For young children, math is rooted in everyday experiences. Though we tend to think of counting as the foundation of early mathematical concepts, the act of counting is dependent upon a child’s understanding of attributes and sets. Before we can count with meaning, we must know what we are counting.
Objects that share attributes can be grouped into sets, which we can then count to see how many we have. The properties of these sets affect our number system. Knowing how to create sets, break them apart, compare and order them gives children the foundational knowledge they need to understand more complex mathematical concepts.
Children develop their understanding of sets through experience. Set knowledge follows a developmental progression that relies on the capacity to recognize attributes. In order to create sets, children must be able to recognize an item’s attributes. Because it is more difficult to consider multiple attributes at once, children begin creating sets by finding exact matches. When children create pairs of socks or mittens or find an exact match in game such as memory, they are creating sets of items that are exactly alike.
After they fully develop the ability to make exact matches, children begin to sort items by a single attribute. An example would be a child who has a box of drawing tools and creates a group of those that are red. The group might have red crayons, red markers, red pens, red pencils.
Next, they are able to make binary sets in which two groups are created based on a single attribute. To use our example of the color red, one group would be made of things that are red and a second group would be made of things that are not red.
Then, they become capable of creating new groups based on different attributes. After sorting the drawing tools by color, they might next sort them by type, to create a group of pens, a group of crayons and a group of markers. Then they might create a group with caps and a group without caps. Finally, they begin to compare sets. They might ask which set has the most and may represent that comparison with a graph or a tally.
At school, we support each child’s unfolding knowledge of sets through many experiences. Some occur naturally as children interact with materials at school. Children naturally notice the attributes of objects and other people. We support conversations about the attributes that children notice andmodel language that describes attributes. Many children have been collecting the leaves we find in our courtyard. As they do, we’re all noticing their attributes and talking about them. Some are yellow, others are red, still others have multiple colors. They have different sizes, different shapes, different textures. The varied attributes of natural materials provide endless opportunities for discussing attributes and creating sets.
Other sets, created by teachers, are a natural part of school life. We keep materials together so that they’re easy to find. Sets of markers are available with the writing materials. Sets of magnatiles are all kept in the same container. Sets of cars live on the block shelves. Often, children will begin to sort these sets into smaller ones. One child may want all the yellow cars. Someone else may want to build with only square magnatiles, yet another may wish to collect all of the baby cheetahs. We support these natural inclinations by discussing them and sometimes asking questions to push their thinking. I noticed you put all the yellow cars together. Do you want a yellow truck to add to that group? How about this blue car? If you don’t want this blue car with all of your yellow cars, where should I put it?
We use many songs and group games that encourage children to think about attributes and create sets. One example is the song “If you’re wearing (insert color or other attribute here), stand up” which requires children to create binary sets. They stand up if they are wearing the color named. They stay seated if they are not. Because the attributes change, they must rethink which group they belong in multiple times. Repeated experiences like these help children to understand that one collection can be sorted in multiple ways.
Though these activities may seem simple, they encourage children to think about the world mathematically. Contemplating these concepts in ways that are meaningful to them helps children to develop a deep understanding of basic mathematical and logical concepts that provide the foundation for increasingly complex mathematical topics.
Ideas for supporting your child’s understanding of sets at home
Have your child match socks. To make it more manageable, choose a few pairs with bold patterns or colors. Use descriptive language as you show them to your child. Choose one sock to hold up and ask your child to help you find the matching sock. Ask them to describe the sock’s color or pattern. Link to sesame street three of these things are the same: https://youtu.be/KQBjd7OCGIE
Have your child sort clean laundry before you fold it. If you have a load of towels, have them sort them by size or color. If you have clothes, ask them to separate all of the t shirts or shorts. Talk about where your child’s clothes are stored. Do all of the shirts go together? Are long sleeved and short sleeved shirts stored in different drawers? Where do pants go?
Putting clean silverware away is another great matching activity. As children put forks, spoons and knives together, they are matching these items.
Go on a walk and collect leaves, sticks or stones. Discuss their attributes and find different ways to group the items.
Create your own version of the story “Five Creatures” based on those that live in your home. Link to Five Creatures: https://youtu.be/jCf3nC7wMaU
Katrina Nousaine & Anita Speck, Park West Co-Op Preschool Teachers, contributed to this post
Park West Co-Op is a progressive preschool located on Chicago’s near Northside in the heart of Lincoln Park. Park West is a diverse group of teachers who are experts in early childhood education. We've dedicated ourselves to understanding and developing teaching methods that cater to each child's individual needs so they can grow in a positive way. Teachers work hand in hand with the parent run Co-Op and offer robust hands on parent education in the classroom.