Basic to the understanding of geometry is the development of spatial sense-an intuitive feel for our surroundings and the objects in them. Spatial capabilities appear early in life, and tapping into these strengths can foster an interest in mathematics. Children who develop a strong sense of spatial relationships and master the concepts of geometry are better prepared to learn number and measurement ideas as well as other advanced mathematical topics. Classroom experiences that focus on geometric relationships will develop children's spatial sense. Children can begin with activities that use words like above, below, and behind and progress to using a computer to reproduce a pattern-block design.
Evidence suggests that the development of geometric ideas progresses through a hierarchy.
Students first learn to recognize whole shapes and then to analyze properties of a shape. Later they can see relationships between shapes and make simple deductions. Instruction must consider this hierarchy because, although learning can occur at several levels at once, the learning of more complex ideas requires a firm foundation of basic skills. For middle school students the informal exploration of geometry can be mathematically productive. Geometry at this level links the informal explorations begun in grades K 4 to the more formal processes of grades 9-12.