It’s that time of year again. Parents and teachers are doing everything they can to get students off on the right foot for the new school year. We want our children to make the most of every moment – every social interaction, science project, and yes, math class.
It’s not a secret that students in the United States consistently underperform in math. Although there are numerous plausible reasons for this, it seems likely that the content of math classes matters.
In typical U.S. math classes, students spend a lot of time learning step-by-step procedures. Although this isn’t inherently bad, the result is a lot of rote memorization without a lot of understanding. For example, why do you “carry the one” on certain subtraction problems? What does it mean to “do the same thing to both sides” of an algebraic equation? I still remember learning to “cross multiply and divide” and not knowing why. Without this deep understanding, students are unlikely to succeed when presented with new math problems and ideas.
One math idea that is particularly hard is fully understanding the equal sign. Students often misinterpret the equal sign, thinking it means “find the total” or “get the answer.” As a result, they solve many problems incorrectly by simply adding all the numbers they see. For example, for the problem 3 + 4 = 5 + __, they often write 12 in the blank (the sum of the numbers) as opposed to 2 (the correct answer).
So how can we get students to solve problems correctly and actually understand why it is correct? Based on research conducted at Vanderbilt University’s Peabody College, I have several suggestions. Although these minor changes will not solve all students’ struggles in math, they are easy to implement at home or at school and provide a step in the right direction.
1. Provide your child with many explanations of the concept. Too often we spend time telling students the steps to solve a problem without explaining the principles behind those steps. For example, explain to students that the equal sign means that two amounts are the same. In every problem with an equal sign, everything to the left of the equal sign should be the same amount as everything to the right of the equal sign. If I have 12 on the left side of the equal sign, how much has to be on the right side? 12! And repeat this in new contexts. Once is not enough!
2. Give your child a chance to apply the explanations. After hearing an explanation of the concept, students need a chance to use that information. Have students solve a variety of problems that rely on the concept. For example, after explaining the meaning of the equal sign to students, have them solve different types of arithmetic problems. Include problems with operations on the right side of the equal sign (e.g., __ = 3 + 4) and operations on both sides (e.g., 3 + 4 = 5 + __).
3. Have your child explain his or her answers to the problems. Students often benefit from having to put their own understanding into words. While they are solving relevant problems, have them explain how they got their answer and why they think it is correct. For example, for the problem 3 + 4 = 5 + __, you can ask students “Why does 2 make this a true number sentence?” or “Why is 2 the correct answer, but not some other number?”
Written by Emily Fyfe, a graduate student studying how children learn in math in the Psychology Department at Vanderbilt University. These suggestions are based on research conducted at Vanderbilt University’s Peabody College under the direction of Dr. Bethany Rittle-Johnson.