By the time students start 4th grade in Jennifer Clark’s class, she hopes they have a solid grasp on their math facts.
“Because we do so much multi-step problem solving, and we’re doing two-step word problems, if they’re spending 10-15 minutes trying to figure out what 9x7 is, they’re doing a lot of extra work, or they get burnt out,” said Clark, a math and science teacher at Mills Elementary in the Austin Independent school district in Texas.
Findings from cognitive science researchers back up Clark’s observation. Math fact fluency is important, they say, because it frees up brain space for higher-order problem solving. (For more, see this story.)
But exactly how teachers should go about making sure their students know their addition, subtraction, multiplication, and division facts is less clear.
Usually, instruction in this topic falls into two categories: strategy instruction, which teaches students methods for deriving facts, and mastery practice, in which students build their speed and accuracy. Some studies have shown that a combination of the two can improve students’ recall of facts, but also their ability to generalize rules about numbers to other problems.
Other research points to additional effective practices. A 2019 study found that a technique called incremental rehearsal, in which students are quizzed on unknown facts in combination with known facts, helps students retain more new information than traditional drills.
Education Week spoke with four educators at different grade levels about why fact fluency matters for their students—when it’s required, how they teach it, and how they provide support for students who struggle.
The goal: For students to be ‘accurate, efficient, and flexible’
Joanna Roche, elementary coordinator of math and science, Shawnee Mission school district, Shawnee Mission, Kan.
When children are first learning their math facts in early elementary school, Roche wants to make sure students understand why numbers work the way that they do.
Students start by counting up to add together all of the numbers in a problem—adding 3 to 4 by counting 4, 5, 6, 7, for example. But this approach shouldn’t be permanent, Roche said. “I can’t have a kid who is counting on their fingers in 3rd grade, trying to figure out their multiplication facts.”
From counting, teachers in the district move onto learning strategies, such as skip counting for multiplication. Then students practice, usually by playing games, so that they can achieve mastery—which Roche defines as either memorization, or being able to employ a strategy so quickly that it feels automatic.
It’s important that children are able to retrieve facts quickly, Roche said, but most practice in the district isn’t timed. Instead, students are encouraged to share their thinking out loud as they problem-solve, making their mental math visible. That way, teachers—and students’ peers—can correct misunderstandings or miscalculations, Roche said.
‘By 4th grade, we need them to be a lot faster’
Jennifer Clark, 4th grade math and science teacher, Mills Elementary, Austin Independent school district, Texas
In spring, Clark sends letters to all 3rd grade parents at her school about math expectations for the coming year. By the time students get to 4th grade, Clark said, they should be mostly fluent with multiplication facts.
“When we get into fractions, if they don’t have a good understanding of division, reducing fractions is a nightmare,” Clark said.
Still, not every student has that understanding. Clark’s class marks a kind of transition point—teaching fact fluency isn’t the goal of most of the work she gives her 4th graders, but she is still able to make time for additional practice.
Most of this practice is focused on automaticity. Second and 3rd grade teachers at Clark’s school spend a lot of time working with students on strategies for deriving facts. “By 4th grade, we need them to be a lot faster,” she said.
At the beginning of 4th grade, Clark puts kids in fact-fluency stations for about 10 minutes each day, having them work with flash cards or online fluency games, “just letting them get comfortable with practicing, either alone or with each other,” she said. Throughout the year, she gradually tapers off this time, spending about 5-10 minutes on it about twice a week. The school also offers an online program that students can use at home if they need extra practice.
For the first time this year, the 4th grade team has started to grade students’ fluency, as a way to signal to both students and parents that getting the facts down is essential. This skill requires practice to sink in, Clark said: “When it doesn’t, you really notice it in 4th grade.”
‘We’re not going to stop and reteach’
Elizabeth Daniels, diverse learner teacher, and Jennifer Getz, middle school math teacher, Nettelhorst School, Chicago public schools
Daniels, a special education teacher, and Getz, a general education teacher, co-teach 8th grade math. Once students are in middle school, they say, fluency with facts is assumed—and required for all grade-level work.
This can pose a problem for some students with math learning disabilities, who may not have their facts down, said Daniels. It can feel like they’re “stalling out” of grade-level work, she said. So that students can access the material, Daniels and Getz provide support tools for children who need them.
“I of course care if they know their facts, but I feel like their frustration level will get too high if I don’t allow them to use a calculator or multiplication chart,” Daniels said.
Kids can get “frozen up” when they see a calculation they can’t do, Daniels added. If she and Getz can offer a scaffold that supports a child through that one part of the problem, then the student can tackle so much more, Daniels said.
Students who need extra practice with facts receive it in interventions, but the teachers also try to embed review when they can. In a recent lesson, for example, Getz paused on the fraction ¾ to check for students’ understanding: What does the fraction line mean?, she asked the class.
“If the majority of the class wants to go over some previously learned concept, we will stop and do that,” Getz said. But in general, she said, stopping regularly to review basic facts would make it impossible to get to all the grade-level standards.
“We just assume they’ve been assessed, they’re in 8th grade now, we’re not going to stop and reteach,” she said.