NCTM President's Message: The need to make homework comprehensible

Dr. Matt Larson
Dr. Matt Larson

By Matt Larson, NCTM President

Whether you are an elementary, middle level, or high school teacher, you are likely to have had parents say to you that they can’t help their children with their math homework. At the secondary level, the difficulty is often the content itself; at the elementary level, however, it is often a function of parents’ unfamiliarity with the instructional strategies that we use today to build conceptual understanding.

In recent years, as new standards and instructional strategies have been implemented at the school and classroom level to build students’ conceptual understanding in addition to helping them meet traditional procedural fluency goals, parental concerns about math homework, particularly at the elementary level, have increased. Social media provide a new vehicle by which parents rapidly share examples and express their concerns about math homework and instructional strategies that they find confusing or unnecessarily complicated.

A recent report from the Fordham Institute, Common Core Math in the K–8 Classroom: Results from a National Survey, found that 85 percent of teachers reported a decline in parental reinforcement of math learning at home because parents do not understand the way that mathematics is being taught in school. This is an overwhelming percentage!

This issue is not new. Mathematics homework has long been a conundrum for students, teachers, and parents alike (see NCTM's Homework History Research Brief and Clip). Today some teachers, schools, and school districts are going so far as to limit or even ban homework in certain grades. To some degree, this is part of a historical cycle in the United States: homework falls in and out of favor every 15 to 20 years. Clearly, however, for many parents today, it is a hot topic that we need to address more effectively.

Despite these calls to reduce or ban homework, most math teachers continue to assign it because we recognize that success—whether in mathematics, music, or athletics—depends on at least two common components: practice and perseverance. Too many adults, and students for that matter, tend to view success in mathematics as dependent on a talent that someone either is or is not born with. Several highly regarded researchers, including Carol Dweck and Jo Boaler, have demonstrated that this simply isn’t the case. Each and every student can learn more mathematics in the same way that an athlete improves his or her running time or a musician masters the technique required to play a piece of music—by receiving appropriate and effective instruction in a supportive environment, by responding to feedback, and by expending effort—trying again and again, while using different strategies—in short, by engaging in meaningful practice.

However, as the Fordham Institute report recommends, we need to make the practice that goes home as straightforward and comprehensible as possible for parents. And we need to recognize that while we may discuss multiple solution methods in class, the goal is not for students to practice and master multiple methods; rather, it is for students to practice and develop proficiency with their preferred, well-understood, and most efficient method.

Making homework comprehensible means, in part, that we need to be responsible for the types of tasks that we send home. Many of the instructional and homework tasks that frustrate parents reflect instructional strategies used to develop student understanding of underlying mathematical concepts. For example, in the fourth grade, an open array model for two-digit multiplication can illustrate partial products, place value, and the distributive property. However, sending home practice that requires students to solve multiplication problems by using an open array may not be advisable, because this approach is likely to be unfamiliar to many parents.

Finally, we need to show parents the solution strategies that we are using in the mathematics classroom. Evidence suggests that once parents are shown, engaged in thinking about, and come to understand the strategies in use, their support increases. NCTM has a number of resources that can support parents in understanding school mathematics today, including the recent publication, "It’s Elementary: A Parent’s Guide to K–5 Mathematics," which offers clear explanations of many of the instructional strategies that parents may not have experienced when they were in school themselves.

As mathematics teachers, it is our responsibility to share with parents the instructional strategies that we use in the classroom and make the practice that we send home comprehensible so that parents can engage with their children in constructive ways and support their mathematical learning.