Understanding how students comprehend mathematics


Recognising and creating patterns could help children better understand mathematics.
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Researchers at Notre Dame University have been studying why some children have such difficulty understanding mathematics and what strategies can be developed to help them. One way might be to concentrate on identifying and creating patterns when young.

"Patterns are things, such as words or numbers that repeat in a logical way," says Nicole McNeil one of the authors of the paper.

"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."

McNeil collaborated with Emily Fyfe, a doctoral student 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 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."

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.

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