The students in Molly James’s kindergarten classroom were tasked with creating a mathematical art gallery. They had each drawn a number and then searched for two types objects they could use to compose a visual number sentence -- such as two rulers plus three scissors to equal five objects.
After photographing and mounting their pictures on the wall in numerical order, the students sat on the floor with their sketchbooks and began to draw and talk. “I had expected them to learn something about number composition,” James said, “but I didn’t expect the remarkable observations they began to have about the photographs.” For example, when one girl looked at a picture of two red scissors and three blue scissors (2+3=5), she noticed that the direction of the handles gave rise to a new number sentence: 4 scissors pointing left + 1 scissor pointing right = 5 scissors.
James, who recently published a paper about creativity in the classroom, said moments like these remind her that “creativity is not fluff or an add-on, but is instead an essential part of what it means to be a mathematician.” In fact, she believes creativity is the key to helping her students become confident and skilled mathematical thinkers.
Heather Hill, a professor at the Harvard Graduate School of Education, encourages teachers to make room for creativity in the math classroom “because there’s heaps of evidence that kids are naturally very creative when it comes to mathematics.” In the same way that kids create their own stories or make up songs, “kids will invent their own methods for solving mathematics problems, even problems that are sometimes very complex.”
In math education, said Hill, creativity is defined as “kids having their own ideas about how mathematics works and being able to work to verify that those ideas are correct." As it turns out, she noted, these are the same traits that are recognized and celebrated in advanced mathematics. When elementary teachers encourage students to ask questions, make observations, and tackle problems in inventive ways, they create an environment that supports creative mathematical thinking.
Here are some ways to tap into that creativity:
Encourage Students to Question and Observe
“Asking mathematical questions is a form of creativity,” said Hill. Kids love to figure out how things work, so when teachers present a new concept, they should also build in time for students to make observations and ask questions. James uses prompts such as, “What do you notice about this [shape, number, story, or design]?” or “How else could we use [addition, graphing, or sorting] in the classroom?” to help students build these habits.
Pose Open-Ended Questions
Teachers can make a habit of posing inventive questions, said Hill -- even something as simple as “How can we figure out whether to buy chocolate or vanilla ice cream for the class party?” The trick is letting kids decide for themselves how to figure out a solution. The teacher’s job, said Hill, is to make sure students have the tools they need to solve the problem and to ask clarifying questions during the problem-solving process. James said that when she poses questions that require “struggle and creative thinking instead of rote application of rules,” students are not only more engaged, she is also better able to assess their understanding of key concepts by observing in real time how they apply their math skills.
Engage in Rich Conversation
One-on-one conversations help students articulate and extend their thought processes. As James circulates through the room, she uses prompts such as “Tell me about that; How did you think of that?; and What steps did you take?” to get kids talking. “I encourage students to share their thinking, and in turn I am open to the unexpected strategy," according to James. "I am willing to say, ‘Wow, I never thought about that before.’”
Apply Skills to New Contexts
During one lesson, James asked her kindergartners to write a number sentence and then invent a story based on that sentence. Students depicted their story in three ways: as an illustration, as a written sentence, and as a number sentence. James was surprised to find that a few kids who zoomed through their math facts really struggled to complete this task. “They wanted to give me a number sentence without a story,” said James. Being asked to manipulate and view numbers in this way “caused them a bit of internal conflict.” To help them through the process, James said she just sat with them -- wondering out loud and asking questions -- until they found their footing.
An activity like this is effective, said Hill, because it posed a question that “stretched kids outside of their comfort zone and called on them to think and invent.” James was asking her students to contextualize, which is “a core mathematical practice.” When young children are given opportunities to apply their math skills to novel situations, they take steps toward becoming confident and creative mathematical thinkers.
How Parents Can Help
Parents also play a key role in nurturing a child’s mathematical mind. They can help kids discover the math that is embedded in our daily experiences. “Anything you can make into a math problem is a win,” said Hill, “because it shows the child how useful math can be, and gives them some practice in applying their own thinking to math problems.”
James and Hill offered these strategies for parents:
Look for Patterns
Be on the lookout for patterns and sequences. For example, said James, a parent could make a plate with one piece of cheese, two tomatoes, three carrots, and four grapes and then ask, “Did you notice what I did with your lunch?” Simple activities such as sorting toys, setting the table, or going on a nature walk can provide opportunities too look for and create color, size, number, and shape patterns. These activities also hone observational skills.
Leave Math Notes
James suggests leaving little, unexpected math messages around the house such as, “Did you eat more pretzels or raisins? How many more?” or “How many different routes can you take to get from the kitchen to the bathroom?” Kids will likely start to leave notes for you to respond to, as well. She also recommends putting a number on a big sheet of paper and leaving it up for a few days, letting everyone in the family add something they know about that number. For example, for the number ten, someone might draw ten fingers while another might write 10 + 2, two less than a dozen, the square root of one hundred, or the names of ten friends.
Have Math Chats
Take time each week to talk about math with your kids in the same way you might talk about letters and stories. “Ask tons of questions,” James said. “Ask them to show you how they know. Ask, Is there another way to do it? In turn, encourage your kids to try to stump you and let yourself be stumped.” Even math facts can prompt creative conversations. Hill said, “If your kindergartner can already add simple sums like 5 + 5 and 4 + 4, give them progressively more challenging problems. At each step, ask how the child figured out their answer - and prepare to be surprised at some of the unusual strategies they will use!” A few minutes of math talk two or three times a week is all that’s really needed to get your child thinking, said Hill. “I do it when the kids are really bored — in the car, on the subway, waiting in the doctor’s office, and so forth. They’re much more willing to do math when bored.”
When parents and educators model creative engagement with mathematics, children come to see math as more than simply a set of facts and operations. “We want our students to become mathematical thinkers, not mathematical machines,” said James. “Even in kindergarten, I want to shape people who love solving problems creatively and who have the skills they need to someday change the world.”