Lifelong learners should know and understand these interconnected and symbiotic mathematical domains. Before students begin school, they already have developed a knowledge of and a curiosity about the physical and spatial world around them. They are exploring size, shape, and position when they buy new sneakers, or select fruit at the farmer's market, or play Simon Says. Teachers can use this natural curiosity and real-world experience to begin helping students build their own mathematical foundation in geometry and measurement. In the early grades, informal and intuitive studies of geometry and measurement are appropriate for tapping students' natural curiosity and engaging them.
Students usually measure objects with nonstandard units, such as shoes or hands, or strides.
These informal, often gross motor, explorations of spatial sense, size, and shape make young learners' mathematical experiences personal and fun. Through them, students discover for themselves the necessity of standard units. As students explore concepts and ideas with the aid of manipulatives such as blocks, geoboards, balance scales, and measuring tools they develop a personal and sensory understanding of mathematical ideas. Ways in which mathematics is used in a wide variety of careers become believable. Geometry and measurement often spark a renewed interest in mathematics for those students who have been turned off for some reason, or heretofore have felt unsuccessful with mathematics learning.