Polygon Properties May Journal Article

Polygon Properties
Teaching Children Mathematics
By Rebecca R. Robichaux and Paulettte R. Rodrigues

http://www.nctm.org/eresources/view_media.asp?article_id=9290

Summary

Can third grade students do geometry? Why, in fact they can do very sophisticated geometry with the right teaching and activities. Students in Mts. Robichaux dove into the properties of geometric shapes in a sorting and classifying activity. According to the van Htele theory of geometric thinking there are three levels of geometric thinking. At the first level, level 0 students think about thing on a visual level, at this point appearance and familiarity with shapes dominates the reasoning about geometric objects. As students progress into the second level, level 1, they develop description; they are about to sort and develop language that allows them to distinguish one property from another. At the third level, level 2, the informal deduction level the students can distinguish properties and even make arguments about why shapes are similar or not similar based on the properties that they do or do not possess.


It is expected that as they enter high school geometry classes that the students have passed through level 0 and level 1 of the van Htelen scale. The students must be comfortable and functioning at level 2. The NCTM standards also require that students are actively using all of the process standards and that each content standard is frequently being revisited and redefined.


In this article the students went through two activities that, through inquiry and exploration, allowed them to define the properties of polygons, distinguish and classify the shapes based on predetermined characteristics and develop questions and riddles based on their understanding of polygons and their properties. In the first activity the students were given shape and sort bags that contained many different polygons, these examples covered every thing imaginable, there were concave and convex polygons, a variety of vertices, edges, angle sizes and varying complexities. The students sorted the shapes as many different ways possible. Each time the students sorted their shapes they identified the qualities that they were looking for and recorded their answers on a response sheet. This process required the students to develop a representation of how each sort was completed. As the students worked through this process they developed more language and terminology which helped them in their discussion. Next, the students worked with geo-boards and attempted to create shapes based on predetermined “riddles.” At this point in their activities the students explored the idea of impossible polygons and determined through trial and error which characteristics could not exist in the same shape. The students then created their own riddle as an assessment, allowing the students to “show off what they know” rather than berating students who still needed additional work with the material. At that point in the activities all of the students could create a riddle; however, some were considerably more sophisticated than others.




Application

This is certainly applicable in the classroom. Activities like these present teachers with a way of teaching material in a way that is real and alive. Polygons are interactive and changing in this activity. They have properties and they can fall into nonexistence when certain properties are combined. They students are working in a hands-on, minds-on activity that allows them the opportunity to make mistakes and discuss their mathematical ideas in a non-threatening and encouraging environment. I hope that I will have the opportunity to use this activity in the classroom one day.

Robichaux, R. & Rodrigues, P. (2010). Polygon Properties. Teaching Children Mathematics. 16(9) 524.