Students are more likely to be able to solve math problems if the concept behind the question is explained to them beforehand, according to a new study from Vanderbilt University’s Peabody College.

Researcher Emily Fyfe set out to determine whether math instruction solely focused on learning skills and procedures, such as answering addition and subtraction problems, was more or less effective than instruction that included explanations of concepts.

Fyfe and two tutors taught a group of 122 Nashville second and third graders the concept of math equivalence—the idea that two sides of an equation represent the same quantity. She and the tutors taught the students that an equal sign in an equation, such as 3+4=4+3, means that there are equal amounts on each side, and gave the group of students practice equations to solve. Half of the students were asked to solve the problem before the lesson, and half solved them after the lesson. Both groups were asked to provide explanations of their process after solving the problem.

Fyfe found that the group that learned the concept before doing math problems was more likely to be able to solve the equations. That group had 67 percent accuracy rate, while the students who answered the questions before learning the concept had a 44 percent accuracy rate.

Fyfe said that typically, math instruction has been based more on skills rather than on understanding the concepts underlying those procedures. She said that her take-away is that some instruction on concepts, rather than just skills, benefits students’ mathematics problem-solving. But, she said, students also need the chance to apply concepts and practice skills. 

Fyfe, a doctoral candidate in developmental psychology at Vanderbilt, said that the research team chose to focus on the concept of equivalency because it is highlighted in the Common Core State Standards, which Tennessee uses for math and reading.

The Common Core standards start emphasizing the concept of equivalency in the first grade. But, Fyfe said, the research team studied textbooks, and most still did not clearly define equivalency or include problems that would reinforce the idea. The majority of textbooks present math problems so that operations are always on the left and the equal sign is on the end (showing, for instance, that 4+2=_ rather than _=4+2), and rarely provide a definition of equal signs, Fyfe said. “It’s in the standards now, but it doesn’t seem they’re going to get this information from the textbook.”

Marci S. DeCaro, department of psychological and brain sciences at University of Louisville and Bethany Rittle-Johnson, associate professor psychology at Vanderbilt’s Peabody College, co-authored the study. The research was supported by the National Science Foundation and the U.S. Department of Education.