating learning trajectories for science, technology, and, engineering. At the same time, we are improving existing trajectories for math. Why are learning trajectories critical to early childhood educators? Learning trajectories help educators understand how children think and learn about STEM topics and at the same time, how to support progressions in child thinking and learning.

About the Authors
Douglas H. Clements'' headshot Douglas H. Clements, Ph.D.
Dr. Clements received his PhD from the University at Buffalo, State University of New York. Previously a preschool and kindergarten teacher, he has conducted funded research and published over 500 articles and books in the areas of the learning and teaching of early mathematics and computer applications in mathematics education.

Julie Sarama's headshotJulie Sarama, Ph.D.
Dr. Sarama received her PhD from the University at Buffalo, State University of New York. Dr. Sarama has taught secondary mathematics and computer science, gifted math at the middle school level, preschool and kindergarten mathematics enrichment classes, and mathematics methods and content courses for elementary to secondary teachers. She designed and programmed over 50 published computer programs, including her version of Logo and Logo-based software activities (Turtle Math™, which was awarded Technology & Learning Software of the Year award, 1995, in the category "Math").


Research-based learning trajectories include three parts:

  1. a goal,
  2. a developmental progression, and
  3. teaching.

The goal is grounded in content knowledge of the topic (for example science, technology, engineering, or math). To reach the goal, children learn each successive level of thinking in the developmental progression. Children move through the progression via teaching designed to build understanding and skill that enables thinking at each higher level. Teaching includes the environment, interactions, and activities. At the core of learning trajectories is children’s thinking and learning. So, their educational experiences are sure to be developmentally appropriate.


For example, we know that most young children learn to keep one-to-one correspondence up to about 5 objects in a line before they learn that the last counting word tells how many in the set the counting, and only later how to keep one-to-one correspondence in unordered sets of objects. This is just a small section of the developmental progression for counting illustrating how it can help sharpen our observation skills and help us plan informal and more intentional activities.
As this example suggests, learning trajectories are well developed in mathematics (and some non-STEM fields such as literacy). But we are also learning how children develop and understanding of science and engineering concepts. So learning trajectories can guide teaching in all STEM domains.


For early childhood educators, assessing, understanding, and teaching with learning trajectories based on the developmental sequences described here is especially important for children with disabilities. Children with disabilities might be operating at levels different from their peers. They may be at quite different levels in one topic (say, counting) than others (such as geometry). Because learning trajectories offer several “ways into” important topics like arithmetic (e.g., counting, subitizing, partitioning), children can build on their strengths. At the same time, they can make developmental progress in other topics. Also, learning trajectories’ levels are broader ways of thinking (e.g., to get to the next level), rather than narrower skills. So, children can both learn and show competencies in each level using a variety of modalities and representations. Most importantly, learning trajectories can be aligned with formative assessment and the Individualized Education Program (IEP) or the Individualized Family Service Plan (IFSP) process.

Most early childhood professionals agree in general with the notion of “meeting each child where they are.” But, in STEM fields especially, few have been supported in understanding a developmental (formative) path that:

  1. describes and explains where children’s level of thinking is,
  2. what the next challenging, but achievable, level is, and
  3. how to support, children, including making accommodations and modifications for
    those with disabilities, to accomplish their goals.


Formative Assessment

Learning Trajectories

Where are you trying to go?


Where are you now?

Developmental Progression

How do you get there?

Teaching (activities)


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