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Learning To Think Spatially
FIGURE 5.11 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.
5.6SPATIAL THINKING AND EDUCATION FOR THE NEXT GENERATION
Spatial thinking is a pervasive and powerful way of thinking that operates across the sciences, social sciences, and even the humanities. For example:
… chemical education demands so much from students. It requires them to understand abstract theories (sometimes two to explain one phenomenon!), to have mathematical skills, to have experimental skills, to be able to communicate orally and in writing, and to visualize in three dimensions given information in two dimensions. And that is just the start. (Molecular Visualization in Science Education Workshop Advisory Board, 2001, p. iv)
Spatial thinking underpins many of the standards documents, yet it is not explicitly mentioned in any of them. Spatial thinking is presumed in many if not all of the sets of national K–12 standards. Despite its apparent predominance in geometry, it is not limited to any one discipline (Box 5.1).
Spatial thinking is the start of successful thinking and problem solving. Skill in spatial thinking is presumed throughout the K–12 curriculum but is formally and systematically taught nowhere. This leads to an educational blind spot. Formal, systematic instruction in spatial ideas is not part of the mainstream educational program. Therefore, although many of the general concepts under the rubric of spatial thinking are not novel, the committee believes that spatial thinking is under appreciated and under instructed in a systematic and coordinated way.
The committee’s experience in reviewing the literature and examining the curriculum leads to a strong recommendation that we remedy the blind spot in the educational system by infusing and integrating diverse spatial thinking activities throughout the pre-college curriculum. Students could, for example, explore perspective in art; the perfect triangle in geometry; three-dimensional model-