Zachary Champagne’s 3rd and 4th graders figure out early on that this math class will be different when their teacher tells them: “I don’t care about the answer.”
The goal is to shift his elementary students’ thinking from some numerical endgame toward the problem-solving process itself. In his more than two decades as a classroom teacher and math researcher, Champagne has found this strategy can be a balm for math anxiety, spur students’ creativity, and pique their curiosity about a subject many find boring and irrelevant.
Telling students the answer doesn’t matter—or throwing it out early on, then working backwards, another of Champagne’s go-to strategies—"can reframe the way we think about mathematics,” said Champagne, who teaches at The Discovery School, a private school in Jacksonville, Fla.
“If we’re thinking about math where the solving is actually the interesting, important part, it frees kids from the stigma of ‘I’m not good at this because I always get things wrong,’” said Champagne, who spent more than a decade working in Florida’s Duval County public schools and served as a math researcher at Florida State University.
This problem-solving or open-ended approach, which emphasizes flexible thinking and real-world situations, is a powerful strategy for engaging the youngest learners in math. Kindergarten through 5th grade is an important time for building students’ skills, confidence, and interest in math—the critical building blocks for middle- and high-school-level math and science, experts say.
Though the approach has been around for decades, districts are striving to incorporate more real-world problem-solving into math class in recent years. California, for instance, recently adopted a controversial framework that puts a heavy emphasis on the approach. And there’s new urgency to get students motivated in math as federal data show students’ math achievement plummeting.
The vast majority of educators—92 percent—say students are more motivated to learn math and science if teachers employ a problem-solving approach, according to a survey of 1,183 district and school leaders and teachers, conducted by the EdWeek Research Center in April. Despite the fact that this approach is highly popular among educators, many have not been trained in how to use it, the same survey found.
Does using real-world problems motivate students?
The Canadian province of Quebec has been using a problem-based approach for decades—and it helps students connect with math and understand how to use it in the real world, said Krista Muis, a professor at McGill University in Montreal, who has studied student perceptions of the teaching strategy.
“When you look at the motivational profiles of students who are just given traditional word problems, or more standard types of math problems, or math content, their motivation is really low when it comes to the value of what they’re learning,” Muis said. “The main question they ask is, ‘why should I care? How is this relevant to me? How am I ever going to use this?’”
But when students tackle common real problems—a favorite of Muis’ asks elementary schoolers to map out the trick-or-treating route that nets the most Halloween candy—they get excited.
“They see the value in it,” Muis said. “And they’re fun problems. They can do them in groups together collaboratively, they can do them individually.”
Quebec students’ higher motivation in math may explain why the province outperforms the rest of Canada—and the United States—on the Trends in International Mathematics and Science Study or TIMMS, Muis said.
In 2019, the most recent year the test was given, Quebec’s 4th graders didn’t perform statistically differently from their U.S. counterparts in math. But 8th graders from the province scored significantly better than their U.S. peers. One reason may be the increased motivation to learn math that Muis believes stems from exposing students to a problem-solving approach early on.
To be sure, a problem-based or open-ended approach to teaching math is often pitted against more traditional, procedural methods—think of the math worksheets full of equations without context.
But many experts and educators see value in exposing students to both strategies.
“I think, really, these things can mutually support one another. And both are necessary,” said Julia Aguirre, a professor and the faculty director of teacher certification programs at the University of Washington Tacoma. “I think we can all agree that a math class that’s only about worksheets would not be a very fulfilling or interesting math class.”
Promote young students’ natural curiosity and creativity
The approach is most effective when teachers apply it to students’ existing interests.
That’s especially important for elementary school students, who start school with a natural curiosity that often dissipates by the time they get to high school, said Molly Daley, a regional math coordinator for Education Service District 112, which serves about 30 districts near Vancouver, Wash.
Thinking about “math is a universal human behavior, and people of all ages engage in math for their own purposes,” Daley said.
Students are using math when they play games and make crafts, she said, or even just look at the landscape.
For instance, a preschool teacher might take a picture of the classroom shoe rack and ask students questions like: How many shoes are there? What patterns do you notice? What shapes do you see?
“If we can honor the math that kids are doing beyond the classroom, then we’re more likely to create a mathematical connection and really allow every person to see how math is not just useful but enjoyable,” Daley said.
In Champagne’s mixed age classroom of 3rd and 4th graders in Florida—which he co-teaches with another educator—students turn to math early in the day, the time when younger students tend to be most able to focus on the subject, in Champagne’s view.
Champagne typically kicks off with a 10- or 15-minute math routine as a warm-up. That might be a “number talk” in which Champagne will put an equation on the board, say 29 plus 15, and then students will solve the problem in their heads.
They’ll spend the next few minutes comparing strategies for finding a solution. One student might have added 30 plus 15 and subtracted one, while another might have added 9 and 5, then 30.
The exercise is aimed at promoting flexibility and the idea that there are multiple ways to solve a problem, Champagne said. It lets students know: “I don’t have to revert to just one strategy. I can think about it in different ways,” he said. The idea is to gives students a chance to use their creative thinking skills in math class.
Students still learn the basics, but lessons are structured so that students can see how seemingly simple problems play out in different, real-world contexts. For instance, if students are learning about dividing with remainders, they may consider how four people can share 31 balloons. In that case, each person gets seven balloons, with three left over.
But what if it were 31 dollars instead of balloons? How does that change the answer? Or what if 31 people needed to get somewhere in four cars? How could they divide up?
Problems can also get more complex—and interdisciplinary—as students advance in elementary school.
Teachers need more training in the problem-solving approach
Tackling big problems with no clear answer is another way to engage elementary school students in math.
Last school year, Aguirre worked with Janaki Nagarajan’s 3rd graders outside Seattle on a project involving a real-life problem with salmon the students had raised and planned to release.
Inexplicably, the fish began dying. So Nagarajan’s students used mathematical modeling to estimate how quickly they were losing salmon, answering questions like: Will we have enough salmon for each student on release day? What can we do if we don’t? Students worked on the problem in groups, and then presented their answers. The class voted on the solution they thought would work best.
The project was “really engaging,” said Nagarajan. She believes that students will be motivated to learn math if they “feel the skills have some purpose outside the classroom.”
But she thinks that many teachers don’t know how common procedures learned in math class could be applied in the real world, so they struggle to make those connections for their students.
Nagarajan began teaching in Renton, a different, Seattle-area school district this school year, largely because it provides more support for teachers to use the real-world problem-solving approach in elementary school math.
Though the approach was encouraged in her previous school, Nagarajan said her new district uses a curriculum that embraces problem-solving and provides coaches who can help her implement the strategy.
Professional development in the problem-solving approach remains uneven. About one in five educators said they “completely agree” that their districts have offered deep and sustained professional development into how to teach math and science from a problem-solving perspective, while just over 40 percent said they disagree—at least somewhat—that they’ve been offered that level of support.
That professional development can be particularly important for elementary school teachers who typically “aren’t math specialists, right? They are generalists,” said Muis of McGill University. “Often, teachers who are not comfortable with mathematics don’t necessarily understand it fully themselves. And so when you bring in complexity that scares them. And then you see teachers kind of stepping back going, ‘I can’t really teach this, I don’t really know what I’m doing.’”
And the approach requires teachers to respond to what students see or notice, which can be stressful for some, Daley said.
“We can get too hyper focused on ‘this is my goal’” in a particular lesson, she said. That can look like: “We’re learning about fractions, but the student made a comment about multiplication. I gotta ignore that.’”
Teachers need to learn not to be afraid if students go off script, Daley said. A problem-solving approach is about “creating more space for students’ ideas and students’ thinking versus just letting your own dominate.”
Making that shift isn’t easy. But if teachers are successful, they positively shape their students’ relationship with math, potentially for years, Daley said.
“Especially with younger learners, when we’re following their lead, that’s how we’re going to tap into their connection and their motivation to engage with math and build up their sense of themselves as a mathematician,” she said.
