The "Polyhedra: Learning by Building" project.

Eva looking through an octahedron with two clear faces

Building polyhedra with large triangles lets people handle and see geometric shapes from the inside as well as the outside. These new experiences have caused excitement and curiosity giving better understanding by children mathematics lessons. The originator of the triangles, artist Eva Knoll, regards mathematics as 'so beautiful it is worth making art out of it', thus drawing people into mathematics. However art is so creative we can use it to encourage creative original thinkers in mathematics, science, technology and design.

Simon Morgan, a mathematics PhD graduate from Rice University, Houston TX, Eva Knoll, now a graduate student in the School of Education, University of Exeter, U.K. and Jackie Sack, Mathematics Chair at Lanier Middle school, Houston TX, have collaborated with the support of Rice University School Mathematics Project to develop activities for geometry teaching in schools using large brightly colored triangles. The triangles are made from kite materials for their size, strength, appearance, precision, and light weight.

In the spring semester of 1999 five activities were tried out with three classes. We started with with an origami based exercise of folding a triangular grid on a paper disc and cutting out a snowflake shaped net that closed up into an icosahedron. Then the lessons in the table were carried out giving hands on experience at building and observing patterns in these shapes. Finally a giant eighty sided 'Endopentakis-icosi-dodecahedron' was made one afternoon for the school artfest.

The children, teachers and parents were all really excited by these activities and the children learned things well that are usually hard to teach. Since then more lessons have been developed through a wide range of grade levels, fifth through high school, and with varying students from gifted and telented to low performing.

Three middle and high school geometry lessons (Lanier, spring 1999)

Lesson

Shapes built

How learning took place
Lesson 1 Filling a tetrahedron
 Double edge length tetrahedra and shapes to fill it  By comparing a small and a large tetrahedron, see how length, surface area and volume scale. A surprise happens when we try to fill the large tetrahedron with smaller shapes.
Lesson 2 Stella Octanguli
Tetrahedra, octahedra, double edge length tetrahedra and stella octanguli  Construcing two stella octanguli in different ways shows how they relate to simpler shapes. There is also is an interesting observation about space filling that can be made.
Lesson 3 Colored Icosahedra
 Icosahedra  Coloring the icosahedron with 5 colors 
 

Co-operative geometric problem solving in going from a colored plan of a net on paper, to assembling a net and closing it up to make the icosahedron