As a pre-K teacher, one of my favorite things to do with my students was to find learning opportunities outside. In the school garden and on the playground, I saw how my students’ eyes lit up with curiosity and fascination over seemingly mundane objects — a smooth pebble, a colorful leaf, a wandering ant. It became clear that, when given the opportunity, they showed a remarkable capacity for problem-solving, inquiry, and exploration. I tried to harness that into both reading and math activities.
One day, for example, we went on a “leaf hunt” around the school, gathering leaves of all different shapes, sizes, and colors. The previous day, we had read “We’re Going on a Leaf Hunt” by Steve Metzger — it was a hit with my students and they were eager to go on their own “hunt.” During the walk, I asked questions like “which one of those leaves is bigger? Are there more brown leaves or yellow on that tree?” Later on, we counted and sorted the leaves we had collected.
This type of “math talk” and inquiry-based learning activities are essential to effective math instruction. That’s according to the Transforming the Workforce report which synthesizes years of research regarding the ways in which children learn and how early childhood educators, working with children birth-through-age eight, can best support their learning. When it comes to early math exposure, the research is clear — mathematical thinking early on helps “form a foundation for general cognition and learning.” In fact, children’s knowledge of mathematics in pre-K is a strong predictor of later achievement, even into high school. And achievement gaps in math in later grades can be traced back to the early years as children from low-income families typically have less exposure to math and, even by pre-K, demonstrate less extensive math knowledge.
And yet, despite the research on the importance of math, Transforming the Workforce finds that “preschool educators tend not to support mathematics learning, and when they do it is often of low-quality.” Early childhood teachers, for example, spend less time engaging children in math than in any other subject. One study that observed early childhood programs serving working- and middle-class families revealed that 60 percent of three-year-olds had no math exposure at all in their classrooms. And when math is taught, the report notes that too often the approach is to emphasize rote memorization and basic concepts like numbers and simple shapes rather than encouraging inquiry, reasoning, and intellectual curiosity — foundations for fostering high-level, conceptual understandings of math rather than seeing it as simply a “guessing game” or “system of rules without reason.”
What’s causing the gap between research and practice? The report points to one major reason that deserves attention — weak educator preparation in the area of math. Compared to subjects like literacy and language, math instruction tends to be much less emphasized in professional learning and development. Many early childhood teachers simply are not taught the pedagogical skills to confidently teach math effectively, if at all. If early math teaching is to improve, increasing math knowledge and pedagogical skills among early childhood educators is a must.
So what does effective math instruction in the early years look like? First, it’s important for children to begin building foundational math knowledge well before first grade, as children have the ability to learn math and develop an interest in it from a very early age. Effective math instruction is intentional, fosters reasoning, problem-solving, and discussion, and takes into account “mathematical learning trajectories.” Learning trajectories refers to the progression, or developmental path, of children’s thinking when it comes to math concepts. In what can be thought of as a learning staircase, research shows that children follow a certain developmental path, reaching gradually higher levels (or steps) of thinking as they grasp new concepts. Effective math instruction sequences learning goals and activities in a way that recognizes children’s developmental learning trajectories and gradually builds on what they already know.
For example, a common math goal for pre-K students is to be able to accurately count a group of objects and tell how many total objects there are in the group. While this may seem like a relatively simple task, there are actually a number of skills packed into this goal that students must grasp before being taught to count and total a group of objects. Students must know how to verbally count, they must have mastered one-to-one correspondence between counting words and objects (one word for each object), they must know to organize the objects in such a way that they can be easily counted (in a line, for example),and they must know that the last counting word they say represents the “total” number of objects they have (cardinality). Effective math instruction follows a progression of learning goals so that children can work their way up to these higher-level math skills.
A learning environment that fosters high-level math thinking gives children the opportunity to explore patterns, quantities, shapes, and spatial relations, invent solutions, and problem solve. Children do this naturally in play-based learning environments, but, as Transforming the Workforce notes, math instruction also needs to be intentional — that is, giving students blocks and puzzles alone is not enough to foster mathematical learning.
Of course, when math is taught in a way that goes beyond rote memorization and basic concepts, lessons and activities may appear less structured or less “academic” to an observer who is unfamiliar with how young children learn. That’s why, as my colleagues have written about, training principals so they are knowledgeable about child development and what teaching and learning should look like in pre-K and early grade classrooms is critical. As instructional leaders, principals should be able to help teachers improve their practice and ensure that they are providing the right kind of instruction and using the best learning strategies for young children. And administrators of other early care and education programs should be equipped to support teachers in building the early math skills of their infants, toddlers, and prekindergarteners.
Given the importance of early math skills and the fact that U.S. students rank poorly internationally in math, it’s imperative that we seek to figure out how best to foster mathematical learning with young children. New America, in collaboration with the Cooney Center, is due to release a paper in the coming months which will make recommendations on how best to approach STEM in early learning. And, in the meantime, New America will continue to unpack the Transforming the Workforce report as part of our efforts to improve teaching and learning in the early years.