Story by Kathy McPherson
Lower School math specialist Emily Pyron firmly believes everyone can be a “math person.” With that in mind, she and Lower School Director Carolyn Ronco wanted to find ways to bring math enrichment activities to all students. Their solution is Cavalier Challenge, a completely voluntary opportunity open to all third- and fourth-graders.
“Anyone is invited. I make it clear to students that it's their choice and not their family's choice, not their teacher's choice,” Pyron said. “If they want to try to do some more challenging math activities that make you think differently, they are welcome to join.”
Cavalier Challenge began during the 2021–2022 school year, which was Pyron’s first year at Durham Academy. This year, more than 110 third- and fourth-graders have chosen to participate in Cavalier Challenge.
“I love being in Cavalier Challenge,” fourth-grader Arden Perreault said. “Math is not my favorite subject, but Cavalier Challenge helps me see it in a different way, and I really love that about it.”
Her classmate, Conrad Fisher, thinks math is amazing, and “when I heard about Cavalier Challenge, I was so happy because math has been my favorite subject since I was little.”
Fourth-grader Maya Bhowmick especially liked a recent Cavalier Challenge activity involving the cut-and-fold theorem that any shape with straight sides can be cut from a single sheet of paper by folding it flat, possibly with many folds, and by making a single straight complete cut.
“I like that math is very different,” Bhowmick said. “You can learn a whole bunch of different things about it, and I like that. I particularly like geometry, actually a lot.”
“The whole goal [of Cavalier Challenge] is to find an equitable way for anyone who's interested to have math enrichment,” Pyron said. “It's not how fast you can solve this addition or subtraction problem. It's bigger, thinking questions. Sometimes they feel more like riddles to students, sometimes they feel more like problems to work together as a team to solve. It gives students a space to feel proud about what they can do with math, even if they don't always feel as successful all the time in their math classes.”
The Lower School operates on an eight-day cycle, and students from each third- and fourth-grade class who chose to be part of Cavalier Challenge meet with Pyron once every eight-day cycle.
Pyron likes to engage students in hands-on activities. In solving a recent problem — “Three adults and two children need to cross a river using a small canoe. The canoe is able to hold one adult or a maximum of two children. What is the least number of times the boat needs to cross the river to transport all five people across?” — she saw students acting it out by rolling their chairs across a rug like they were in a river.
“Math is not just pen and paper, math is fun and exciting, and it's OK if we don't get the answer right away,” Pyron said. “Sometimes we don't get an answer. I think that's been really interesting for students. Sometimes we will stop before we get to an answer and there's this “oh, what's the answer" frustration. … It might be the end of the period, or we decide we've worked really hard on this, we're going to come back to it later because sometimes our math brains work better after they have had some time to rest.”
She wants to give students the experience of knowing that the answer is not the most important part of math.
“The important part is how you work together, are you trying to find a solution, are you using a strategy that will work for you?” Pyron explained. “We want an answer in the end, but it's not the biggest part of our day. We don't want to try to always find it the fastest, we want to find the way that works the best for us. What's interesting about math is not the answer, the answer is not interesting. I think it's how we get there. If you had a class here solving a problem with 18 students, there might be 18 different ways they solved it, because everyone thinks differently about math.”
Lower Schoolers learn different strategies as part of their regular classroom math instruction, and they develop what Pyron calls “a toolbox of strategies. Some students really like one strategy, some students really like another strategy and some mix them together to what works for them. I think that's the most interesting part: hearing students explain their thinking.”
Pyron said she “did not like math as a kid, and I really didn't like it when I was told you have one minute to do as many multiplication problems as you can. I see that stress for students now, too. It's scary when you have to do something that you don't know the answer to and you're asked to do it really quickly. We're trying to give students other ways to learn their math facts and be successful in a way that eventually they will know them, where they can do them quickly but we don't need to do speed rounds to learn them. … That's memorization, that doesn't mean we know how to use the numbers.”
Pyron began to feel differently about math when she was a second-grade teacher and “had to teach everything. And I didn't have one specific subject that I really, really loved. And then I started learning how to teach [math] this way. Seeing all the light bulb moments children had of ‘I get this, this makes sense to me,’ made me want to go back to school to be a math specialist.”
She wants students to leave the Lower School “maybe, hopefully, loving math, but at least being intrigued by it and not being scared of it. That's the main goal, in the end, everyone being comfortable with a challenge.”
Gaining that comfort level is something that Pyron sees with students in Cavalier Challenge. The first day she meets with them she asks them to look at a problem they have never seen before. Without giving them an introduction, Pyron says, “I want you to think to yourself, how would you solve this? That feels really tricky at first, that they have this open forum where they can do whatever they want to solve it. Then after multiple times of doing problems where they can do whatever they want to solve it, they come in here, they see the problem on the board, and they just go.
“They know that there's no wrong way to do something, but we're going to learn from each other as we do it. I think the biggest thing is the reluctance to do whatever you want to do to solve it, then feeling empowered to do whatever you think would be the best way to solve it and being able to share your thinking.”
Third-grade teacher Jeff Burch said there is “lots of positive energy [with Cavalier Challenge] and creative thinkers — not just the most mathematical students — are the ones who solve problems.”
It goes back to the idea of bringing math enrichment activities to all students.
“Something that I want to do more of is have more time to share with families, what we can do to support students, not just in their learning of math, but how they feel about math and how they feel about themselves as mathematicians,” Pyron said. “A big goal of mine is to make sure everyone feels like they're having a positive experience with math, and math isn't something that's for one type of person.”