Resources and Tools for Elementary Math Specialists and Teachers

Solid Geometry Early?

This discussion is part of a collection:Exploring Geometry Concepts

From a paper by Volkert, U. of Cologne:

“If one accepts the idea that teaching should be genetic then it is clear that Euclid’s way of building up geometry is not the best. What we know – and what pupils know – is basically the three-dimensional world and its objects (that is solids). [Volkert, 2008]

“[Three-dimensional geometry] is vital for describing the world throughout science, engineering, and architecture. Also, three-dimensional geometry fosters both our intuitive understanding and our geometric imagination. It teaches us to see things in the round. It also trains us to see all sides of an argument simultaneously, as opposed to algebra and computing which emphasize thinking sequentially.” [Zeeman, 2005]

Unfolding a corner flap of clear plastic wrap, and picking up a triangle to inspect and better understand it – the first is a difficult problem in three dimensions, and the second, a two-dimensional impossibility. It must be admitted that the manipulatives we use as models for plane figures are solid.

Volkert [2008] admits that the properties of formal 3-D geometry are more complex than that of 2-D, and that students do most of their work in two-dimensions, but can 3-D and informal transformations in the early grades be useful in bridging to the more formal and abstract Euclidean geometry to come? In what ways?


Most students should know their 2-dimensional figures (at least be name and some characteristics) by the end of Kindergarten. These concepts obviously get fine tuned over the next few years as students build their mathematical vocabulary and learn to classify and categorize these polygons and non polygons by their characteristics. All of this vocabulary building is essential to understanding 3-dimensional figures, which can and should be introduced in primary grades so students at least have a name for the objects around them even if they cannot describe their characteristics in precise geometric terms.

This post prompted me to view "Geometry" under the "Standards by Domain" category on this page of the CCSSM site:
It's a relatively new feature of their site and can be found near the bottom of their left navbar.

I thought it would be interesting to see if solid geometry appears in the early grades. I found this under "Kindergarten"
"Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”)."


Thanks, Suzanne. What spurred my comment is how one state is moving to eliminate this and other topics that receive light treatment in CCSS. The statement below can be found in a downloadable doc "Vermont's transition ..." at the site
"Teachers can begin to phase out these mathematical topics as a means to teach [others] at a greater depth. [among others listed are] K-4 3D geometry; K-5 Transformations; K-6 Probability"