Notre Dame paper examines how students understand mathematics

http://www.eurekalert.org/pub_releases/2015-05/uond-nd052715.php

Public Release: 27-May-2015
University of Notre Dame

t's both the bane of many parents and what has been called a major national vulnerability: the inability of many children to understand 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 the University of Notre Dame, and the researchers in her lab.

A new paper by McNeil and Emily Fyfe, a former Notre Dame undergraduate who's now a doctoral student at Vanderbilt University, 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.

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