Worcester Polytechnic Institute (WPI) researcher Erin Ottmar has launched a three-year project that will determine how using visual elements in mathematical equations, specifically spacing around numbers and colorful type, could help students learn algebra.
The project, funded with a $667,617 grant from the National Science Foundation, focuses on how visual cues could shift attention to different elements that students perceive when working on algebraic equations. The findings could impact math curricula and classroom teaching.
“When students look at a math equation, they see numbers and symbols in space,” said Ottmar, an associate professor in the Department of Social Science and Policy Studies and principal investigator (PI) on the study. “Our idea is that by using a colored font and spacing around groups of numbers in both helpful and unhelpful ways, we can help students recognize and think about correct or incorrect ways to solve an equation.”
The research is based on perceptual learning theory and focuses on a critical mathematical concept known as the order of operations, which dictates the sequence of steps to follow when solving a mathematical expression with multiple operations. Students learn to solve operations inside parentheses first, followed by exponents, multiplication, division, addition, and subtraction to reach the correct solution. Failure to follow the order of operations can lead to incorrect solutions. Ottmar said that in her research, students who struggle with math often do so because they ignore the order of operations.
Working with collaborators in Virginia and Indiana, Ottmar will examine the individual and combined effects that using a colored font and spacing around different numbers can have on students’ ability to correctly follow the order of operations while solving math problems. The researchers expect to recruit a total of 1,800 students for two studies in Virginia and Georgia. An important issue will be whether color and spacing, when combined with technology interventions, could lead to better, longer-lasting learning.
The project builds on Ottmar’s previous research into real-time artificial intelligence tools for teachers to better detect, assess, and predict students’ math strategies and knowledge; the role of perceptual learning in mathematics; children’s physical gestures and eye movements when learning to solve equations; and using physically active games as an aid to math learning.
Ottmar will work on the project with four co-PIs: Ji-Eun Lee, a research scientist in WPI’s Learning Sciences and Technology Program; Caroline Byrd Hornburg, an assistant professor at Virginia Tech; Avery Harrison Closser ’19 MS, ’22 PhD, a postdoctoral scientist at Purdue University; and Jeffrey Bye, a cognitive scientist and consultant.
“This research benefits from bringing together scholars with expertise in education, psychology, math, and the learning sciences,” Ottmar said. “Knowledge from these fields will help us address the core problem, which is that we need to intervene to help younger students develop the core skills needed to succeed at algebra so they do not fall behind and give up on math.”
