Students can learn to see the structure and symmetry around them. Using concrete models, drawings, and dynamic geometry software, students can engage actively with geometric ideas. With well-designed activities, appropriate tools, and teachers' support, students can make and explore conjectures about geometry and can learn to reason carefully about geometric ideas from the earliest years of schooling. Geometry has long been regarded as the place in the school mathematics curriculum where students learn to reason and to see the axiomatic structure of mathematics. The Geometry Standard includes a strong focus on the development of careful reasoning and proof, using definitions and established facts.
Technology also has an important role in the teaching and learning of geometry.
Tools such as dynamic geometry software enable students to model, and have an interactive experience with, a large variety of two-dimensional shapes. Using technology, students can generate many examples as a way of forming and exploring conjectures, but it is important for them to recognize that generating many examples of a particular phenomenon does not constitute a proof. Young students are inclined naturally to observe and describe a variety of shapes and to begin to notice their properties. For example, students in prekindergarten through grade 2 may observe that rectangles work well for tiling because they have four right angles. At this level, students can learn about geometric shapes using objects that can be seen, held, and manipulated.