About Geometro
Workshop for teachers in TSBVI
  Texas School for the Blind and Visually Impaired, 2012
  Elementary, Montessori and Special Education Teachers

With every new tool training is essential. Geometro workshops help teachers become more effective in their teaching of geometry. The workshops show new pedagogical ideas and bridge different parts of curriculum making geometry richer and more relevant for students. The workshops are customized according to grade level and special needs. The following areas of geometry teaching are typically covered during a workshop, as appropriate:

  • building and exploration of 3-D solids - some familiar, like pyramids and prisms, some newer like anti-prisms and bi-pyramids. And some even more exciting like Platonic and Archimedean solids.
  Workshop for teachers in Froebel Centre
  Froebel Education Centre, Misissauga, Canada 2010
  • decomposition of 3-D solids into nets – to learn a number of age appropriate activities to investigate the connection between 2 and 3-dimensions. How many different nets are possible for a given 3-D solid? When are two nets different? Is it always possible to make a 3-D solid out of a given 2-D arrangement? Why? This part of the workshop presents rich opportunity to experience activities that train visual and spatial imagination, memory, spatial reasoning and coordination.
  Workshop for teachers in Johannesburgh
drawing nets of a cube
  Maths Centre for Professional Teachers, Johannesburg, South Africa 2013
  • how to demonstrate spatial concepts in concrete, touchable way? Learn, for example, how to make diagonals in a cube, observe and touch where the diagonals intersect; make and touch a height in a pyramid or a prism; show orientation of lines: parallel, perpendicular and skew, using edges of different solids.
  touching diagonals in a cube
  Maths Centre for Professional Teachrs, Johannesburg, South Africa 2013
  • new ways to easily demonstrate and explore rotation and mirror symmetry in 3-D. Here we would work with plastic rods appropriately inserted into the solids to act as rotation axes. For exploring the mirror symmetry, we will work with 3-D fragments of solids and reflect them in mirrors, see reflection symmetry of cube. Exciting and mind challenging!
  • review the ideas of how 3-D geometry connects with science, engineering, art and history. The structures of molecules, viruses, crystals, minerals and bridges are made up of the same 3-D solids that are built during the workshop. Paintings of Salvador Dali, etchings of M.C. Escher and works of modern sculptors will be linked with the ancient symbolism of Platonic Solids.



  University students
  Workshop at McMaster University
  McMaster University, Hamilton, Canada, 2010

Workshops for university or collage students delve into more advanced 3-D concepts, such as relationships between various polyhedra and 3-D crystal structures. So, after building Platonic solids they would find duals and observe the relationships between their symmetry elements. Subsequently they would derive most of the Archimedean solids through vertex and edge truncation of the Platonic solids, investigate space filling with polyhedra and build models of crystal structures.





Classroom activites

  Children making structures with Geometro
  Occasionally we have a great day of working with children in a classroom - these are wonderful experiences. The most recent one was in the six grade classroom of Ms Aviva Dunsiger. She shared impressions in her blog here.
  Our three favourite classroom activities:

Activity 1:

In this initial activity students typically work in groups to construct any structure they like and to write instructions to make it. Subsequently they present and describe their creations, usually also in groups, but sometimes individually. With older students (grades 6-8) the variation of the exercise is to afterwards swap the instructions among the groups and follow with construction of the structure from the instruction of another group. Subsequent comparison between the two structures is always interesting and an excellent occasion to learn the importance and challenge of technical communication.


Activity 2:

Another super exciting activity for a whole classroom of grade 3 or 4 students is to find all different nets for a solid. Most of the time we worked with 6 squares per student (or two students) to make a cube and to discover all 11 nets for it. As children were drawing their proposed nets on the blackboard the whole class would be frantically checking if this was a correct net, and if none already on the blackboard was the same - as a byproduct they were practicing mental rotations and reflections of complex patterns and having lots of fun with it. The more nets on the blackboard the harder it was to come up with a new possibility and the excitement was running high. Once all 11 nets were found the students copied them to their journals. Finding a systematic pattern between the nets was the next task.


Activity 3:

In the next activities the students learn one thing first - to describe 3-D solids by specifying the kind and number of polygons that meet at a vertex. For example - in cube there are 3 squares that meet at each vertex, in pentagonal prism there is one pentagon and two rectangles in each vertex (in special case these might be squares), and so on. Armed with this understanding the children, even quite young, are able to make remarkably complex solids all by themselves. This systematic and pattern oriented approach to building structures is very constructive and immensely satisfying for children. It also easily leads to important insights into the nature and relationships between 3-D solids. Although we only rarely had occasions to conduct enough workshops in one classroom to be able to fully explore and practice all the possibilities, the feedback from teacher workshops is very enthusiastic.



Below a nine-year old boy is building a soccer-ball structure (also known as Buckyball or truncated icosahedron). He is following only one rule – two hexagons and one pentagon have to meet at every vertex of the structure.


Making buckyball Making buckyball Making buckyball Making buckyball


Making buckyball Making buckyball
  Parents and children

The first workshop for parents and children was presented in May 2011 at a conference of Ontario Association for Mathematics Education (OAME) in Windsor, Ontario.




  The presenter

Aniceta Skowron Geometro presenter


The workshops are presented by Aniceta Skowron, Ph.D. Aniceta is a crystallographer, researcher and an educator.

View testimonials from workshops participants.


Contact Aniceta to arrange for a workshop or to get more information.



Copyright © 2004 - 2017 Aniceta Skowron, Geometro. All rights reserved. brightsidemedia.com 2011