Today, students are confronted with many of the same needs their ancestors confronted thousands of years ago. They need to understand the structure of space and the spatial relations around them, measure many aspects of their environment, and communicate this structure and these relations and measurements to others. To address these needs, all students should be given opportunities to develop their spatial sense and measurement abilities. Before students begin school, they have developed some knowledge of and a natural curiosity about the physical and spatial world. They explore size, shape, position, and orientation of objects when they are involved in everyday activities at home, at school, in the neighborhood playground, or at a supermarket.
Children use the language of measurement and geometry in their everyday communication.
However, teachers must be aware that the everyday use of the language of measurement and geometry often differs from the formal use in mathematics, and that these differences must be addressed through instruction. At all grade levels, students should be encouraged to use precise language, previously discovered relationships, and appropriate explanations for their conclusions and conjectures. In the early grades, children should have opportunities to explore shapes and the relationships among them that build on their natural and intuitive understanding. As they progress through elementary school, students identify the components, attributes, and properties of different shapes, including sides, corners or vertices, edges, interiors, and exteriors. With time, students develop procedures to identify and categorize shapes by referring to their components, attributes, and properties.