Psychology Professor Seeks to Understand How Students Learn Mathematics

Author: William G. Gilroy

Nicole McNeil Nicole McNeil

It’s both the bane of many parents and what has been called a major national vulnerability: the inability of many children to learn mathematics.

Understanding that problem and developing strategies to overcome it is the research focus of Nicole McNeil, Alliance for Catholic Education (ACE) Associate Professor of Psychology at Notre Dame, and the researchers in her lab.

McNeil's work with Emily Fyfe, a former Notre Dame undergraduate who’s now a doctoral student at Vanderbilt University, appeared in the journal Child Development and was featured in the media, including an article in the Boston Globe.

Their research paper examines if the labels educators use to identify patterns affects preschoolers’ understanding of patterns.

“Patterns are things, such as words or numbers, that repeat in a logical way,” McNeil said. “For example, the stripes on an American flag are laid out in a repeating pattern of red, white, red, white, etc. Children’s ability to identify and create patterns is an important early math skill that supports their social and cognitive development. In fact, research has shown that teaching children about patterns improves their achievement in reading and mathematics.”

Members of the CLAD (Cognition, Learning, and Development) Lab that McNeil directs at Notre Dame recently collaborated with Fyfe and other colleagues at Vanderbilt University to examine if the labels educators use to identify patterns affects preschoolers’ understanding of patterns. They compared concrete labels, which refer to the changing physical features of the pattern (e.g., “red, white, red, white”), to abstract labels, which describe the pattern using an arbitrary system that mimics the pattern (e.g., “A, B, A, B”). Children in the study solved a set of patterning problems in which they watched an experimenter explain a model pattern using either concrete labels or abstract labels and then tried to recreate the same pattern using a different set of materials.

“Children who were randomly assigned to the abstract labels condition solved more problems correctly than those assigned to the concrete labels condition,” McNeil said. “Thus, even though concrete labels seem better because they are more familiar and accessible to children, abstract labels may help focus attention on the deeper structure of patterns. These findings suggest that something as minor as the types of labels used during instruction can affect children’s understanding of fundamental early math concepts.”

This research result converges with several other findings from McNeil’s lab in recent years that have shown that relatively minor differences in the structure of children’s input can play a role in shaping and constraining children’s understanding of fundamental math concepts.

“Researchers and educators often focus on the macro-level environmental differences (like quality of early child care setting) and how they affect cognitive development,” she said. “However, a growing body of research suggests that even differences in relatively specific, microlevel factors can affect how children understand certain concepts. I think this means that we need to be very purposeful about structuring lessons and our instructional input to ensure that we are setting children up to construct an understanding of the most important concepts.”

Although the lab’s research is primarily focused on mathematics, the results may possibly be applicable to other areas of learning such as reading and spelling.

McNeil, along with colleagues at the nonprofit research agency West Ed, also recently received a $3.5 million grant from the U.S. Department of Education’s Institute of Education Sciences, which aims to improve students’ mathematical achievement in elementary school and beyond.

The new grant, the largest grant awarded to McNeil’s work, will allow a large-scale trial of an educational intervention McNeil and her CLAD Lab research team have developed to boost math learning by helping students grasp the concept of mathematical equivalence. Such a concept supports problem solving reflected in a statement such as “two plus two equals four.”

The lessons and activities she proposes for elementary schools to change students’ learning about mathematical equivalence have been used successfully at Santa Cruz Catholic School, a Notre Dame ACE Academies school serving inner-city children in Tucson. Several second-grade ACE teachers from around the country served as participants in the pilot study and helped refine McNeil’s approaches.

Originally published at