How do young children categorize objects?

To find out, Sarah Dufour, an assistant professor in the didactics department of the Faculty of Education at Université de Montréal, conducted a study in which children were given toy groceries and asked to organize the food on shelves.

Dufour observed how the children, aged three to five, developed their strategies and analyzed the mathematical operations they used to categorize everyday objects.

To study the processes underlying categorization, Dufour observed the children in two 30-minute sessions and noted how they sorted, classified and grouped objects.

Categorization in theory

"Categorizing means organizing objects according to one or more criteria," Dufour explained. "According to the scientific literature, objects can be categorized by sorting, classifying or grouping them. We wanted to see how children apply these processes in practice."

Sorting means arranging objects in order; for example, lining up pencils from lightest to darkest. Classifying means separating objects based on a predefined criterion, such as putting the pencils in bins by color. Grouping means forming sets based on a common characteristic defined by the children themselves.

"For example, a child might notice that three pencils in their collection are blue and put them together, even if they are different shades of blue, justifying their choice by the similar color," Dufour said.

Categorization in practice

To capture the children's reasoning in action, Dufour used a qualitative and interpretive approach. "My aim was to observe how these processes emerge and connect spontaneously, without giving strict instructions," she said.

"That's why I used toys rather than, say, abstract geometric shapes. We know children can manipulate basic figures such as circles, squares and triangles at an early age, but I wanted to go further and explore their thinking to understand how they construct their categorizations."

She used grocery-store-themed toys that could be categorized in multiple ways—small boxes, fruits, vegetables and so on.

Research has shown that children are capable of complex reasoning, even creating subgroups within their categories.

"This principle of class inclusion reflects advanced thinking," Dufour said. "But although primary school students are able to classify objects, they often have difficulty explaining their approach and describing the criteria they used."

In her study, Dufour set out to show that children's reasoning can be accessed if they are given the right support.

"Some of the children alternated between grouping and classifying," she reported. "When they noticed an inconsistency, they spontaneously adjusted their groupings based on a new attribute."

Beyond the binary

The study showed that young children can go beyond simple binary classification, which divides objects into two categories: those with an attribute and those without.

"We often think that children start categorizing by opposing two groups: a red crayon goes in one category and all the others in the other," Dufour said.

"But our study shows that they are capable of developing more complex categorizations and creating several groups based on various criteria."

These findings open up new pedagogical possibilities and suggest that, with appropriate support, children can develop sophisticated mathematical reasoning from an early age, she added.

The paper is published in the Canadian Journal of Science, Mathematics and Technology Education.