Geometry for Children

Geometry is the area of mathematics that involves shape, size, position, direction, and movement and describes and classifies the physical world we live in. children’s spatial sense is their awareness of themselves in relation to the people and object around them.

In the 1850s Friedrich Froebel designed a curriculum with suggested instructional practices based on the use of geometric forms and their manipulation in space. In this curriculum Froebel designed “gift” for Kindergartners—special materials to enable them to explore and grasp basic forms and relationship. The first six gift included balls of different colors, cubes, spheres, cylinders, and complex sets of geometric block that children manipulated and observed in a series of progressive tasks. (Balfanz, 1999 dalam Coupley, 2000:105)

Key aspects of geometry and spatial sense, according to the NCTM standards for early grades (2000: 97) are:

a.       Analyzing characteristics and properties of two and three dimensional geometric shapes and considering geometric relationships,

b.      Specifying locations and describing spatial relationship using coordinate geometry and other representational systems

c.       Applying transformations by recognizing and applying slides, flips, and turns as well as recognizing and creating shapes containing symmetry

d.      Using visualization to create mental images of geometric shapes using spatial memory to recognize and represent shapes from different perspectives, and to recognize geometric shapes and structures in the environment and specify their location

Spatial sense and contruction come into play in art, science, social studies movement and music, and reading. For example, spatial thinking skill emphasized in geometry are critical to the making and reading of maps—essential skills in social studies. Children notice shapes in natural objects of all kinds. They discover many things about shape and geometry in their block play. Manipulating shapes in space introduces children to vocabulary words about position guishing between letters of the alphabet involves attention to shape and position. In art, spatial relationship and geometric forms are critical elements in both two dimensional and three dimensional creations.

Level of Geometric Thingking

Describing childres development of geometry and spatial sense, researchers and educators often often present Pierre Van Hiele and Dina van Hiele-Geldofs Levels of Geometric Thinking (van Hiele 1986). Most children up through the primary grades have not progressed beyond Level 1, and many preschoolers are operating at Level 0. Research suggest that to move through these levels, children must be exposed to many experiences and participate in numerous activities. Progress is often very slow.

1.      Level 0 : Children learn to recognize geometric figure such as squares and circles by their holistic physical appearance. For example, a given figure is a circle because it “look like a clock”. Children at this level do not think about the attributes or properties of shapes.

2.      Level 1 : Children begin to learn isolated characteristics or attributes of the forms, such as “a square has four equal sides”

3.      Level 2 : Children establish relationship between the attributes of a form. At this level, for example, children can determine that a square is rectangle because it has all of a rectangle’s properties

Young children naturally love to explore geometric and spatial aspect of the world around them. There are many opportunities for the teacher to scaffold children’s understanding by asking questions, suggesting other activities, showing various transformations (such as two same-size right triangles forming a reactangle), and providing, additional materials.