Monique, like many toddlers, loved emptying and filling everything. She filled pots and pans with wooden blocks, took the lid off her shape sorter bucket and filled it with rubber balls, and she delighted in emptying her small basket of toys. At the same time, through interactions with caregivers she was learning positional words and phrases such as in, on top of, and under.
Shortly after her second birthday, while playing with her wooden block set, Monique noticed a sphere lying next to the base of a cone, and announced “I-skeem!” excitedly. Her mother, looking over, took a minute to realize that Monique saw what looked like an ice cream cone in the arrangement of blocks.
At school several months later, Monique was burying toys in the sandbox. Teacher Jorge watched as she hid two small toys. After talking with her about “seeds” (they had read The Tiny Seed, by Eric Carle, earlier that morning), he watched as she accurately retrieved both toys from where she had buried them.
What is this all about? What do positional words, three-dimensional shapes, and buried toys have to do with each other?
Our visual and tactile world consists of objects situated in space. Gaining an understanding of the attributes of those objects and where they are (and especially how we can get to them!) are some of the most important aspects of development in a young child’s life. Here are few reasons why:
We are born spatially aware. At birth, we can discern and track our parents’ movements. Minutes after birth, infants are more likely to track a human-like face than a blank head outline, and prefer face-like patterns to patterns in which facial features are scrambled, suggesting that they can discriminate between the two. Even at this young age, humans pay attention to features of objects.
Before young children have the words to describe on top of or under, they have the ability to distinguish the difference between a picture in which dots are above a line and one in which dots are below a line. Similarly, by age four months, infants notice the difference between a picture in which dots are to the left and one in which dots are to the right of a line.
Let’s dissect some of these skills and abilities and examine what they mean in a young child’s mathematical development.
Perceptions of objects/shapes and their attributes. By about 18 months of age, children’s acquisition of vocabulary increases greatly, including the ability to verbally name and categorize objects. Children’s developing cognitive skills let them see even part of an object, for example, a dog’s nose peeking out from under a bed, and know that it is part of a whole object. Even infants can know that when they observe a dog in a variety of representations (sitting down, jumping up, trying to catch his tail) and partial views (nose only), he is still a dog. Children become capable of recognizing objects in different orientations, illustrating their developing spatial knowledge.
Physical and mental manipulations of objects/shapes. When children have opportunities to explore two- and three-dimensional objects, they develop an ability to coordinate movement and alignment of those objects (for example, pushing a triangular prism through the triangle hole in a shape sorter). When children have ample opportunities to explore their environments, resulting in the gain of greater fine and gross motor control, they learn to navigate more skillfully. You might notice young children insisting that toys be placed in a certain location or orientation or stipulating that they have to walk on the lines in the sidewalk. These are all instances of children’s developing spatial manipulation and awareness skills. These skills are important and useful in children’s everyday lives, but they are also early skills related to later mathematic performance.
Spatial language. Spatial language provides children with essential tools to describe their environments and negotiate their wants and needs. And, it turns out, young children’s use of spatial language predicts children’s later skills at spatial problem solving. Spatial language includes words describing location/position (under, in front of), attributes (long, high, side, angle, same, symmetrical), orientation and mental transformation (left, turn, match), and geometric shape names (rectangular prism, triangle, sphere).
Teachers and caregivers play an important role in supporting development in geometry and spatial relations by providing opportunities for non-structured and structured activities. Fortunately, these activities can be among children’s favorites in the classroom.
Non-structured activities include puzzles (orientation and mental transformation), block play (orientation, mental transformation, spatial awareness and relations), tangrams (orientation and mental transformation), and drawing and sandbox play (all of the above).
More structured or teacher-guided activities include guessing the name of a hidden shape when attributes are provided (“I have a shape that has four sides the same length and four right angles. Who can guess my shape?”). Playing active games such as Musical Shapes (a game similar to musical chairs, but with large shapes drawn on the playground that hold the same number of children as there are sides) supports gross motor, spatial awareness, and geometry development. Teachers can also support children’s spatial vocabulary development through games like I Spy, asking questions like, “I spy something above the chalkboard and below the ceiling.”
Like other areas in mathematics, geometry and spatial development require attention to pedagogy and content in the preschool classroom. Understanding how we can support development through the environment, materials, activities, and interactions is important. Children are excited about learning new words and ways of interacting. We should be, too!
This article is adapted from "Objects and Our Place Among Them," first published in the Spatial Relations module of the DREME teacher educator website. To see the complete article and our other free, research-based resources for teacher educators, please visit DREME TE.
Linda M. Platas is Associate Chair in the Child and Adolescent Development department at San Francisco State University. A member of the Early Math Resources for Teacher Educators project of the DREME Network, Linda is also a developer of DREME TE, a website of free early math resources for teacher educators.