Spatial Concept Perspectives

We have gathered ~300 excerpts from published works about fundamental spatial concept terms. These have been cross-referenced with the concept lexicon appearing on the left. Those terms were drawn from the U.S.National Science Education Standards (NSES 1996) for topic areas B - Physical Science, C - Life Science, D - Earth and Space Science, as well as from the 1994 U.S. Geography Teaching Standards for grades 9-12. Those standards can be browsed here.

spatial concept terms

disciplinary perspectives on "symmetry"

local symmetries

...the existence of a center and the existence of a local symmetry are closely related. Wherever there is a local symmetry there tends to be a center. ...overall symmetry in a system, by itself, is not a strong source of life or of wholeness...oversimplified overall symmetries in buildings is most often naïve and even brutal (p 186). In many cases a symmetry is used to establish an elementary center. Indeed an overwhelming majority of centers are locally symmetrical....local symmetries provide a glue which binds the field of centers, thus making centers more coherent (p 194).

Alexander (2004)

The Nature of Order, Book 1: The Phenomenon of Life

symmetry

[See also chirality.] The regular proportions in symmetrical objects or patterns are defined by 'symmetry operations' - (1) A physical or mental lateral shift (translation); (2) A reflection in a virtual mirror (or point) cutting through the object; or (3) A rotation of the object by some fraction of 360 degrees about an axis. At the completion of the operation the object looks identical with the starting configuration. Translational symmetry creates tiling patterns or tessellations. Frequently the only symmetry the novice recognizes is two-fold reflective (bilateral) symmetry.

Science Education

Mathewson, J. H. (2005)

The visual core of science: definition and applications to education