This is a summary of Infants and Toddlers Exploring Mathematics
Eugene Geist, Young Children
Click here to check the original version.
This article makes a case that math learning starts well before preschool. Geist argues that everyday infant and toddler behaviors, such as dumping blocks, banging drums, and filling cups, are early forms of mathematical thinking. He structures the piece around specific behaviors, explains the underlying math concept for each, and gives teachers concrete ways to build on them.
Exact matches
Sorting blue blocks into a pile shows classification, but at this age, children can only make exact matches. They can’t yet hold two attributes at once, like round and blue versus square and blue. This early classification skill eventually feeds into measurement, patterning, algebra, and geometry. Teachers can support it by offering blocks and toys in varied shapes, colors, and sizes, observing what children do, and naming attributes out loud: “You made a big pile of blue blocks.”
Banging a drum or shaking a tambourine reflects a child’s slow development of number sense and a concept of quantity through interaction with the world. These early ideas eventually grow into one-to-one correspondence and counting. Teachers can offer sound makers like bells, pots, and rhythm instruments, encourage movement to music, and describe the action: “Shake, shake, shake. You made your own music.”
Making connections
Pretending to drink from a cylindrical block shows a child recognizing similarities and differences between objects, since the block resembles a cup. This kind of connection-making eventually lets children compare and contrast groups of objects, starting with more and less and developing into addition. Teachers can set up dramatic play areas with props that invite sorting, comparing, and manipulating by size and shape.
Fitting containers of different sizes inside each other draws on the senses and motor skills, and builds toward order and sequence. That, in turn, leads to understanding quantity, how much and how many, and comparisons like more and less. Teachers can offer toys built for sensory comparison: xylophones, stacking rings, shape boxes, texture balls.
Using math
Helping slice bananas for snack or sorting blocks onto labeled shelves shows children using math the way adults do, to solve small daily problems. Geist notes this matters for the long term: children who see math as part of daily life grow more comfortable with it as adults. Teachers can point out comparisons during routine activities, “These apples are hard and crunchy, the bananas are soft and mushy,” and introduce math words plainly: “These blocks are longer than those blocks.”
Crawling through a tunnel or climbing in and out of a box uses the whole body to explore spatial relationships, laying groundwork for geometry. Teachers can offer tunnels or taped-together boxes and pillow stacks for climbing, and narrate the experience: “You were in the box, then you climbed out.”
Filling and emptying containers at a sand or water table touches on conservation, the understanding that changing an object’s shape or arrangement doesn’t change its quantity. This doesn’t develop until around age four, and it builds slowly through repeated hands-on play with containers and materials like sand and water. Teachers can offer containers of different sizes and shapes and ask guiding questions: “Do you think all the sand will fit in this bucket?”
Making patterns
Making patterns with blocks or beads requires children to notice, create, and repeat relationships, whether by color, size, or number. Patterning is an early step toward seriation. Teachers can comment on the patterns children make, join in, and offer a model pattern for children to copy, like a row alternating giraffe and tiger figures.
The teacher’s role
Geist closes on the teacher’s role. Across every example, the adult functions best as a facilitator, not an instructor. That means actively observing what children do, offering materials at the right level of challenge, and encouraging children to notice relationships and question their own assumptions, rather than delivering direct math instruction.
The piece ends with two related NAEYC resource recommendations: Copley’s “The Young Child and Mathematics” and Andrews and Trafton’s “Little Kids, Powerful Problem Solvers”, both aimed at helping teachers recognize and build on children’s natural mathematical thinking.