When he teaches a math class, Tom Fisher wants students to feel confused. At least, he wants them to feel that way occasionally and temporarily.
Mostly an administrator these days, Fisher still teaches honors algebra at Breakwater, a pre-K-8th independent school in Portland, Maine.
For Fisher, it’s important to mingle math and play.
It’s not the conventional way to teach the subject, Fisher says. Too often, math teachers present information through lecturing and worksheets to students, forcing learners to decipher the context and usefulness on their own.
But for Fisher, there’s a reason that students in later grades often question why they are learning math. It’s because when instruction is devised for tests it’s not sensitive to whether the knowledge it imparts is long-lasting, Fisher says. Worse, such a heavy-handed approach prevents students from developing a tolerance for confusion by figuring out problems on their own, he argues. That robs students of the valuable experience of conquering problems that appear impossible at first.
So in class, Fisher tries to focus on nurturing a sense of play, and he’s found it helps to focus on real world examples. These examples are messy and can cause temporary bafflement. “Everything is not nice and neat,” Fisher says, adding: “It requires some extra thinking and some extra pondering.”
For instance, when it came time recently to build a lesson about fractions, Fisher had students come up with comparisons.
One pair of kids from his class ended up comparing the person with the most toes in history to the person with the fewest toes.
Another compared the length of videos.
Still another looked at the temperature across several days.
Fisher asked them to consider what made these questions easier or harder to figure out, and they discovered that when one number was twice as much as another, it was easier because of the obvious relationship, but when they were comparing a 403-second-long video to a 391-long one — or comparing the coldest day in the month to the warmest day — it was tougher. The discovery captures a feature of the relationships between numbers and how we use them, Fisher says.
What made the lessons work is that students were selecting what to compare, Fisher says. That gave them a sense of agency and motivated them to tackle complex problems.
It’s an approach some researchers think is too often missing from the classroom. When it comes to math, they argue, there isn’t enough emphasis on play. But with concerns over students’ development in these areas, especially postpandemic, would focusing more on play help math learning?
Learning the Playbook
There’s a false dichotomy between math and play that’s common, especially in early childhood, says Doug Clements, a professor at the University of Denver, Colorado. Even among researchers, this can cause “bulimic” partisan commitments to one or the other, he adds. It’s unfortunate, because research has shown that they are deeply connected, Clements says. For instance, a study showed that the best “social-dramatic play” — where kids take on roles and interact based on rules — occurs in classrooms where there’s both math and literacy curriculum. So some intentional teaching time plus play seems to be most powerful in supporting learning, Clements adds.
The general usefulness of play for learning is well established, particularly in the younger years. For instance, play in early education reinforces the development of social-emotional skills and critical thinking. Some research has even suggested it has the ability to reduce socioeconomic inequality.
But what’s meant by play?
For researchers, “play” happens when students take control of what they are doing. It’s flexible, willingly-chosen and yes, fun.
But that doesn’t mean it’s chaos, a nonstop free-for-all.
Just like when learning sports, language or music, structured practice is really important for math, Barbara Oakley, distinguished professor of engineering for Oakland University, wrote in an email to EdSurge. So more fun can be helpful, provided it builds on pathways of automatic math knowledge in students’ brains. But at the same time, emphasizing “ fun” in math can be harmful if it neglects structured practice. “The problem is that, if not done properly, ‘fun’ in math is the equivalent of teaching a child to play the guitar by teaching them to play air guitar. I mean, it’s fun! It’s easy! But it’s going through all the motions without actually teaching how to play the guitar,” she added.
So part of the goal is to build those skills. For that, researchers see usefulness in some unstructured time as well.
An important element is mixing free play with “guided play,” which has some direction from an instructor. The National Association for the Education of Young Children has catalogued a continuum of play: from “free play,” where students play without direction, to classroom instruction, where students receive an endless stream of instruction. The different forms of play can be complimentary, according to researchers like Clements, of the University of Colorado, Denver. Fundamentally, it’s important to have both guided sequential development, where students are introduced to new math concepts, and also free play where they can try out those concepts, Clements says.
How does that translate into the classroom? In early education, where Clements specializes, he usually constructs intentional lessons, and then sets up the classroom so that as students are playing, they bump into mathematics at every turn. That could mean preparing the classroom with labels and blocks and other spacial and mathematical items. But another way is to teach a small group of students a game and then turn them loose, Clements says. This seeds students’ minds, he says, and it gives them more ideas to play out. The goal is for students to have spontaneous recognition of math concepts out in the world. Once, a mother came back to report that her preschooler had noticed that the walkway they were trotting down was made of hexagons, Clements says.
But thoughtful classroom approaches that blend play and instruction are rare, according to Clements. Instead, many schools either give students too little math instruction — or too little play.
Some also wonder if emphasizing play in math too strenuously can transmit an unintended message.
Another Word for Fun?
These days, almost every math curriculum in early childhood and elementary school includes games, usually a board or dice game, says Yvonne Liu-Constant, a practitioner specialist for Project Zero. Early on in a student’s progression, there are also a lot of items for students to physically handle, such as linking cubes or colorful plastic bears that students use to count, she says. That’s the result of a push to make math more playful over the past few decades, she says.
When Liu-Constant started teaching, she was all about that.
But lately, she’s wondered if it isn’t somewhat misguided. The problem? Over the years, it gradually dawned on Liu-Constant that she kept hitting a wall in math instruction. Eventually, she blamed it on a hidden message: When you devote yourself to making math “fun,” you are almost implying that math isn’t already enjoyable, Liu-Constant says. We’d never say that about art, she adds. The assumption is that art is inherently interesting. And for people who love math, it’s already like art, she says.
It’s crucial for the sense of play in math to extend beyond just activities and games, she says. It should be more pervasive. That’s how it is with her brother, an engineer in Taiwan, who finds math so absorbing he could spend all his spare time thinking about numbers, Liu-Constant says.
So these days, in her work with Project Zero’s Pedagogy of Play, a research arm at Harvard relying on a “whole school approach” to learning, Liu-Constant has tried to reconstrue play as a strategy for learning, and not simply a set of activities for which teachers need to find time.
It’s about uncovering the fun that’s already in math, rather than trying to use games as an apology for teaching math, she says.
For those in the classroom, play works.
Seeking Patterns
Back in Maine, Fisher argues that his approach is impactful.
Fisher’s school, Breakwater, is small, with about 180 students and class sizes of around 15 students. Unsurprisingly, this exerts different pressures on teachers than public schools. Breakwater also stopped standardized testing years ago, according to Fisher. While they still rely on state standards, they no longer regularly perform assessments from NWEA, a widely used assessment company affiliated with the K-12 textbook publisher HMH. Fisher admits that this makes it difficult to compare the long-term effects of this approach to alternatives such as regional public schools. Not everyone in the school uses this approach, either.
But Fisher, who does use this approach, notices a difference.
Ultimately, Fisher feels that a playful approach makes math more memorable, the lessons more sticky. It teaches students to come up with strategies for performing math, he says. In his eyes, thoughtful play elevates math instruction.
In older grades especially, it’s difficult for people to imagine what play looks like, he says. But a pivotal component is self-direction. It can happen in small ways. Sometimes, Fisher says, it’s as simple as letting students discover a concept rather than having it explained to them. It’s about giving some agency to students, he adds.
