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Understanding numbers, the quantities those numbers represent, and low-level arithmetic by the end of first grade are key to better success in learning mathematics through the end of fifth grade, according to a soon-to-be published longitudinal study from the University of Missouri.

Professor of Psychological Sciences David Geary and his research team followed 177 students from 12 different elementary schools for five years, from kindergarten through fifth grade. In a , Geary said this study reinforces the idea that without a strong foundation in basic math concepts, students will struggle as math gets more complex.

“Once students fall behind [in math], it’s almost impossible to get them back on track,” stressed Geary. Geary controlled for intelligence and working memory, finding that number sense and basic arithmetic skills in the first grade make a big difference in later success. Number sense refers to concepts such as understanding relationships between numbers, mental math and estimating with a number line. For example, as part of the study students were given a blank number line that had two marked endpoints “0” and “100” and asked to show approximately where the number 45 would be. Researchers found that first-graders who understood how to complete this task showed faster growth in math skills than their peers who did not. 

This type of research should help inform teachers’ math instruction in the early grades. But that can only happen if teachers themselves have a strong foundation in how to teach early math. According to a from the National Council on Teacher Quality, elementary teachers’ preparation often leaves them poorly prepared in math. The report’s authors concluded that teachers need a deeper understanding of elementary math, with a heavier focus on the foundations of algebra.

In our own paper, “,” we wrote about the need for an overhaul in the preparation of kindergarten, first, second and third grade teachers. In most states, teachers who desire to teach in these early grades have two options: a teaching license for grades K-5 or a license for pre-k through third grade. (State teaching licenses or certifications drive how colleges of education structure their preparation programs.) But not all preparation is created equally.

Kindergarten through fifth grade preparation tends to focus more on what teachers need for the upper elementary grades (fourth and fifth), while pre-k through third preparation tends to focus more on how young children learn new concepts. So it’s possible a first grade teacher could have been prepared to teach kindergarteners through fifth graders, but not deeply how to teach the basics of numbers and their relationships to one and another.

We recommended that states rethink their teaching licenses and consider reducing the overlap in the early grades. We think that by doing this, states could spur education schools to structure their preparation programs in a way that would better meet the academic and developmental needs – including those for early mathematical foundations – of children in the early grades.

We’re looking forward to reading Geary’s full findings in his paper, “Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study,” which will be published this fall in the journal Developmental Psychology.

Geary also intends to follow these same students through Algebra 1 in the tenth grade, with future studies focusing on fractions and algebra.