Understanding a child's mathematical thinking helps professionals make principled decisions about how to provide challenges and supports to children's learning.

For more information, click on For Teachers and Home Visitors!

For families at home with young children during the COVID-19 crisis, we hope our website can be a place for you to find high quality, fun early math activities!

For more, click on For Families!

We will use this section to provide additional materials for parents and educators coping with the COVID-19 crisis. 

Check out our Guide to Games to decide which game might challenge your young mathematician.

Our games work on most platforms, including PC, Mac, iPad, Amazon Fire,and Kindle tablets.

Click on Our Games to learn more!


This section of our site has printable pdfs of some of the most common materials used in our activities, such as Numeral Cards, Dot Cards, Tangram Puzzles, and more!!

We also have pdfs showing how the Learning Trajectories align to Common Core State Standards and widely used systems, such as Teaching Strategies GOLD.


Research shows that when teachers understand how children develop mathematics understanding, they are more effective. These resources are for people offering professional development.

For more information, click on For Professional Development!

Suggested Citation

Clements, D. H., & Sarama, J. (2017/2019). Learning and teaching with learning trajectories [LT]2.
Retrieved from Marsico Institute, Morgridge College of Education, University of Denver.

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