How Teaching With Symmetry Improves Math Understanding By Katrina Schwartz



How Teaching With Symmetry Improves Math Understanding

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Salk Institute courtyard, La Jolla, California. (Christian Ronnel/Flickr)



There’s a part of the brain that enables us to perceive magnitude — we can compare loudness when hearing different tones or compare the number of dots in a group at a glance. Neuroscientists have identified this region responsible for perceptual comparison (the intraparietal sulcus) as linked to symbolic comparisons, including integers in math. That discovery led scientists to realize that symmetry plays a big role in how humans compare integers.

‘On these problems where you have to learn new things, suddenly you see that symmetry stuff showing up and it’s basically because kids had a much better structure to organize new ideas and new information.’Dan Schwartz, Director of Stanford AAALab

Building on this background research, Stanford education researchers tested a teaching strategy explicitly focused on using symmetry to teach integers to fourth-graders. They wanted to see if recruiting the visual symmetry parts of the brain would improve students’ facility and understanding of the concept. Their findings, published in “Cognition and Instruction” in May, indicate that teaching with symmetry could have a big impact not just on students’ understanding of integers, but also on more advanced concepts that go well beyond the scope of instruction as well.

“Finding a fundamental discovery in neuroscience about how the brain is processing these numbers led us to realize the instruction needs to change,” said Daniel Schwartz, director of Stanford’s AAALab and one of the authors of the study.

When people are asked to find the distance between a negative integer and a positive integer oriented in a blank space, they are able to do so much more quickly when the numbers are spaced around zero. For example, people can more quickly calculate the difference between -2 and 3 than they can -5 and 3. Furthermore, an fMRI scan of the brain while this calculation is taking place reveals that visual symmetry is in play.

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