- Decomposing and rearranging provide a geometric way of both seeing that a measurement formula is the right one and seeing why it is the right one.
- In addition to decomposing and rearranging, shearing provides another geometric way of both seeing that a measurement formula is the right one and seeing why it is the right one.
- Geometric images provide the content in relation to which properties can be noticed, definitions can be made, and invariances can be discerned.
- Symmetry provides a powerful way of working geometrically.
- Geometric awareness develops through practice in visualizing, diagramming, and constructing.
- Tools provide new sources of imagery as well as specific ways of thinking about geometric objects and processes.
- Geometric thinking turns tools into objects, and in geometry the process of turning an action undertaken with a tool into an object happens over and over again.
- Naming is not just about nomenclature; it draws attention to properties and objects of geometric interest.
- Definition can both generate and reflect structure: definitions are often dependent on a specific classification.
- Conjectures can emerge out of a problem-posing process that generates claims that need to be justified.
Sinclair, N., Pimm, D., & Skelin, M. (2012) Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 6 - 8. Reston, VA: The National Council of Teachers of Mathematics, Inc.