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.

When a toddler takes two objects and brings them together to play, he is creating a relationship between them.  Sometimes, the two objects are not meant to go together; think – a small wooden block and a plastic bowl from the housekeeping area. They weren’t designed to go together, but through the imagination of the toddler, they become relational.  The child may put the block in the bowl and then take it out if the bowl. Sometimes, the two objects are meant to go together.  We call this “functional – relational:” think – a cup and a saucer.  The child puts the cup on the saucer and then takes it off again. In and out, on and off, together and apart are all concepts explored through this kind of play.   These spatial experiences are mathematical.

Now consider the toddler who repeats the same sequences in her play.  She takes the play phone off the shelf, lefts the receiver to her ear, pulls on the cord, and drags the phone around.  She then repeats this experience in the same order; listen, pull, and drag. This repetitive play reinforces sequencing concepts.

Both of the examples above are typical experiences many toddlers have in child care.  You can further support the play by providing language to the experiences.  Use math vocabulary with the children to reinforce spatial relationships and sequencing.