Exploring Early Math Concepts

Exploring Early Math Concepts

Let’s play a quick game of word association! When you hear the word “math,” what comes to mind? I invited family and friends to play along, and their responses included: numbers, addition and subtraction, equations, geometry, counting, algebra, and finally, one enormous groan. When we imagine mathematical thinking and young children, it might seem like a stretch to connect these lofty concepts to early childhood development. It may even trigger our own math anxieties -- current or from the past. Good news! We’re not suggesting algebra on the chalkboard with preschoolers! Instead, here’s an invitation to try out a new way of thinking about math and how it can be integrated into each part of your day.

I didn’t fall in love with math until I became a teacher, finally thinking about the continuum of mathematical through my growing understanding of child development. Realizing that the early childhood years are the foundation of the concrete component of the concrete-pictoral-abstract developmental progression, I grew to appreciate phrases like “Math is all around us!” and “Everything is math!” Math is indeed everywhere, and it can also be joyful! With an intentional approach, almost any hands-on experience helps build children’s math thinking and number sense. Pouring water from one cup to another in the sensory table? That’s math! Passing out teacups to friends in the dramatic play center? Math! Admiring a classmate’s block creation and carefully attempting to replicate it? You guessed it – also math!

If you’re not there quite yet never fear. Together we’ll explore common early math concepts and, hopefully, inspire new ways of integrating these skills throughout the day. While special supplies and complicated plans are not required, it can be helpful to think about materials that might be particularly suited to support specific learning goals. You might even notice that some of the most compelling materials support children’s development across several early math concepts at once!

Let’s get started!

Number Sense, Counting and Operations

These early math concepts are the most straightforward connections, and a great place to start. Young children are growing their sense of quantity at the exact same time that they are mastering counting by rote. Add in a still-developing sense of one-to-one correspondence, and we can really begin to appreciate how much is happening in young brains. Fortunately, there are so many opportunities to integrate these skills into routines, play, games and activities.

Sets and Pattern

The concept of sets, from an early math lens, refers to a child’s growing understanding of collections or groups of items, objects, and ideas. This expands as children assign meaning to these groupings and their ability to name attributes. When children are exploring the concept of sets, you will see them sorting materials or creating categories during their play. “Only the little animals live here by the water. The big animals live by the cave.” Throughout their development, children begin to apply conceptual categories to their sets, for example, sorting dinosaurs by carnivores and herbivores. This requires more complex cognitive processes as they apply their knowledge about dinosaurs to their sorting activity without visual cues. In other words, prior knowledge about dinosaurs and their eating habits is necessary for an observer to discern the rules by which the collection was sorted.

Engaging with the concept of pattern demonstrates children’s emerging understanding of distinct attributes. To identify and extend patterns, it is necessary to define the elements that are being repeated. In early phases, pattern play can be isolated to concrete items with clear attributes than children can manipulate physically. Eventually children will generalize their understanding of pattern to concepts that repeat in a predictable sequence, like days of the week or seasons of the year.

Teachers often discover that materials supporting exploration with sets and attributes are also ideal for patterning invitations and activities. Materials made for this purpose offer thoughtfully chosen easily discernible attributes. Natural materials and household items are often engaging for sorting and categorizing as well. Shells, pinecones, and leaves are easily collected and invite hands-on investigation of their unique attributes. Are the edges of your leaves smooth or bumpy? How many different shades of green do you notice?

Measurement

Measurement is the process of quantifying an attribute such as length, height, weight, time, or temperature. We can measure with standard units (universally understood units that are accepted in a specific setting, such as inches, miles, hours, or pounds) or non-standard units. Examples of non-standard units of measurement include measuring a child’s height with rectangle unit blocks or washing hands for as long as it takes to sing Happy Birthday two times. Exploring measurement with young children focuses on introducing the concepts, tools, and practice of quantifying the attributes that are being assessed. It’s also valuable to explore why measurement is important. Can children think of real-life examples that highlight why measurement is helpful? They might share about measuring ingredients for a recipe, or a time when their grandparents bought them the wrong size shoes.

While height/length is the most accessible attribute to measure for very young children, think about how to encourage children to consider other measurable attributes. The idea of time, quantity, age, and temperature as being measurable is an exciting conceptual leap for children. Extensions might include questions like: Why might we need both a ruler and a tape measure in our home? Why are some tape measures rigid while others are made of flexible material? When would we choose to use one tool instead of another?

Data Analysis

Through an early childhood lens, data analysis refers to the process of collecting information, recording that information (data) in a chosen format, and then interpreting the information collected. In a preschool classroom, this might look like taking surveys, voting on community decisions, recording daily weather, seeing how many children have birthdays each month, etc.

These data collection opportunities invite interpretation. Which read aloud has the most votes? Which month has the fewest birthdays? Were there more sunny days or rainy days at school last month? Representing this information visually or with concrete objects will help children analyze the data they’ve collected. You could use a journal or chart paper with a graphing grid to make a bar graph or collect tally marks. Pocket charts are another way to track data that children collect on an ongoing basis. Physically representing information with concrete objects is a great way to scaffold data interpretation for young children. Using Unifix cubes or other materials that connect or attach to each other in a linear method can help children physically manipulate quantities and compare information to draw conclusions.

Spatial Relationships

Spatial relationships describe the conceptualization and application of a child’s understanding of oneself and physical/positional relationship to other objects in the world. Our understanding of spatial relationships represents our own point of view. We can describe the relationship between objects and places with positional language (under, over, besides, above), directional language (up, down, sideways, left, right), and by incorporating measurement (“two inches away,” or “five feet deep”). As children develop more refined spatial awareness, you might notice them using positional language with more accuracy, being interested in reproducing block structures, and exploring concepts like symmetry. Spatial relationship concepts can be explored and extended with many types of play and construction materials.

Shapes

Children begin to apply concepts of regular shapes to objects, photos, and images by refining their understanding of both two-dimensional shapes (ex: circle, triangle, rectangle) and three-dimensional shapes (ex: sphere, cube, cylinder). As children become more grounded in their experiences with early geometry, they will notice and name two-dimensional shapes, and eventually begin to recognize three-dimensional shapes as well. Using geometric language like side, angle, corner, and face supports children’s growing awareness of the unique attributes of various shapes. Offer hands-on opportunities to combine and separate shapes. Building a square from two triangle unit blocks is a powerful experience that reinforces the characteristics that define each shape.

Math is All Around Us

Exploring these concepts and the materials that support development of early math skills reinforces the sentiment that math truly is everywhere we look. Our daily routines and familiar materials offer so many opportunities to notice mathematical thinking that is already taking place! Once attuned to these openings, teachers can use a thoughtful lens to assess children’s competence in various math skills and plan for extending their learning.

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References

Christine Murray is an Early Childhood Education Specialist with Becker’s Education Team.
As an educator, coach and leader, Christine is inspired by the curiosity, joy and wonder that children so generously model for us. She earned her M.A. in Innovative Early Childhood Education at the University of Colorado Denver and loves collaborating with and supporting others in the field. Grounded in relationships and guided by empathy, Christine is always learning, connecting and creating.