Developing Spatial Sense - a Moving Experience!
Andrews, Angela Giglio, Teaching Children Mathematics
A new mother's diary includes these entries about her daughter, Emily:
(Three months) Today Emily reached up to grab my glasses. She's been flailing her arms around for awhile now, but today I am certain she took aim and was determined to touch those glasses!
(Twelve months) Emily loves to play "peek a boo" with her daddy. She moves around and behind her chair, laughing when Bill pretends he can't see her.
(Eighteen months) Emily loves to climb through my legs. Today she spread her legs apart and laughed when I could not fit through her legs. We both ended up on the floor and had a good laugh together about that!
Although she may not be aware of it, Emily's mother is not only recording her daughter's explorations in a special book but also recording Emily's beginning experiences with geometry.
When we stop to think about young children and geometry, we realize that their first geometric experiences involve moving. They expend much effort moving about as infants and toddlers. As they develop motor skills, babies roll over and sit up in space, constantly changing their location and orientation to objects in a multispeed environment. Toddlers grasp edges and crawl through and run around shapes.
As preschoolers, children build their learning on such activities as stacking blocks, which we know to be cubes, rectangular solids, and pyramids. They throw and roll spheres. They place puzzle pieces next to each other, fitting edges together. Playing with balls that roll, blocks that stack, and puzzle shapes that fit together are integral parts of children's lives as they explore. These actions serve as the foundation for developing understanding about spatial relationships and shapes long before children are formally introduced to geometric concepts.
We can strengthen these intuitive understandings about space and objects by building on children's natural interests. Geometry instruction can begin while helping children develop an intuitive feel for their surroundings and the objects in them (NCTM 1989). For young children, geometry is a skill of the eyes and hands as well as of the mind. Motion is a major component of extending children's spatial awareness. Consequently, an important step in geometry instruction involves getting the children moving. Teachers can present activities that include opportunities for indoor and outdoor movement, movement games and stories, and moving through space with music.
Indoor and Outdoor Moving Activities
Children's ongoing and spontaneous activities on the playground offer many opportunities to investigate and describe spatial relationships. The teacher supervising the children's play may say, "Walk carefully around the slide," "Kelly is getting near the top," or "Jules went behind the tunnel a minute ago. Maybe he is crawling through it now."
Naturally occurring events in the classroom often provide the context for extending children's geometric and spatial understandings and connecting language to actions and ideas. In the following example, the teacher capitalized on a "teachable moment" by using her knowledge of outdoor games to nurture personal spatial awareness in children. At the beginning of the kindergarten year, the children were discussing their vacations. When the teacher asked what one child remembered most about her vacation to Disney World, the child quickly replied, "The crowds!" The teacher remembered a similar comment in a lecture about children's perceptions of crowds, decided that it might be interesting to focus on the concept of crowds with her kindergarten classroom. She encouraged children to recall and share their perceptions of what constitutes a crowd, where they have seen crowds, when they had been in crowds, and how did it feel to be in a crowd. The game of "crowds" resulted from this investigation.
For this activity, students divided themselves into four crowd situations: a beach crowd, a Disney-World crowd, a great-American crowd, and the Fourth-of-July-fireworks crowd. …