By: Mia Daucourt

Parents and family members receive all kinds of input from many different sources about the importance of shared reading with the children in their lives. In fact, I’m pretty sure that nobody would argue with the point that reading to your kids and other children in your life is important for children to learn how to read and continue to develop their reading skills. We eagerly follow this advice, giving books at baby showers so mommies-to-be can start reading to their babies as while they’re still in utero, and it’s common practice to ritualistically read a bedtime story or two with your children or the kids you are babysitting. It’s just what you do because it’s what you’re “supposed” to do. Of course this shared reading practice is not always consistent, and some families simply cannot find the time, but we at least have some indication that we *should* read to our kids.

When considering math, on the other hand, the advice and guidelines for how we can support children’s math skill development are much less clear and universally known. We teach young kids how to indicate their age by showing the correct number of fingers, and they already have an innate sense of when a shared cookie is broken in half unevenly. However, math is so diverse that it’s hard to tell all the different kinds of math we should introduce to and practice with kids. What are the math skills a preschool-aged kid needs to know?

Although preschool may seem like a combination of fun art projects and games of dress-up, it is actually a fundamental time in children’s lives during which they build the foundational skills necessary to do well in school. In fact, it’s in preschool that we start to see achievement differences, with some kids understanding concepts more quickly than others, and unfortunately, the kids that start off behind when they are so young tend to stay behind their higher achieving peers for the rest of their time in school. So, like we covered before, we know to read with our kids, but what can we do about math? What should we be doing to helping set up our kids for math success?

A recent study by Milburn and colleagues (2019) took on this challenge. Using a statistical technique called categorical confirmatory factor analysis and a sample of 1630 low-income preschool children, who were all in Head Start or another state-subsidized preschool program, they investigated what the main math skill areas are for preschoolers. The best way to explain categorical confirmatory factor analysis is to describe it as a scientifically-driven grouping technique. The researchers took all the separate items on a common, standardized preschool math assessment and then, using statistical analysis software, they created categories based on the items and grouped all the related items into their common categories. So what are the kinds of math activities we should do to help kids develop their math skills? The researchers found that preschool math was comprised of four different math skill domains: Numbers and Operations, Geometry, Measurement, and Patterning.

Let’s break down what each of these broad categories mean. To begin, Numbers and Operations, which the researchers found to be made up of 3 subcategories, including numbers, operations, and relations, is a broad category that involves an understanding of number order, like teaching children how to count and that 5 comes before 7 when counting, how different numbers are related in terms of quantity (7 is greater than 5), and how to perform operations, like addition and subtraction with numbers. Some examples of activities that would target this skillset include teaching children how to count and talking about how numbers are related to each other in terms of being more or less than one another. For operations, activities would include using flashcards or even objects to show how different numbers can be combined to create a bigger quantity (addition) or removed to create a smaller quality (subtraction). I can tell you from personal experience that children especially love when you use edible props, like M&M’s for operations lessons!

The second category of Measurement involves understanding the size of objects and things and how they relate, how objects and things can be divided up into equal parts, and conservation, which is the concept that an object stays the same size even if it is moved or rotated. To work on this category parents would focus on comparing objects on physical dimensions with their kids, showing them that their parents’ arms are longer than their arms or that two cookies stacked up is taller than just one cookie on the counter. Cookies could also be used to show kids how to divide an object up into equal parts. Another easy way to show this concept is by folding up a piece of paper. To focus on conservation, parents and family members can show children household objects in different rotated positions that make them look different but then reiterate the fact that the object has not changed in size. One example that combines both an understanding of physical dimensions and conservation used by Piaget is to put quarters in a row on the counter and then spread them apart. Although the row of quarters is now longer than before (physical dimensions have changed), there amount of quarters remains the same (conservation).

The third category of Geometry involves recognizing and analyzing two- and three-dimensional objects and reasoning about spatial orientation, like direction and distance or proximity. This starts out with knowledge about physical shapes, like triangles, circles, and squares, and then moves onto being able to mentally picture a physical shape, then finally explicit geometric knowledge, like squares have four equal sides and four 90-degree angles and when split in half diagonally, they make two triangles. To help children notice and learn about shapes, you can use common household objects (placemats are circles and coffee tables are sometimes rectangles), and good old fashioned paper to draw, cut-out, and even form shapes by folding.

The fourth and final category of Patterning involves the ability to recognize and duplicate patterns in a given set of elements, either with numbers or objects. This can be based on concrete properties, like color and shape. For example, there is an ABAB pattern followed when you make a row of star stickers that alternate red star, blue star, red star, blue star. When looking specifically at numbers, there are growing patterns, like in the string of numbers “2, 4, 6,” which is going up by two and maybe a repeating pattern that goes “2, 4, 6, 2, 4, 6.” These kinds of activities can be easy and fun and turn something simple like playing with stickers into an educational activity that helps kids develop their math skills.

There is one more important question the researchers investigated in their preschool math study: Are boys better than girls at math? Although past research has found sex differences in math as early as kindergarten, Milburn and colleagues (2019) found no sex differences in any of the four math domains. That means: Nope, preschool boys are not better at Numbering and Operations, Measurement, Geometry, or Patterning. Instead, girls and boys are equal in all these preschool math realms.

Not only was Milburn and colleagues’ work important for parents and family members of children, giving parents and family members some foundational knowledge about what kinds of math subjects to work on with their preschoolers. It was also important work for schools and teachers because each different math domain they found requires specific tasks and curricular activities to promote the development of and measure progress in each math area.

Citation: Milburn, T. F., Lonigan, C. J., DeFlorio, L., & Klein, A. (2019). Dimensionality of preschoolers’ informal mathematical abilities. *Early Childhood Research Quarterly, 47*, 487-495.