It’s a familiar scene in childhood: kids building a tower of blocks, carefully placing each one, until, through trial and error, their construction stands tall and secure. But there’s a lot happening below the surface of this common activity–more than mere child’s play, it’s actually the beginning of mathematical thinking and problem-solving. Through their everyday exploration, children naturally “mathematize” the world around them (studies show that even babies recognize number groupings), and it’s our job as educators to harness their natural inquisitiveness and lead them to greater discoveries.
This view of learning—in which children are actively constructing knowledge from their experiences—is known in ed-speak as “constructivism,” and it’s the framework Calhoun educators use to teach math in early childhood. Calhoun teachers focus on creating learning experiences that actively engage students and help them make important mental connections. Math teaching in our early-childhood classrooms isn’t restricted to worksheets; children investigate puzzles, ask a lot of questions and are given the space to come to their own “aha” moments. Research shows that this is the type of learning children hold on to for the rest of their lives.
“Math is an abstract language,” says Anthony Yacobellis, Lower School – Early Childhood Math Coordinator. “In order to make sense of that language, children need to have experiences behind the curtain.” The math curriculum in our early-childhood program is very hands-on, in order to give children concrete encounters with abstract ideas. For example, Lower School teachers frequently organize activities with Cuisenaire rods, colored bars that represent numbers, to illustrate concepts such as addition, subtraction or place value. Being able to touch, see and manipulate these types of objects provides children with a tangible frame of reference, an essential foundation for the higher-level math that is to come.
The way our youngest students learn math is akin to learning a foreign language by becoming immersed in a country, rather than just memorizing a list of vocabulary. We create lessons that put the language of math in context. First graders recently learned about the fictional “Masloppy Family,” who needed help organizing their house. The story inspired the students to take an inventory of the objects in their classroom. They quickly realized that counting by ones was an inefficient strategy, and so they started to bundle items in groups of five or ten. Through this hands-on activity, children explored concepts of place value and multiplication in a way that connected to their lives and was ultimately much more powerful than if a teacher had simply stood in front of the room and told them how to skip-count.
When math is put in context for kids, it becomes an important part of their worlds, and they start to feel a real sense of ownership over the subject. “When we find ways to put math into what [children] are already doing, they do a whole lot more math, have more fun doing it and start to think of themselves as mathematicians,” explains Anthony. It’s no wonder, then, that Little Calhouners are unmistakably excited about doing math. “Everyone here feels like a mathematician,” observes Alison Rothschild ’85, Director of Lower School – Early Childhood.
Little Calhouners are also learning a very important aspect of what it means to be a mathematician—it’s not always easy. “Challenge is an important part of the early-childhood math experience,” says Alison. “We want students to learn to work through difficult problems and understand that being a mathematician means trying things multiple times until you find a solution.” Calhoun teachers deliberately lead kids outside of their comfort zones to help them build resilience and confidence as problem-solvers. We create an environment in which struggle and mistakes are normalized, combating the idea that only certain students are “math people,” and further diminishing math anxiety.
The most important way we create challenge for kids is by helping them delve deeper into the concepts they’re studying. We want children to be able to understand the “why” of math beyond just the execution of a series of steps. “Kids might be able to mimic what you’re doing, but it doesn’t mean they understand the concept,” says Anthony. “Memorization is not learning; it’s regurgitation.” We continually challenge students to articulate why they know what they know, to think critically and to develop new and efficient strategies for tackling problems. This focus on articulation of understanding over the memorization of procedure helps kids gain a fundamental grasp of the relationships between numbers. They become agile mathematical thinkers who can apply their knowledge to unstructured or unfamiliar problems. They can even begin to invent things that haven’t been seen before.
When you talk to Calhoun teachers, they are full of stories about students making big discoveries in math: a third grader who figured out a quicker way to do three-digit subtraction, a fourth grader who found a new way to multiply by six. Calhoun students are embracing their identities as mathematicians, thanks to the foundation they’re receiving in early childhood. One teacher recalls that one of his students loves to exclaim, “I have a theory!” Indeed, Calhoun math classrooms are places where students can have theories and pursue them, so there’s ultimately no limit to what they can discover next.