Using symmetry to teach whole numbers

A new article in Cognition and Instruction looks at how children’s natural perceptuo-motor skills can be harnessed for teaching and learning mathematical structure, specifically the integers (positive and negative whole numbers and zero).

The authors’ starting point was existing research that suggests that adult mental representations of integers use perceptuo-motor functionalities involving symmetry. For example, people find it easier to find the halfway point between -7 and 5, which are nearly symmetrical around zero, than between -9 and 3, which are not. Based on these findings, they designed a hands-on curriculum that emphasized symmetry to teach integer concepts.

At a San Francisco primary school, 74 Year 5 (fourth-grade) children were assigned to three groups. Two groups taught integers in traditional ways (by jumping along or stacking blocks on a number line). The third group used symmetry, folding blocks around the zero position on the number line. Compared to the two control conditions, children in the folding group showed evidence of incorporating symmetry into their mental representations of integers and also performed higher on problems beyond the scope of the teaching, including negative fractions and algebra-readiness problems.

Source: Learning to “See” Less Than Nothing: Putting Perceptual Skills to Work for Learning Numerical Structure (2015), Cognition and Instruction, 33(2).