Talk, listen, model

What adults can do to foster children’s mathematical thinking

colorful plastic magnetic numbers

Adults may expect that learning mathematics is just like learning to read, since both are a focus of schooling. Math and reading do both involve learning formal symbols—namely, letters and numbers. And both reading and mathematics involve much more than these symbols.

But when learning individual letters, children associate each letter with a sound, not a concept (excepting some one-letter words, such as “I” or “a”). When they learn individual numbers (digits), however, each number is associated with a concept, not just a sound.

A child who correctly reports, “I’m three,” for example, may not understand the similarity between being three years old, having three stuffed bears, his or her address (3 Maple Drive), three o’clock, and three pairs of shoes. The child is also not likely to know that 23 is smaller than 31. It’s a wonder that children learn number concepts at all when you think of the inconsistency across these instances of the word “three” and the abstractness in what unites the examples. These number concepts are not straightforward and may take time, input, and feedback to develop.

All of us can support young children’s mathematical thinking by talking, listening, and modeling. The following examples apply to young children, but the principles apply to older children, too.


Talk to children about numbers, relationships, shapes, and patterns, and refer to mathematics terms, properties, and processes. This helps to nurture their mathematical thinking and provide the vocabulary for expressing their thoughts. Discuss similarities and differences (more/less comparisons), categorize toys you play with, count sets and actions (such as the number of stops from when you board and later get off a bus, or the numbers and types of fries available at the fair), and solve daily problems together (like “How many bananas should we buy to make sure everyone has two?”).


Listen to when and how children use mathematics. This helps to recognize and praise their effort and cleverness (“You figured out how many we need!” or “You added those together”). It also may help to to discern sources of difficulty or misconceptions interfering with a child’s mathematical thinking or learning.


Model the use and enjoyment of mathematics. This includes avoiding unintended negative messages about math as “hard.” Instead point out when math is exciting (discovering Fibonacci patterns in nature or mathematics principles underlying a new skateboard trick) and useful (tracking a bank account or baseball statistics), and share how problem solving is rewarding.

Read more about numeracy research in “Knowing Numbers,” by Michèle Mazzocco.

By Michèle Mazzocco | Winter 2015