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It鈥檚 the end of math class at Forest Hills Elementary School in Sidman, Pennsylvania, and after a short break, fourth-grade teacher Dawn McCall鈥檚 students are getting down to business鈥攚ith an additional 20 minutes of math work.听

McCall鈥檚 students know the routine: They pair off with a partner鈥攗sually a higher-performing student and a lower-performing one鈥攁nd work through short sets of problems together that target weak or missing skills, like multidigit subtraction or multiplication. One student solves the problem while describing their thinking aloud; the other student offers support and highlights mistakes. Then they switch roles.听

This is SpringMath, a short and that McCall鈥檚 school is implementing for all students, regardless of their achievement levels. The targeted daily practice is designed to strengthen foundational skills, and it鈥檚 rapidly putting grade-level math mastery within reach for a lot more students, according to McCall. 鈥淭o succeed at fractions and decimals, you have to know your multiplication and division facts,鈥� McCall said. 鈥淚f you know those multiplication and division facts, things like reducing fractions is going to be a lot easier. It鈥檚 that little extra bit of practice every day.鈥澛�

Since Forest Hills Elementary began implementing the math intervention at the beginning of 2018鈥攕lowly adding a few grades at a time, beginning with fourth through sixth grade鈥攕tudent test scores for some participating groups have steadily improved, according to assistant superintendent Dr. Rob Dill. In 2022, 56 percent of fourth graders at the school scored proficient or advanced on the Pennsylvania System of School Assessment state test; by fifth grade, 76 percent of those same students scored proficient or above. Meanwhile, math achievement across the nation is headed in the opposite direction. Only scored proficient in math on the 2022 National Assessment of Educational Progress (NAEP) after a historic five-point drop following pandemic school closures. For the decade before that, scores had hovered around only 40 percent proficiency. Eighth-grade achievement dropped even more鈥攄own eight points from 2019, with only scoring proficient; 40 percent scored below basic.听

Now, a of researchers, school leaders, and educators are calling attention to research-based solutions to combat slippage in math, including the crucial role that adequate practice time plays in student performance. 鈥淭hey are considered dirty words, but drill and practice, and explicit instruction on how to procedurally solve math problems, are evidence-based strategies that work,鈥� said SUNY University at Albany math researcher Ben Solomon. There鈥檚 often a misconception that rote math practice is dull and uninteresting, but 鈥渢hink about how adults thought phonics was boring, but kids actually feel awesome when they can be successful at learning to read,鈥� said University of Winnipeg professor of mathematics Anna Stokke. 鈥淚t鈥檚 the same with math. Teaching foundational math skills does not need to be mindless and boring.听Adults who have already mastered a topic don鈥檛 view things with the same sense of excitement that kids do. Kids get excited about math when they feel successful, regardless of the topic.鈥澛�

The Fluency Question

A key missing ingredient in higher math achievement is math fluency, especially in the basic operations of addition, subtraction, multiplication, and division. that fluency in these foundational skills is critical to math performance and achievement, but experts and educators say there鈥檚 a disconnect between how much practice students need to achieve fluency鈥攅specially students who struggle with math鈥攁nd how much they often get in classrooms. The includes the importance of practice in basic operations among its top findings and recommendations鈥斺�滳omputational proficiency with whole number operations is dependent on sufficient and appropriate practice to develop automatic recall,鈥� the authors write鈥攜et schools and teachers say that, for a variety of reasons, students aren鈥檛 getting enough practice to solidify foundational concepts.听

Researchers like Solomon say that , , and the dreaded worksheet of problems actually matter to long-term math achievement because they help students build the kind of domain knowledge in foundational skills needed to perform more complex math鈥攁nd that some kinds of math practice are better than others. Evidence shows that go hand in hand and are mutually reinforcing, but experts say that in many classrooms an overcorrection has been made that puts too much focus on conceptual understanding at the expense of procedure. 鈥淐onceptual understanding really has been overemphasized to the point that students don鈥檛 have procedural skills,鈥� Stokke said.听聽聽

Lack of procedural skill often keeps students from ever reaching the creative, open-ended side of math. 鈥淲e need to give them the basic tools and then play with them in many different ways so they can explore the beauty of math,鈥� said , professor and Canada research chair at the University of Western Ontario in London, Ontario. 鈥淏ut first they need the basic building blocks.鈥�

Obstacles to practice time

Math practice gets shortchanged for a constellation of reasons鈥攁n overstuffed curriculum and the drive to cover an overwhelming number of standards; test-prep pressure; and instructional philosophies that consider repetitive practice, sometimes negatively referred to as 鈥渞ote鈥� or 鈥渄rill and kill,鈥� to be uniformly harmful and to be avoided at all costs.听

When Lee Williams, mom to two middle school students in Williamson County, Tennessee, checks in on their homework, she said, the most notable thing is that they鈥檙e moving through math at lightning speed鈥攁 common refrain among parents interviewed for this story. Both kids are tackling complex concepts in math class, yet they haven鈥檛 mastered the fundamentals of arithmetic that make learning more challenging topics possible. 鈥淭hey move to a new topic every week in elementary and don鈥檛 ever master the basic functions,鈥� she said. 鈥淭hey start with algebraic concepts before they even have multiplication and division facts at the ready鈥攊n third grade.鈥�

In classrooms, teachers say there鈥檚 just not enough time for extra practice. Pressured to cover every state standard with equal emphasis, they often can鈥檛 spend extra time on fundamentals like memorizing multiplication tables, or even on the standards themselves. 鈥淚t鈥檚 a huge problem,鈥� said Sarah Powell, associate professor at the University of Texas at Austin, who researches math instruction and trains teachers. Some districts go so far as to put out a calendar dictating what every teacher should be working on every week of the year鈥攔egardless of how far along (or behind) their students are in the curriculum, Powell noted. 鈥淲e have trapped ourselves with having so many expectations; at each grade level there are these standards, and you are supposed to cover these 30 things and not let anything go,鈥� she said.听聽

But when it comes to standards, it鈥檚 important to recognize that they鈥檙e not all of equal importance, said Phil Daro, who helped write the Common Core math standards. Some of the fundamentals, such as single-digit addition, subtraction, multiplication, and division for the youngest students, are critical to spend ample time teaching and have kids practice. 鈥淪tudents need to know foundational math facts fluently,鈥� Daro said. 鈥淧ractice needs to focus on the foundational skills. If you fill that practice bucket with more and more stuff, that will dilute the amount of time and effort available for practicing the real foundation.鈥�

Adding to the problem, researchers say that popular math curricula, and even some teacher training programs, de-emphasize practice鈥檚 crucial role in math learning. 鈥淢any of the newer textbooks don鈥檛 provide enough practice problems,鈥� said Doug Rohrer, a professor and math education researcher at the University of South Florida. 

Where does practice belong? 

A few years ago, SpringMath founder Amanda VanDerHeyden overheard a tutoring session聽where a student was trying to divide 148 by 3. Instead of doing long division, the student skip-counted by 3s all the way to 148, which didn鈥檛 work out evenly. After several more attempts, the student finally arrived at the correct solution. 鈥淭he student has the horsepower, he conceptually understands,鈥� she thought to herself at the time. 鈥淏ut he has been deprived of the most efficient way to get there.鈥澛�

Like learning any skill, after students learn a particular concept like long division, in order to consolidate that learning and reproduce it in the most efficient way possible, they have to practice until it becomes second nature. But because learning isn鈥檛 a linear process, students should regularly be moving between foundational skills and application, with teachers frequently planning tasks that encourage retrieval of that material in a variety of ways. In most math classrooms, says VanDerHeyden, students are required to stop working on a skill too soon, cutting short valuable opportunities for repetition and limiting their ability to lock the learning into long-term memory.

SpringMath is based on a learning framework called the , a framework for how students acquire new skills that includes , including acquisition, fluency, generalization, and adaptation. According to this model (and there are a variety of learning frameworks), teaching looks different in the acquisition stage when students are brand-new to a concept, compared with when students can take a skill like long division and adapt it to other things, like complex story problems. A deeper awareness of how learning works, said University of Florida school psychology assistant professor Kathrin Maki, makes it easier to use techniques like inquiry learning at optimal times鈥攂ut not when kids haven鈥檛 yet had enough practice to adapt new skills to new problems.听

鈥淚nquiry learning isn鈥檛 necessarily bad,鈥� said Maki. 鈥淚t鈥檚 that those techniques are only helpful when kids have basic, prerequisite skills. Something we struggle with in math instruction is trying to implement those [inquiry-based] techniques too soon. Kids who are in the acquisition and proficiency stages, those are kids who need a lot of repeated practice and explicit instruction.鈥�

The goal of practice is to move foundational skills into long-term memory so they become quick and automatic. Since math constantly builds new skills on top of existing ones, it鈥檚 鈥渞elentlessly hierarchical,鈥� said Maki, and once foundational skills like addition and multiplication facts are locked into long-term memory, learning new, more complex math skills like multiplying fractions gets easier; working memory doesn鈥檛 have to work so hard. 鈥淟ong-term memory is effectively limitless; that鈥檚 our superpower,鈥� . 鈥淭hings that are extremely hard to do when you鈥檙e a novice become easy when you鈥檝e got lots of stuff in your long-term memory.鈥澛�

Best practice for practice

Improving math fluency doesn鈥檛 necessarily require endless hours of drilling, research shows. Short but frequent bursts, using a variety of strategies鈥攖hink flash cards and brain dumps, for example, that get students to identify what they know about a concept, thus strengthening long-term retention鈥攁re . 鈥淭eachers tend to focus on getting info into students鈥� heads,鈥� said cognitive scientist Pooja Agarwal, coauthor of Powerful Teaching: Unleash the Science of Learning. 鈥淏ut a big component of learning is getting the information out of our heads.鈥� Frequent low-stakes quizzes, entry and exit tickets, and some digital games, like , can offer effective retrieval practice.听

Retrieval strategies like , where students revisit concepts over a period of time with breaks in between, and , where mixing up different types of math problems helps students remember information better than when they work through long blocks of one type of problem, are strongly backed by the science of learning. Interleaving is so effective, University of Florida researcher Rohrer said, because students must decide which problem-solving strategy to use before solving. 鈥淚n math textbooks, students don鈥檛 have a chance to choose a strategy because a typical math assignment is devoted to a single concept,鈥� he said. 鈥淲hich means that they usually know the strategy for each problem before they even read it.鈥� Interleaving, however, 鈥済ives students a chance to learn what they need to know.鈥澛�

In the Forest Hills school district in Pennsylvania, assistant superintendent Dill said a series of evidence-based reforms, including a new curriculum, have rewired how the district teaches math from kindergarten to high school鈥攂ut the importance of the extra daily practice can鈥檛 be understated. 鈥淜ids who are now fourth- and fifth-graders, they鈥檝e been doing this for a few years,鈥� Dill said of the intervention. 鈥淎nd their skill development is far better than we鈥檝e ever seen before.鈥� And in McCall鈥檚 classroom, she鈥檚 seeing overall math confidence blossom. 鈥淭hey know they can do it,鈥� she said. 鈥淭hey鈥檝e learned those math facts.鈥�