Nicole McNeil and Colleagues Awarded $2M Grant to Improve Children’s Understanding of Mathematical Equivalence

A team including Nicole McNeil, a professor of psychology and the director of the Education, Schooling, and Society program at the University of Notre Dame, has been awarded a four-year, $2 million grant to leverage technology to improve children’s understanding of mathematical equivalence.

Funded by the U.S. Department of Education’s Institute of Education Sciences, McNeil will work with colleagues Jodi Davenport, Yvonne Kao, and Kristen Johannes of WestEd and collaborators from the ASSISTments Foundation to better understand the role of feedback in learning while also improving a previous math intervention developed by McNeil and researchers in the Cognition, Learning, and Development (CLAD) Lab at Notre Dame.

In that work, the CLAD Lab team developed Improving Children’s Understanding of Equivalence (ICUE), a research-based intervention for elementary students to help them better understand mathematical equivalence, or whether two quantities or expressions are equal. Understanding equivalence is a fundamental precursor to algebraic thinking, such as recognizing and analyzing patterns, understanding relationships, and analyzing how things change.

In prior studies, the ICUE intervention has led to substantial improvements in students’ overall rates of proficiency, but several students still did not develop a correct understanding of equivalence. With the support of the new IES grant, McNeil and her partners will further develop ICUE’s problem-solving activities through the ASSISTments platform to help students understand equivalence by giving them immediate, individualized feedback – meaning that students will not have time for misconceptions about equivalence to linger.

“Mathematical equivalence presents an interesting case because the strategies children learn in math class don’t always work. Students may look at a problem set, think it’s ‘easy,’ and forge ahead with well-known arithmetic strategies without realizing they’re solving all the problems wrong,” McNeil said. “With 25 to 30 students in a typical math classroom, it’s not realistic to expect teachers to provide each student with immediate, individualized feedback on each problem in a problem set. But by moving ICUE’s problem sets to the ASSISTments platform, we can tailor feedback to common incorrect strategies and test the type of feedback that works best.

“It’s a win-win because it helps us advance the basic science of the role of feedback in conceptual change, while providing a practical tool that helps math teachers respond to students’ needs in real time.”

By the end of the project, the team will create a suite of 32 fully developed online problem-solving exercises to support students in understanding mathematical equivalence.

Watch a four-part video series on Improving Children’s Understanding of Equivalence

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