Curriculum and Learning Strand: Measurement, Geometry, and Spatial Sense

Measurement, geometry, and spatial sense are crucial components of any effective PreK-12 mathematics curriculum. All involve practical and realistic application; few if any students do not encounter each on a daily basis. They are related to each other, to other areas of mathematics, and to other subjects. In Principles and Standards for School Mathematics (NCTM, 2000), the National Council of Teachers of Mathematics asserts that measurement is the assignment of a numerical value to an attribute of an object. As such, the development of student understanding and abilities in measurement proceeds in tandem with progress in number properties and reasoning, from preschool ordering of longer and shorter objects to measurement and understanding of quantifiable attributes and spatial relationships among objects. Likewise, students progress from their initial visual perceptions of geometric shapes and patterns to quantifiable and measurable attributes (e.g., lengths of sides and degree angles) and conjectures and proofs that involve spatial and numerical reasoning. In the National Science Education Standards (NRC, 1996), the National Research Council stresses that students in the early elementary years should begin to manipulate simple measurement instruments as tools for data collection. From these abilities they can logically proceed to inquiry that involves the integration of quantifiable spatial and geometrical concepts such as area, volume, and density. In addition to inclusion of these understandings and abilities to do scientific inquiry in the national science standards, the NSES Program Standard C states that the "science program should be coordinated with the mathematics program to enhance student use and understanding of mathematics in the study of science and to improve student understanding of mathematics." Also as we might expect, the mathematical relationships of coordinates to direction and location, and of measurement to the concept of distance, are reinforced in the study of geography through interpretation and application using maps and associated representations and tools. In Geography for Life: National Geography Standards (NCGE, 1994), the National Council for Geographic Education devotes its first three standards to student understanding and application of these concepts within unique spatial arrangements. This use of mathematical tools as models, and for modeling and working with representations in realistic situations, is just as pervasive in scientific inquiry. It is noteworthy that these ties within and among subjects are not the result of mere serendipity—just as the science standards explicitly call for the integration of mathematics, the math standards devote the entire process standard "Connections" to the relationship of mathematical concepts with a multitude of studies certain to be encountered by students throughout their lives.

As with our other strands, expect the curriculum and learning strand Measurement, Geometry, and Spatial Sense to expand with time.

Check out our initial synthesis of developmental research and instructional resources below, as we look first toward the earliest grades and the concepts of linear measurement.