About Our Research

Preschool Math Study, 2011-2017

If you are a participating family, we would like to thank you and your child for all of your time and contributions to the MU Math Study. The Preschool Math Study project included 255 children, many of whom participated from age 3 through First Grade.

These students and their families participated by allowing us to do activities (reading, math, and memory tasks) with the students 3-4 times per year, and by keeping in touch with us so that we could compare data across years as the students progressed through First Grade. Dr. David Geary, Dr. Kristy vanMarle, and the math study team would like to thank these families, Columbia Public Schools, and all the teachers and principals that have helped us conduct this study. The study was funded by the National Science Foundation.


Although we'll continue to publish articles based on the project, the main and most critical finding is detailed in this article, published in the journal Psychological Science.

We were interested in children's understanding of numbers and the relations among them – number system knowledge – at the beginning of first grade, because this predicts employment related quantitative abilities in adolescence better than math achievement test scores in first grade; we discovered this in our 10-year MU Math Study. We gave the same number system knowledge tasks to the children in the preschool study when they entered first grade, and focused on identifying the preschool knowledge that predicted this later number knowledge.

The results were very clear. Teachers and parents know that children's understanding of the cardinal value of number words is critical; cardinal value is the quantity represented by the number word (e.g., 'two' = **). The new finding here is that the age at which they become cardinal principle knowers – they know, at the very least, the quantities associated with "one", "two", "three", and "four" – is related to school-entry number system knowledge above and beyond the influence of general cognitive ability, executive functions, parental education, or any other types of quantitative knowledge.

Moreover, children who were not cardinal principle knowers by the end of the first year of preschool were significantly below average on number system knowledge in first grade. This will put them at risk for long-term problems with mathematics, independent of other factors (e.g., general cognitive ability or parental education). We also found that children's recognition of and ability to name numerals was important.

The take home message is that a focus on the meaning of number words (e.g., having children count out four toys from a pile) and recognizing numerals up to 10 will be very helpful for young students. And, ideally, they should acquire this knowledge before the end of the first year of preschool, that is, by the time they are about 4 ½ years old. Refreshers during the second year, before entering Kindergarten, will be helpful as well.

What next? Some of our colleagues have been testing several interventions to try to boost children's cardinal knowledge. Once we know more about what works, we will update here with our colleagues' reports.

It will take us several more years to complete all of the data analyses based on this study. We will provide periodic updates of our new findings on our website.