Focusing on Early Mathematical Thinking

Young woman and little girl with autism playing at home

Whether they’re in preschool, child care or at home, much mathematical learning takes place in children between the ages of two and five years.  They become interested in numbers (How many cookies did I get?), spatial relationships (How high can I build my tower?), problem-solving and predicting (I wonder what will happen if…), and a host of other mathematical concepts.  Appropriate mathematical experiences challenge young children to explore ideas related to patterns, shapes, numbers, and space with increasing sophistication.  Positive, supportive exploration can help children develop an early disposition for math as they learn to trust their own abilities to make sense of math concepts.

As teachers, parents, and care providers, we can embrace and enhance children’s natural interest in things mathematical by building on their curiosity and enthusiasm and connecting math concepts to their world.  Math concepts can be integrated into many of our naturally occurring activities — in group times we count who’s there, at snack we talk about putting all the apples on one plate — and we can (and should) help families plan systematically into the child’s day.

Number Sense
Counting, representing, identifying, estimating

  • Count the computer squares where other classmates appear—changing the configuration of screen squares is one way to represent the number and do a simple math operation—one square per child equals…? Do the same with carpet squares if you are in the classroom.  If you are hybriding, children can count the squares of the children who are present as well as the carpet squares of children who are not there…a way to learn about addition AND subtraction (how many are not here; how many will there be when everyone is here?)
  • Match numerals, cards, or dice (who has the card that looks like this…it has three cats on it.)
  • How many boys do you think (or estimate) are on the playground?

Comparing, ordering, properties, tools, perspective, time

  • What block (or doll or stuffed animal) is taller/shorter; who is tallest/shortest in your family; which is further—the art area or the house area; which is larger—your sofa or the chair? How can we find out (what tools might we need? Rulers, yardsticks, measuring cups/spoons, etc?)
  • How many cups of flour do we need to make play dough?
  • Is the tree that’s far away smaller than the tree that’s in our yard?
  • Does it take us longer to read a story than to eat snack?

Shape, size, space, position, relationships, properties

  • Recognizing shapes and their properties (a circle is round; a square has four sides. Include both two and three-dimensional shapes.)
  • Playing with position words: stand next to…; put the cup on the table; put the big block next to the small block.
  • Map-making—creating streets with blocks and trucks; drawing maps of the school, play-yard, or neighborhood (let’s make a map of our room—is it square or round?  Where would blocks go; the art table? The stove; the refrigerator?)


  • Let’s divide the cookie in half;
  • I’m going to take some of the cars. Half of them will be left.
  • When I eat this piece of pizza, there will be three pieces left—that’s three quarters of the pizza.

Patterns, relationships, analyzing change and transformation

  • Sorting and classifying—put all the red pieces in this cup; if we wanted to build a new block center what would we need to have in it (classifying what’s needed for building.)
  • Can I use two short blocks to make the same length as one long one?
  • Create patterns with blocks, beads or other materials (including themselves); predicting a pattern (1 blue, 1 red, 1 blue, what comes next?)
  • Discuss how things grow—seeds we planted are taller today than they were last week (and you can measure their growth)—and change—if I push the top and sides of a square, I can make a different shape.

This article was submitted by Mary Perkins for the January 2021 edition of the Early Childhood Express.