FIGURE 5.14 Use visualization, spatial reasoning, and geometric modeling to solve problems. SOURCE: NCTM, 2000. Reprinted with permission from Principles and Standards for School Mathematics, copyright 2000 by the National Council of Teachers of Mathematics. All rights reserved.

ing in biology, chemistry and physics; and multidimensional reasoning in design aesthetics, literature, and psychology. They should have an opportunity to see connections between the use of graphs in economics and phase diagrams in physics. They should be able to understand the connection between changes in point of view as a function of degree of rotation in the horizontal and vertical planes. They should be able to practice skills in paper-and-pencil mapping, physical model building, and computer representation.

Teaching about spatial thinking is of particular significance now because, on the one hand, the capacity to support spatial thinking is increasing through the prevalence, power, and opportunities available from computers and software and, on the other hand, there is an increasingly urgent need to make sense of the increasing volumes of spatialized or spatializable data that are readily available.

Spatial thinking is also significant now because of changes in the process of education and in the ways in which we characterize knowledge. Increasingly, teachers are adopting the inquiry

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