Software such as Logo enables students to draw objects with specified attributes and to test and modify the results. Dynamic geometry software provides an environment in which students can explore relationships and make and test conjectures. Students should have the opportunity to apply geometric ideas and relationships to other areas of mathematics, to other disciplines, and to problems that arise from their everyday experiences. There are many ways to make these connections. For example, measurement and geometry are closely linked, as illustrated in the problem in figure 5.11, where geometric properties are used to relate the areas of two figures of different shapes.
Geometric models are also important in investigating number relationships.
Number lines, arrays, and many manipulatives used for modeling number concepts are geometric realizations of arithmetic relationships. In addition to its utility in exploring and understanding other areas of mathematics, geometry is closely associated with other subjects, such as art, science, and social studies. For example, students' work on symmetry can enhance their creation and appreciation of art, and their work on coordinate geometry is related to the maps they create or use in their study of the world. The study of geometry promotes a deeper understanding of many aspects of mathematics, improves students' abstract reasoning, and highlights relationships between mathematics and the sciences.