Unfuzzy math: U.S. needs to do better 

The latest results of the Trends in International Mathematics and Science Study show that U.S. students’ math scores trail those of many of their global peers. They also reveal that U.S. math scores were lower in 2023 than they were in 2019. The test was given last year to fourth- and eighth-graders around the world.

In this edited conversation with the Gazette, Heather Hill, Hazen-Nicoli Professor in Teacher Learning and Practice at Harvard Graduate School of Education, details a “disappointing picture,” including the damage inflicted by pandemic learning loss, and offers ideas on how schools and students might rebound.

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How do you interpret these results?

They first show that the U.S. is not where it wants to be in terms of these international comparisons. They also show that the work that we’ve put in over the last 20 to 30 years to try to improve our standing internationally has not paid off. There are not a lot of surprises here because we’ve been also seeing the same signal coming from the National Assessment of Educational Progress. It is a disappointing picture. If you think about kids sitting in classrooms who are going to graduate without being able to reason mathematically or apply mathematical concepts to new problems, it’s just discouraging.

How much of the decline has to do with pandemic learning loss?

A large majority of the decline is due to COVID. Many kids, particularly our most disadvantaged children, lost half a year of math learning because they weren’t in school or they were in a hybrid learning situation. A couple of things about this. First, while the majority of this learning loss occurred at the beginning of the pandemic, teachers reported that even after schools were back to in-person learning, students had forgotten how to “student,” meaning they had forgotten how to attend to instruction, how to do homework in a timely manner, and had lost ground on some of the positive social behaviors that we expect in classrooms. I think most teachers would say that things are now back almost to where they were before COVID, with maybe the exception of cell phones being so distracting for children, but it took several years.

Second, math is cumulative, and students who missed half a year of math are going to struggle to learn new material. A student who has not learned basic fractions in the fourth grade is going to have trouble with more sophisticated fractions in the fifth, sixth, and seventh grades, and when they reach algebra, they are going to have trouble with equations that contain rational expressions. And this leaves teachers struggling with the dilemma of whether to present new material or to spend time helping kids finish up the learning they didn’t quite get through during COVID. Math teachers’ time with their students is limited, and many teachers feel this dilemma acutely.

“Kids’ primary pathway to learning math is in school, and the only way to improve math instruction is through the constant improvement of what happens between teachers and students.”

How would you describe the state of math education in the U.S.?

It is highly variable. When I watch classrooms, I see some teachers knocking it out of the park — meaning I see kids talking about the math, solving sophisticated problems, and applying mathematics to new situations. And in other cases, the math is not taught very crisply, in the sense that the lesson might be a little bit conceptually disorganized, or the math may be hard to understand. Many teachers have a mix — a fair amount of student reasoning but also some disorganization around the mathematics.

Another thing is that the pandemic has changed the teaching labor force in the U.S. There are many more novice teachers, and they are therefore inexperienced with the math curricula.

One of the things that’s been promising is that in the last eight or nine years, there’s been more of a focus on high-quality curriculum materials and getting those in front of teachers, and having teachers learn how to use them and adapt them smartly for their children. As this movement continues to build steam, I’m hopeful that we will see improvements in math classroom quality.

Why is math so hard for so many U.S. children?

Some of this is about social pressure. Kids take in the messages that they hear from society about math. It’s common to hear messages like, “Oh, I’m not good in math” from friends or, from adults, “It’s OK not to be good in math; you’ll find something else to do.” Whereas in many other countries, math is seen as a prerequisite to a good life, and the understanding that even if it is a hard thing, you’re going to invest in it, and you’re going to do well.

Also, for many kids, math feels very foreign. They don’t see people like them doing math, and what happens in their math classroom doesn’t connect to their own interests and knowledge. Recently, scholars in my field have begun to think about how to revise curriculum materials so that they feature, for instance, mathematicians from other cultures or successful doers of math that look like the kids that are learning math.

Finally, we’ve moved away from giving students opportunities to practice the mathematics they’ve learned in class. This move comes from two sources: curriculum materials whose lessons contain little time for practice, and recent homework bans. Many of the homework bans are predicated on concerns about children’s unequal access to caregiver support for homework as well as concerns that some schools assign too much homework. But for a content area like math, it matters that kids have a chance to practice what they’ve learned in class.

How can the U.S. education system help students improve their math scores?

One thing that could help is changing the narrative about mathematics from one that says, “It’s OK if you don’t do well in math” to one that says, “If you work hard, you’re going to learn math because it’s logical and there is help.” There are ways everybody can learn math.

Working on teacher-student relationships can, maybe surprisingly, assist with math learning. When teacher-student relationships are strong, they result in better outcomes for kids across the board. In math, one reason may be that teachers can more easily engage kids in the work.

There’s such a scarcity of math teachers, which is driving some of the instructional quality issues. We have teachers who don’t have a background in math teaching math, and we also have folks without a background in teaching or math teaching math. Solving teacher pipeline issues is also key.

Kids’ primary pathway to learning math is in school, and the only way to improve math instruction is through the constant improvement of what happens between teachers and students. This means continuing to work on the quality of curriculum materials and engineering ways to enhance instruction.