By Mark Mabry, Head Teacher
We often think of math learning as consisting of concepts—addition, subtraction, counting, or number recognition—that are taught didactically. However, as young children play, they are constantly and actively exploring these ideas and constructing their math knowledge by observing, experimenting, and sharing insights with one another.
When children encounter mathematical ideas in the context of their play, they are motivated to delve into these ideas deeply and gain personal hands-on understanding of the underlying concepts. Rather than writing down equations using “+,” “-,” and “=,” they count the children sitting at their snack table that day and then think together about the empty chairs to figure out how many of their friends didn’t come to school, or they posit, “But we forgot to count the teachers! Now, how many are there?” They often think about their ages and how that might relate to their heights. They want to quantify how many wood pieces, nails, and connectors they used in their woodworking projects. They display a natural affinity for balance, symmetry, and pattern as aesthetic qualities in their artistic and constructive endeavors.
Math is about quantifying the relationships that exist between the things we encounter in our everyday lives, and children are naturally attuned to exploring these connections.
There are any number of premade materials to inspire and enhance numeracy experiences, including Unifix Cubes and Cuisenaire rods, both valuable additions to our classroom. But there are also so many organic mathematical opportunities that our children encounter on a daily basis in their play. It is worth noting that many of these math topics overlap and integrate with each other—for instance, the concepts of symmetry, patterns, and geometry intertwine.
Symmetry
Children are often exposed to the idea of “the same on both sides,” or bilateral symmetry, when they construct projects using items such as Legos, blocks, and art materials. They carefully study one side of their project and create the mirror image on the other side.
Patterns
Patterns can appear as simple or complex repeated sequences in mathematical thinking. Children are naturally drawn to create these arrangements as they play with manipulative objects, create art and design work, or build with blocks.
Counting / One-to-One Correspondence
Counting is more than being able to recite the numbers from 1 to 10 and beyond; it entails understanding one-to-one correspondence and keeping track of what has already been counted. Children are continually counting how many blocks they used in their construction, how many children are sitting at their snack table, and more.
Measurement
Rather than thinking in terms of conventional and arbitrary units, such as inches or ounces, children are interested in determining how high, how long, and how much, using units of their own devising, such as a length of yarn or their own height.
Geometry
Children develop their spatial understanding of an object’s distance, shape, size, and position as they explore these relationships while playing with blocks or Brio train tracks and experiment with connectivity, lines, and curves.
Sets
Sets are an important part of math knowledge as objects that share characteristics—including shape, size, and color—can be grouped together. Children instinctively like to sort the materials they play with, grouping miniature animal by species, perhaps, or dividing cubes according to color.
Sequencing
Sequencing refers to arranging objects, often in a linear way, to represent a mathematical element like height, quantity, volume, or color. In the process of sequencing, the concepts “less,” “more,” and “equal” arise, prompting children to investigate further by sorting and lining up their play materials, say, from shortest to tallest.
These are just a few examples of how children engage with math in their everyday play. As teachers and parents, one of the most powerful things we can do to encourage and enhance their exploration of these ideas is to notice and acknowledge their “mathematizing,” while recognizing their joy of discovery in play. Rather than rush them to embrace abstract representations of math, our role is to invite and allow them to construct foundational knowledge of these essential concepts.
