Mathematical Thinking Across the Preschool Curriculum

Math ideas play large roles in children’s daily lives, though they may not be aware of it. The National Council of Children (NCTM)’s position paper Mathematics in Early Childhood Learning advocates for educators to “capitalize on the wonder and joy children naturally bring to their mathematical learning and their observations of the world.” Young children and their teachers need not feel anxious about doing math. This toolkit provides ideas and links to resources preschool teachers can use to encourage mathematical thinking in all content areas.

Doing Preschool Math: Basics for Educators

Have a Framework

When a teacher plans to use math across the curriculum, it helps to have an organizing framework. This toolkit uses Big Ideas of Early Math by the Erikson Institute’s Early Math Collaborative. This framework builds upon nine important concepts in children’s mathematical thinking. They are:

1. Sets – A set is a collection of things, grouped or classified in meaningful ways, such as size. Understanding sets is a basic part of math knowledge.
2. Patterns – Recognizing patterns in all aspects of life is necessary for humans to survive. It allows us to predict what might happen next. Children notice patterns at a very early age. Much of math is based on predictable patterns.
3. Number sense – Recognizing and comparing quantities is basic to math learning. Related concepts include all,some, none, more, most, and fewest, along with specific number names.
4. Counting – True counting, not just number calling, requires understanding that any number name stands for a specific quantity.
5. Operations – Operations refers to how quantities change when we add items, take them away, or divide a set. That awareness is essential to understanding algebra in later years.
6. Measurement – Measurement is one way humans collect data. It helps us describe items or events by traits such as size, duration, and temperature. Measurement also allows us to compare two or more things, based on specific traits.
7. Spatial relationships – A young child’s experience with spatial relationships includes what something looks like, what place it occupies, and how it compares to other things.
8. Shape – Shape is important data about an object. Knowledge of shapes is the basis of geometry. Preschoolers are expected to recognize particular shapes, but understanding specific attributes of shapes and their relationships to each other is more important.
9. Data analysis – Data analysis is the process of collecting and presenting information in ways that allow people to make meaning of it by comparing sets of data or noticing trends. Making lists and creating graphs are among ways children can analyze data.

Talk with Young Children About Math

One challenge of bringing math to early childhood settings is that young children are hands-on learners, while much of math is abstract. However, abstractions are rooted in physical actions and real-life situations. Giving voice to big math ideas is a powerful way for teachers to affirm that math is part of daily life.

Teachers can create occasions to put their own math processes into words for the children. “I count one, two, three of you who signed up for play-dough. There’s not much left. Let’s do the math here. Do we have enough for you three? Should we make more?”

When a child replies, the teacher might ask “What makes you think so?” to encourage them to talk about their own math ideas. For example, if Ngozi says, “There’s not enough dough,” the teacher might say, “You’re saying it’s not enough. What makes you think that?” That gives her a chance to explain her ideas. When their classmates respond, and they can all decide if more dough is needed.

Bringing Math to Other Content Areas

This toolkit considers math in six content areas. A few potential math connections are included for each area.

Math in Language Arts

Talking about the math they use builds children’s competence in listening and speaking. It can increase their vocabulary. The article What Is Math Talk? offers inspiration and topic suggestions that may be applied in the classroom.

Picture books that focus on specific concepts can spark math conversations and inspire related activities. The Best Children’s Books for Early Math Learning lists preschool-appropriate picture books related to each of the mathematical big ideas.

Some of the most popular children’s books are those that repeat phrases in predictable patterns. Teachers can encourage the class to notice the patterns: “In The House That Jack Built, some words get repeated over and over. It’s a pattern! If you want, say those words with me when I read it again!” The article Predictable Books: Recommended Reads from the Children’s Collection at the Education Library lists many books a class might choose.

Math in Science, Technology, and Engineering

As the acronym STEM suggests, math is tightly interwoven with science, technology, and engineering. Children doing Project investigations use math ideas to build, construct, and collect and analyze data. For examples, see Project examples such as “Where Does the Water Go?” Investigating Pipes and Plumbing and The Squirrel Project.

Exploring tools, equipment, and machines helps children learn that technology means more than just electronics. Children can count, compare, measure, and construct models of these things. Project examples that illustrate this kind of involvement include Farm Implements: Learning About Tractors and Combines and Tools People Use.

Making collections of specimens such as leaves, rocks, and tools involves counting, making sets, measuring, and analyzing data. The video Shoe Graph and the tip sheet The Path to Math: Real Graphs for Preschoolers show how children can sort objects into a variety of sets.

The science of cooking involves measurement, spatial relationships, and counting. The Project examples Recipes for Learning: A Baking Project and The Pizza Project: A Delicious Learning Opportunity illustrate these ideas.

During choice time, construction toys and blocks allow exploration of spatial relationships. For example, see the videos One Morning at the Construction Table or One Morning in the Block Area.

Adults might engage children’s mathematical thinking by asking low-stakes questions about what they’re doing. For examples, see the adult-child interactions in the videos Counting Chickens and Comparing Capacity at the Sand Table.

Math in Visual Arts, Music, Creative Movement, and Dance

Many people value the fine arts for enabling us to express feelings and ideas. They don’t always recognize that artistic expression often draws upon math concepts.. For example, spatial relationships and shapes are basic to 2- and 3-dimensional visual arts. The blog post Challenge Young Artists to Create in 3 Dimensions and the article

Picture This: Using Art to Explore Math (and Math to Create Art) suggest math-based arts activities a teacher can adapt for a preschool classroom.

Music is many young children’s first exposure to math. Any piece of music is a set of sounds that express patterns such as melody and tempo. Music involves counting, number sense, patterns, and measurement. The tip sheet Out and About with Preschoolers: Make Some Music suggests ways to engage children with the math in music.

Dance and creative movement combine spatial awareness with the math of music (counting, number sense, patterns). Teachers can talk with the class about the math in a dance or movement sequence to make the math connection clear. For activity suggestions, see the tip sheet Out and About with Preschoolers: Dancing on the Sidewalk.

Math in Social Studies

Social studies, the study of human beings, involves all nine mathematical big ideas. The IEL podcast episode, Mixing Early Math and Social Studies within Preschool Classrooms featuring Dr. Jennifer McCray, has many suggestions for making the math explicit in social studies activities.

Measuring people’s opinions and interests through surveys and voting involves several math ideas, such as:

• sets – who want X, who wants Y
• number sense – concepts such as all, none, more
• counting – how many chose this
• data analysis – graphic organizers comparing final results

Teachers can find suggestions in the tip sheets Project Approach: Children Taking Surveys and Children’s Votes Count!, the blog post Surveys for the Win! Building Investigation and Language Skills, and the tool kit Voting, Leaders, and Elections: What Preschoolers Can Learn About Democracy.

Economics uses number sense, counting, operations, and data analysis to study what people need in order to survive, and how they meet those needs. For examples, see the tip sheets Math Sense: Learning about Coins, “It Takes Money”: Economics for Preschoolers, and Things We Need: Economics for Preschoolers.

Geography describes humans’ relationships with the spaces they occupy and involves measurement, sets, counting, patterns, shapes, and data analysis. Teachers can find geography activities involving math ideas in the tip sheets Where Are We? Maps and Young Children and Out and About with Preschoolers: The Places You’ll Go!.

Math in Physical Development and Health

Math big ideas are present in learning about healthy living habits and in learning ways to stay active: how much to eat, what groups of foods to consume and what types to avoid, how much sleep to get, and which activities are best.

Teachers can invite children to see the counting, patterns, spatial relationships embedded in exercise. Children are often eager to explore the tools used in athletics and other physical activities, including pedometers, fitness apps, and manual timers. For example, the lesson plan Run, Walk, Crawl invites children to use tools such as stop watches to determine if one form of movement will get them from place to place faster than other forms. Following an obstacle course, and helping set one up, call for thinking about spatial relationships. The article 25 Obstacle Course Ideas to Improve Gross Motor Skillsand the online resource Spatial Relations offer inspiration for complex obstacle courses.

Math in Social and Emotional Development

Playful mathematical thinking is the basis for many popular games that also engage children socially. Card games and board games generally involve such big ideas as number sense, counting, operations, and making sets. Some experts recommend making specialized decks or adapting card games to match preschoolers’ math knowledge. For example, Quantity Cards for Subitizing, A New Focus for Familiar Card Games, and Using Board Games to Teach Math to Young Children provide useful suggestions.

A number of active social games take a playful approach to counting, number sense, operations, and patterns. The circle game “Alice the Camel,” for example, involves singing about a camel that gains or loses humps. The blog post Learning Math through Games takes an in-depth look at mathematical ideas in outdoor or indoor active games.

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