Before children begin studying geometry the way we understand it, they explore the world of “topology.”  Topology is the study of space and shapes; their properties and their relationships.  They consider their own place in space, where they are, and how far they are from their others.  They think about the relationships between objects and the properties within objects.

When I ask new teachers why it is important to provide clay, play-doh, or silly putty in their program, they will often say that children need plenty of tactile experiences throughout the day.  I don’t disagree.  However, the manipulation of these materials is another way that children study topography.  Exploring the physical properties of clay, allows the children to take a ball and squish it into a snake.  The amount doesn’t change but the shape does. Rubber bands and geoboards provide other types of opportunities for children to explore shape by stretching and manipulating the rubber bands to create all sorts of shapes.

Encourage vocabulary associated with topology by posing questions about where things are located or questions about direction.  Play games that ask children to move further away and closer toward.  Use systems that provide boundaries for children, like tape on the floor, or the edge of the rug.

Allow large block play everyday.  No excuses.

Topology is a much more engaging and realistic way to engage young children in early geometry.  It is far more interesting than asking them to draw shapes.

## 2 Replies to “Geometry and Topology”

1. Len says:

A useful geometric/topological concept that is easy to explain to youngsters is convexity. If any two points in a set can \”see\” each other, in the sense that the straight line connecting them stays entirely in the set, then the set is convex. For example, a circle or an oval is convex. On the other hand, a block letter L is not convex since a point on the top cannot \”see\” the bottom branch of the L.

1. Jen says:

Thanks Len, I never would have thought of this but it makes sense. I also appreciate the use of mathematic vocabulary to support the concept. Do you have a good idea for \”concavity\” as well?

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