Geometry for Children (6/29/2000)

Prepared by:

Joseph Malkevitch

Mathematics and Computing Department

York College (CUNY)

Jamaica, New York 11451-0001

Email: malkevitch@york.cuny.edu (for additions, suggestions, and corrections)

The exposure that children have traditionally had to geometry at home and in lower grades has been very limited. Typically students learn to give names to a variety of shapes (e.g. rectangle, square, circle, sphere) and learn a few basic ideas about area and perimeter. Since primary school teachers rarely have majored in mathematics, such teachers understandably may not know about graph theory, tilings, polyhedra, etc. Yet these are subjects that offer intriguing opportunities to introduce small children to interesting geometry. Furthermore, again understandably, primary school teachers are rarely aware of the role that geometry is playing in the development of many applications and technologies (e.g. image reconstruction, robotics, telecommunications).

One approach to dealing with this situation is to develop materials for parents to use with their children. Geometry projects for parents and students offer parent/child interactions that parallel those that parents have with children learning to read or improving their reading and writing skills. Not only does this allow parents to share innovative looks at geometry with their children but it helps educate parents to emerging trends in geometry and mathematics.

As part of a program at the elementary public schools that my son, now 8, attends, which encourages parents to make in-class presentations related to their jobs, I have presented interactive experiences for kindergartners, first graders, and second graders dealing with geometry. To complement these presentations I have prepared work sheets and accompanying notes for parents to repeat these activities in a more leisurely manner with their children. Below are the materials that I prepared for these presentations:

Adventures in Geometry for Kindergartners

Activities include construction of a tetrahedron from an envelop; making cylindrical and Möbius strip surfaces; traversing the edges of a graph (Euler circuits).

Adventures in Geometry for First Graders

Activities include learning how to interprete the barcodes that appear on letters that translate the zipcode into a machine readable form. Codes in general, in particular error-correction codes are also highlighted.

Adventures in Geometry for Second Graders

Activities include learning how to pack bins and schedule machines. Templetes for packing bins appear at the end.

Adventures in Geometry for Third Graders

Activities include learning how to compute the "taxicab" distance between two locations in an urban grid. Also, the optimum route for trick-or-treating is investigated. Coordinates help compute the taxicab distance between points and mention is made of the fact that in the taxicab plane there are many shortest routes between points.

I have developed some ideas about geometry for K-12 students, that emphasizes how broad the interests of geometers has become. Here are some geometry problems which illustrate some new directions I would like to see explored in lower grades. Surprisingly little geometry is currently taught, especially in grades K-6.

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